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## Third term JSS2 Mathematics Lesson note

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JSS 2 THIRD TERM MATHEMATICS

SCHEME OF WORK

WEEK     TOPIC

• Angles in a polygons

(a) Types of polygons: convex, concave, regular, irregular

(b) Sum of interior angles in polygon (number of triangles in a polygon)

(c) Sum of exterior angles of a polygon

(a)  Horizontal and vertical plane

(b) Angles of elevation and depression

(c) Relationship between angle of elevation and depression

(b) Scale drawing

(c) Pythagoras

• Bearing and distances

(a) The compass directions (major and minor)

(b) Types of bearing (Compass, acute-angle, three figure)

(c) Converting acute-angle bearing to three figure bearing and vice versa

(d) Reciprocal/ back bearing

(e) Scale drawing to find bearing and distances

• Use of ICT in Mathematics
• Using computers to solve simple Mathematical calculation (using EXCEL)
• translation of word problem into Mathematical expression
•  Computer Application

(a)Use of punch cards to store information

(b)Writing familiar words in coded form

•    Construction

(a) Construction of special angles (Revision)

(b) Constructing triangles

(i) 2 sides and included angles (ii) Two angle and a side between them. (iii) all the 3 sides

(b) Bisecting angles: bisecting angle 90, 60 and bisect any given angles.

• MID-TERM BREAK
•      Data presentation: (a) Frequency tables (ungrouped and grouped)

(b) Construction and interpretation of pie charts

•      Probability

(a) Definition of terms in probability

(b)Experimental probability

(c) Theoretical probability

•        Revision
• Examination.

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JSS2 Third TERM MATHEMATICS LESSON NOTE MS-WORD

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## Lesson Note on Mathematics JSS2 Third Term

Enote on Mathematics – Edudelight.com

SUBJECT: MATHEMATICS

CLASS: JSS 2

SCHEME OF WORK

WEEK    TOPIC

• (a) Revision of Second term’s examination

(b) Re-presentation of real situation an graph and the reason(s).

• Angles and Polygon: (i) definition of angles (ii) Construction of move angles (iii) Definition of polygon with examples (iv) sum of interior angles of regular polygon: (n – 2) x 180 o
• Angles of Elevation and Depression
• Bearing and Distances
• Statistics: Data Presentation
• Statistics (Continued)
• Review of first half term’s work and periodic test
• Probability
• Pythagoras’ Theorem
• Review of third term’s work and periodic test.
• Revision and Examination
• Examination
• WABP ESSENTIAL MATHEMATICS FOR JSS BK 2 BY A.J.S. OLUWASANMI
• NEW GENERAL MATHEMATICS BY J.B. CHANNON & ETAL

TOPIC: LINEAR GRAPH IN TWO VARIABLES, USING GRAPH TO SOLVE REAL LIFE SITUATION

Distance – Time graph

Velocity Time graph

Re-representation of real-life situation of graphs

Choosing scales.

Distance – Time Graph

Graphs are used to show the relationship between two quantities. A continuous graph is in the form of a continuous line and shows the relationship between the two quantities.

A distance-time graph shows the distance travelled against the time taken and is used to calculate speeds.

A distance-time graph is also called a

Travel graph. In travel graph, the time is usually plotted x – axis and the distance on y-axis.

The graph below shows a man’s journey from home to another town. Use the graph to find:

• The time taken to travel 75km
• The distance travelled in 3 hours
• The time taken to cover a distance of 175km
• The man’s speed in km/h

Solution with explanation

The horizontal (or x-axis) shows the time in hours.

2 units on the x-axis = 1 hour

The vertical axis (or y-axis) shows the distance in km.

2 units on the y-axis = 50km,

We can use a travel graph to find a distance and time at any point on the graph.

For example:

• The time taken to travel 75km is 1 h 30 mins (see the arrow)
• The distance travelled in 3 hours is 150km (see the arrow)
• It took the man 3 hours 30 mins to cover a distance of 175 km.

= 50km/hr

• A girl walks along a road at a speed of 100m per minute
• Copy and complete the table
• Using a scale of 2cm to 1min on the horizontal axis and 2cm to 100m on the vertical axis draw the graph of the information
• Use the graph to find
• How far the girl has walked after 4.6mins
• How long it takes her to walk 380m

Essential Mathematics Chapter 16, pgs 184-187 AJS Oluwasanmi

Exercise 16.6 Nos 1 & 3 page 201

GRAPH OF REAL LIFE SITUATION

Choosing Scale.

In choosing a scale, choose a big scale while drawing graphs. Refer to the given data to find the upper and lower limit of the scale. Always show the origin if possible on 2cm graph paper use scale of 2cm to 1, 2, 5, 10, 20, 50, 100

GENERAL EVALUATION:

• The labour charges preparing a television set consists of a standing charge of N 500 on all bills and an hourly rate of N 200 per hour.
• Make a table showing the total labour charges for jobs which take 1 / 2 h, 1h, 2h, 3h, 4h,
• Choose a suitable scale and draw a graph of the information
• Find the total labour charge for a job which takes

i. 2 1 / 2 hrs           ii. 24min

New general mathematics, UBE Edition, chapter 122. Pages 105 – 107

Essential mathematics by A J S Oluwasanmi, chapter 18, pgs 187 – 191

WEEKEND ASSIGNMENT

• Which of the following statements in not true about the equation of the form y = mx + c?    A. x and y are called the variables.    B. only c is the constant term    C. the graph of this equation is always a straight line     D. the intercept of the graph on the y axis is c.

The graph below shows the cost of cloth (in naira) and length of cloth (in metre). Use the graph to answer questions 2 to 5

• Find the cost of 12 metres of cloth.   A. N 2000     B. N 2200    C. N 2400     D. N 2800
• Find the cost of 38 metres of cloth    A. N 7600     B. N 7200      C. N 7400     D. N 7800
• How many metres of cloth can be bought for N 4400?    A. 20m    B. 25m    C. 24m   D. 21m
• How many metres of cloth can be bought for N 7800?    A. 35m    B. 37m    C. 38m    D. 39m
• Essential mathematics bk. 2 exercise 16.6 number 1 page 201
• The table below shows the speed of a train at various times
• Draw a velocity – time graph for the journey
• Find the acceleration during each stage of journey
• Find the distance covered by the train in the first 4 hours.

TOPIC: ANGLES IN POLYGON

CONTENT:   (i) Sum of interior angles of a polygon

(ii) Sum of exterior angles of a polygon

DEFINITION OF A POLYGON

A polygon is any close plane figure with straight side. A regular polygon has all sides and angles equal.

Polygon are named according to the number of sides they have. Examples are:

Triangle                       a 3- sided polygon

Pentagon                     a 5- sided polygon

Hexagon                      a 6- sided polygon

Heptagon                    a 7- sided polygon

Octagon                      a 8- sided polygon

Nonagon                     a 9- sided polygon

Decagon                      a 10- sided polygon

The diagrams below represent some common polygons.

(3 sided)                                  (4- sided)                                 (5- sided)                     (6- sided)

Essential Mathematics for junior secondary school Book 2, chapter 9, pages 87 – 88

Sum of Interior Angles of a Polygon

The angles inside a polygon are called its interior angles as shown in the figure below:

e = exterior angle

i = interior angle

The number of triangles depends on the number of sides of the polygon. For a polygon with ‘n’ sides there will be (n-2) triangles. The sum of angles of a triangle is 180 0 .

Alternatively, since 180 0 = (n-2) x 2 x 90

= 2(n-2) 90

= (2n-4) 90

Thus, the sum of the angles of an n-sided polygon can be represented as (n-2) 180 0 or (2n-4) 90 0

The table below shows the sum of interior angles of a regular polygon of a 3 sided polygon up to a sided polygon.

Worked Examples:

• Calculate the size of exterior angle of a regular nonagon (9 sides)
• Calculate the size of exterior angle of a regular hexagon (6 sides)

• Sum of exterior of a polygon = 360 0 . Number of sides of a nonagon = 9

Size of each exterior angle = sum of exterior angles/number of sides.

= 40 o

• Sum of exterior angles = 360 o

Hexagon has 6 sides.

GENERAL EVALUATION

• The interior angles of a triangle add up to …………………………
• The sum of the interior angles of a regular polygon is 1080 o . How many sides has the polygon?

REVISION QUESTION

• Calculate the number of sides of each of a regular polygon whose interior angle is 162 o
• The sum of the 3 angles of a hexagon is 345 o . If the other angles are equal. Find the sizes of each of the angle.

Essential Mathematics for junior secondary school Book 2, Chapter 19, page 252 – 255

Exercise 19.5 No 1 page 255

• The sum of interior for angle of a regular pentagon is   A. 240 o       B. 720 o     C. 540 o      D. 640 o
• Calculate the size of each of exterior angle of a regular hexagon.   A. 60 o     B. 30 o      C. 45 o      D. 125 o
• The size of each angle of a regular octagon will be ____ A. 95 o      B. 75 o      C. 105 o      D. 135 o
• How many sides has a polygon if the sum of interior angles of that polygon gives 3240 o ?     A. 18 o       B. 15 o       C. 17 o      D. 20 o
• Calculate the size of each exterior angles of a pentagon     A. 30 o      B, 72 o       C. 60 o      D. 90 o
• Calculate A. The total internal angels of an octagon B. The size of each angle of a regular octagon
• Calculate the
• Exterior angle
• The number of sides of a regular polygon with an interior angle of 72 o

TOPIC: GRAPHS OF LINEAR EQUATIONS

CONTENT:   (i) Equations and table of values

(ii) Plotting points from the table of values

(iii) General form of linear equations

Equations and Table of Values

y = 2x – 5 is an equation of x and y. the equation connects the two variables x and y so that for any value of, there is a corresponding value of y. For example if x = 3, then y = 1 and if x = -2, y = -9. Table below is a table of values that shows corresponding values of the variables x and y for the equation y = 2x – 5. We say that y is the dependent variable since the value of y depends on the value of x. c is the independent variable.

Evaluation: Copy and complete the table above.

Plotting Points Fromthe Table of Values:

Table above contains the following set of ordered pairs of corresponding values of x and y. (-2, -9), (-1, -7), … These ordered pairs are equivalent to a set of coordinates of points that can be plotted on the Cartesian plane. y = 2x – 5 is a linear equation in x and the variables in a linear equation are always separate and have a power of 1 (i.e. there are no terms such as xy, x2, y3 etc.). The graph of a linear equation is always a straight line. In general, a straight line has an equation in the form y = mx + c, where x and y are variables and m and c are constants.

Evaluation: Draw the graph of y = 4x – 7 for values of x from -3 to +3. From your graph find:

• The value of y when x = 2.5
• The value of x when y = -1.3
• The coordinates of the points where the line cuts the axes.

General Form of Linear Equations:

The general form for the equation of a straight line is y = mx + c. Where m and c are constants.mis the coefficient of x and it is often called the gradient of the line. c is called the intercept on the y-axis. When a linear equation is given in this form, the values of m and c can easily be obtained. As shown below.

If y = -5x – 4, then m = -5 and c = -4

ax + by + c = 0 is another form of equation of a line. Notice that the terms are in alphabetical order. Where a, b and c are constants.

For example: 3x – 2y – 10 = 0 is in the form ax + by + c = 0, where a = 3, b = -2, and c = -10

To obtain m and c in the above equation, there is need to convert it to the form y = mx + c

Example: Find the values of m and c in the equation 2x – y + 7 = 0

Given: 2x – y + 7 = 0, add y to both sides

i.e. y = 2x + 7  (in the form y = mx + c)

Thus, m = 2 and c = 7

Evaluation:

• The equations of six straight lines are:

y = x + 3; y = 2x – 3; y = x – 3; y = 2x + 8; y = 2x – 7; y = x – 5

• Which of these lines are parallel?
• Write down the values of m and c, where m is the gradient and c is the intercept on the y-axis.
• Draw the graph of y = 3x – 4 for values of x from -2 to 2
• Write down the coordinates of the points where the graph cuts the y-axis

• Find the coordinates of the points where the line cuts the axes.

WABP Essential Mathematics.AJS Oluwasanmi. Chapter 16 pg. 182 – 185

Exercise 16.3 No 5&7 page 191

WEEKEND ASSIGNMENTS

• Given that y = 3x – 5, find m    A. -5        B. -3       C. 3        D. 5
• If y = -2x + 7, find c     A. -2       B. 7       C. 2      D. -7
• Given an equation of a straight line: 2y + 6x – 10 = 0, find the gradient   A. 6    B. 3     C. -6     D. -3
• In question (3) above, find the intercept on the y-axis    A. 2     B. 6     C. -10     D. 5
• Given the equations (i) y = 2x – 3, (ii) y = x + 3 and (iii) y = 2x + 8. Which of these are parallel?     A. i and iii      B. i and iii       C. ii and iii      D. i, ii and iii
• Draw the graphs of the functions y + 3x – 4 and x – y = 5 on the same axes. Write down the coordinates of the point where both lines intersect.
• Find the x and y intercepts of  the following lines  a. 3x – 9 = 2y     b. 2y – x + 3 = 0

WEEK 3                                                                                            DATE………………

TOPIC: ANGLES OF ELEVATION AND DEPRESSION

CONTENT:   (i) Horizontal and vertical lines

(ii) Angles of elevation

(iii) Measuring angles of elevation and depression

Horizontal and Vertical Lines

Horizontal lines are lines that are parallel to the earth. For example, the surface of a liquid in a container, floor of a classroom, etc. Seethe diagram below:

• Say whether the following are horizontal or vertical or neither.

a) A table top        b) A door        c) A table leg               d) Top edge of a well

NGM BK 2 Chapter 17, pg 173

Essential Mathematics for JSS BK 2, Chapter 17, pg 173

Angles of Elevation

The angle of elevation of  an object from a given point is the angle formed when an observer looks up to see an object his head. See the diagram below.

angle of

Horizontal plane

V = view point, T = top where the object is, F = foot of the vertical plane, e = angle of elevation

NGM BK 2 Chapter 20, page 165

Angle of Depression

Thus the angle of elevation is equal in size to the angle of depression. (Alternate angles are equal i.e. d = e)

NGM BK 2 Chapter 20, pgs 166 – 167

Measuring Angles of Elevation and Depression

When constructing angles of elevation and depression, the use of scale drawing is necessary in order to have effective construction of angle. Consider the diagram below; find the height of the flagpole to the nearest metre using suitable scale.

By construction, choose a scale of 1cm represent 2m.

The height of the flagpole PT = 3cm, converted to m, will give 2 x 3 = 6

Example 2: The angle of elevation of the top of a tower 42m away from a point on the level ground is 36 o , find the height of the tower.

The length TR = 5.0cm converting back to metre, we have;

Length TR = 5 x 6 = 30m

Example 3: From the top of a building 20m high, the angle of depression of a car is 45 o , find the distance of the car from the foot of the building.

T = top of the building, C = car, F = foot of the building

CF is the distance of the car from the foot of the building

Since angle of depression equal angle of elevation;

By construction, using a suitable scale of 1cm represents 5m

Length CF 4cm

By conversion, length CF = 4 x 5 = 20m

• A tower PQ is 10m high, if the distance from point R to P is 50m on the ground, find the angle of elevation of Q from R
• From the top of a cliff of 200m high, Martins observes that the angle of depression of a boat at sea is 35 o , find the distance between the boat and the foot of the cliff.
• A boat is 180m from the foot of a vertical cliff of height 80m. find by scale drawing the angle of depression of the boat measured from the top of the cliff.
• A boy is flying a kite. The string is 25m long and is at an angle of 42 o with the horizontal. Using a scale diagram, find the high the kite is above the boy’s head?
• The angle of elevation of point P from point Q is 40 o . PQ = 45km. How high is point P above the level of point Q.
• A girl with eyes-level height of 1.65m observes that the angle of elevation of the top of the tower 20m away is 40 o . Calculate the height of the tower.

NGM BK 2 chapter 20, page 166 – 169

Essential mathematics for JSS BK 2, chapter 23, pg 295 – 297

Exercise 23.1 No 1, 2 & 3 page 296

• Calculate the size of the fourth angle if three angles of quadrilateral are 65 o , 115 o and 125 o respectively     A. 35 o      B. 55 o      C. 45 o     D. 75 o
• Calculate the number of side of a regular polygon whose total angles is 1080 o      A. 4     B. 6      C. 8     D. 10
• PRQS is a rectangle with the side 3cm and 4cm, if its diagonal cross at O, calculate the length of PO.      A. 3.5cm     B. 5.0cm      C. 2.5cm      D. 4.0cm
• If the angle of a quadrilateral could be x, 2x, 4x and 5x respectively, what would be value of x?     A. 60 o      B. 90 o       C. 15 o      D. 30 o
• If the angle of elevation of a building from a point on the ground is 43 o . What is the angle of depression?     A. 47 o     C. 53 o     C. 43 o      D. 32 o
• From the top of a building 50m high, the angle of depression of a car is 55 o , find the distance of the car from the foot of the building.
• Find the height of the flagpole in the diagram below to the nearest metre.

TOPIC: BEARINGS

CONTENT:   i. Compass bearing

ii. Three figure bearing

iii. Finding the bearing of a point from another

COMPASS BEARING

A bearing gives the direction between two points in terms of an angle in degrees. The two types of bearing are compass bearing and three- figure bearings.

The four major compass directions are North (N) South (S) East (E) and West (W)

In compass bearing, the angles are measured from north to south depending on which one is nearer

Apart from the four main points or directions, there are also four main secondary direction i.e. NE (north east), SE (south east), SW (south west), NW (north west). The angles between each point is 45 o

Worked examples

Draw a sketch to show each of these bearings marketing the angles clearly.

a) N35 o W      B. N70 o E      C. S58 o W

• N35 o W means from N, measures 35 o toward the W or 35 o W of N

In a), the direction start from a wrong point (W) instead of N, therefore,

90 – 18 = 72 o

i.e. N72 o W

In b), the direction starts from a wrong point (E) instead of S therefore:

90 – 55 = 35 o i.e. S35 o E

Evaluation: Class Work

Find the compass direction of point A from point O in these diagrams.

NGM BK CHAPTER 23, page 185 – 187

Essential Mathematics for JSS BK 2, CHAPTER 24, pg 246-247

THREE-FIGURE BEARINGS

Three-figure bearings are given as the number of degrees from north, measured in a clockwise direction. Any direction can be given as a three figure bearing. Three digit are always given but angles less than 100 o need extra zero to be written in front of the digits e.g. 008 o , 060 o , 070 o up to 099 o

Worked Examples

• The arrow N shows the direction N, NXA = 63 o . the bearing of A from X is 063 o
• NXB = 180 – 35 = 145 o . The bearing of B from X is 145 o
• NXC clockwise = 180 + 75 = 255 o . The bearing of C from X is 255 o
• NXD clockwise = 360 – 52 = 308 o . The bearing of D from X is 308 o .

In the figure below, find the bearings of A, B, C and D from X.

NGM Bk. 2 Chapter 23, page 180 – 190.

To find the bearing of B from A

By constructing line N 2 A

<N 2 BA is 57 o , similarly, N 1 AB = 57 o (alternate angles are equal). From point A, starting from the North,

180 + 57 = 237 o

• The bearing of B from A is 237 o
• The bearing of A from B is 057 o
• The bearing of X from Y is 319 0 . Calculate the bearing of Y from X.
• In each diagram, calculate i) the bearing of B from A and ii) the bearing of A from B.

From a point P the bearing of a house is 060 o . From a point Q 100m due east of P, the bearing is 330 o .

Draw a labeled sketch to show the positions of P, Q and the house.

• A girl is facing East. If she turns clockwise through 2 right angles, then the direction she would be facing is ……………………..
• A student is facing South East. If he turns anticlockwise through 1800, then the direction he would be facing is …………………..
• The bearing of X from Y is 196 o . The bearing of Y from X is     A. 016 o        B. 074 o       C. 106 o      D. 196 o
• A boat sails on a bearing of 225 o . Using compass bearing, in what direction is the boat sailing?     A. South East     B. North East     C. South West     D. North West
• The bearing of point A from B is 058 o . Find the bearing of point B from point    A. 058 o      B. 122 o      C. 302 0      D. 238 o
• Which of the following statements is not true when we specify a direction with bearing?   A. Measure the angle from North   B. Measure anticlockwise     C. Measure clockwise     D. Always use three digits
• In the diagram below, which of the following angles is the bearing of P from Q?   A. 065 o     B. 245 0      C. 295 o      D. 115 o

WEEK FIVE

TOPIC: DATA STATISTICS REPRESENTATION

CONTENT:   1. Definition

2. Method of collecting data

3. Classification of data

• Statistics: is the branch of study of data. It involves (a) Gathering (i.e. collecting) data    (b) sorting and tabulating data      (c) presenting data visually by means of diagrams.
• Data: (SINGULAR DATUM) means information which are usually given in the form of meaningful. Data may be categorized into quantitative and qualitative
• Quantitative data: a numerical data, which is usually given in the form of a number or measurement is called quantitative data e.g. number of cars, height, number of towns etc. quantitative dateis either discrete or continuous.
• Discrete data: are data which can be obtained by counting (not by measurement). Discrete data can only exact values such as whole numbers. E.g. 2 boys, 3 houses etc. hence discrete data have definite or exact values
• Continuous Data: are data that can be obtained by measurement (not by counting). Continuous data can take any values within a given range. E.g. height 1.6cm, height 40.56cm etc.
• Qualitative Date: this is a non-numerical value which is concerned with qualities such as names, places, color, taste, opinions, brightness etc.

Explain briefly with an example (i) Discrete data    (ii) Continuous data

METHOD OF COLLECTING DATA

There are two discrete ways of collecting data. These are (a) by carrying out experiment (b) by survey

• By Carrying out Experiments: Data can be obtained from experimental work carried out in the laboratories by students or scientist for example, various measurements, such as temperature, pressure, weight and height of an object can be obtained by setting up an experiments.
• By Survey: This collection of information or data on a subject. A survey may be carried out by using the existing published data, making observation and asking questions.
• Using existing published data: Existing data may be obtained from libraries, schools, newspaper, and government’s publications such as annual abstract of statistics, stake statistics, employment gazettes, books journals and other publications.
• Making Observation: This method involves collecting data by observation e.g. you can do a round traffic survey by counting and recording the various types of vehicles that ply a particular road.
• Asking questions: You can ask other people questions to obtain their views or vital information in two ways: i. by interviewing them ii. By giving those questionnaires to fill in their response.
• By Interviewing: This involves asking other people questions in order to obtain vital information or strict pattern or information, in which the questions asked only general formal but the order or the way the questions are presented can vary. It must be noted that the interviewers must avoid bias, misleading ambiguous and offensive questions.
• Questionnaires: This is the most popular method of collecting data. Questionnaires are list of questions designed to obtain or discover particular information in a survey. In questionnaires, everyone is asked the same questions. The questionnaires may be given directly to an individual or sent to them by post to fill in their response. The main advantage of postal questionnaires is that it can be sent to many people in another towns or cities.

Mention two major ways that data can be collected.

Essential mathematics for JSS 2 by AJS Oluwasanmi pages 180 – 182

CLASSIFICATION OF DATA

Data can be obtained either by direct collection from respondents or form a data bank of a data collection agency. Data collected directly from information’s are called

• Primary Data: are those from data banks are called secondary data.
• Secondary Data: these are obtained from data collection agencies, engaged in routine data collection for research and planning some of these agencies include:
• Federal Office of Statistics (FOS) Principal agency
• Central Bank of Nigeria
• Statistics units of Ministries/Parastatals
• Commercial Companies/ Industries.
• Name two broad ways of classification of data
• Mention two agencies we can collect secondary data

Michael obtained the following scores in a Basic Technology examination:

65, 72, 58, 82, 74, 64, 78, 70, 80, 75, 68

Arrange these scores:

• In ascending order
• In descending order

Essential Mathematics for JSS 2 by AJS Oluwasanmichapter 23 pages 298–302.

Exercise 23.2 No 2&3 page 300

• Data that is written in radius order is called    A. qualitative data    B. raw data    C. quantitative data     D. discrete data     E. continuous data
• Which of the following most a questionnaires be?     A. simple     B. misleading     C. ambiguous     D. irreverent      E. offensive
• We can represent data by _____________    A. line    B. dist    C. number     D. picture    E. double lines
• Statistics deals majorly on ___________     A. building     B. dancing    C. data    D. fish    E. animals
• Mention 3 things you must avoid when designing a questionnaires
• In carrying out a survey, mention two ways, you can obtain information from people.

WEEK SIX

TOPIC: PRESENTATION OF DATA: IN LIST, TABLE AND LINE GRAPH

CONTENT:   i. Rank order list

ii. Frequency table

iii. The line graph

RANK ORDER LIST

Raw data: Data which is in random order (i.e.) arranged in any kind of order is called raw data. One way to present or organize the data in a more meaningful way is to arrange it in rank order or sorting it into categories. Rank order means in order from highest to lowest. Note: Data should be presented clearly. Good presentation makes statistical data easy to read and understand.

Example: B,C,A,B,A,D,E,C,A,B,B,E,B. this 15 grade are given rank order below:

A,A,AB,B,B,B,C,C,C,D,E,E,F.

• New general mathematics for JSS 1 by JB Channon and other page 125
• Essential mathematics for JSS 1 by AJS Oluwasanmi page 183

FREQUENCY TABLE

Raw can also be arranged in a table called the frequency table as shown in the diagram below. The number of times each particular value occurs is called its frequency. The frequency table is usually made up of three columns.

• The first column contains each item (or each of the events) given in the raw data and they are usually arranged in order of magnitude starting with the smallest.
• The second column contains the tally charts which represent the number of times a particular item or events takes place.
• The third column is called the frequency column. To find the frequency of each items, simply add or count the tally marks in each row. To find the total frequency must be equal to the following raw data shows the number of vehicle owned by 25 business men in Lagos.

Example: 2, 5, 4, 6,3, 4, 7, 5, 7, 7, 8, 9, 5, 3,4, 4, 8, 2, 2, 2, 5

The following figures show the number of children performing in a sample of 40 households.

1, 2, 4, 3, 5, 8, 3, 2, 2, 3, 4, 5, 6, 5, 4, 2, 1, 3, 2, 4, 5, 3, 8, 7, 6, 3, 8, 6, 3, 5, 7, 5, 4, 3

• Use a tally mark to prepare a frequency table for this data.
• What is the highest frequency to numbers of children per family?

Essential mathematics by AJS Oluwasanmipage 184 – 185

THE LINE GRAPH

A line Graph is a bar-chart with bar replaced by straight lines which represent the frequency of each item.

Example: The scores of 30 students in mathematics test are shown below

8, 6, 2, 0, 0, 2, 4, 1, 0, 6

4, 2, 8, 8, 1, 0, 0, 2, 4, 2

2, 8, 6, 4, 1, 0, 0, 6, 2, 4

Use the frequency table to construct a line-graph solution

GENERAL EVALUATION QUESTION

Twenty four pupils went out to pick some pears. The number of pears picked by each pupil was recorded as follows:

6, 4, 3, 2, 3, 4, 1, 3, 5, 1, 6, 2,

2, 3, 2, 2, 3, 5, 2, 4, 3, 3, 1, 6

• Prepare a tally sheet and frequency table for the data
• Construct a line-graph for the distribution
• Which is the least number of pears picked?

The shoe sizes of 20 boys are as follows:

8, 10, 9, 10, 11, 9, 8, 9, 12, 9

10, 9, 9, 8, 8, 9, 10, 19, 9, 11

• Which shoe size is the most common among the boys?
• How many boys wear size 10 and above?

Essential Mathematics for JSS 2 chapter 23,pages 295 – 298

Exercise 23.2 No 7 pages 301

• What number is represented by the tally marks shown below?

A. 18   B. 23   C. 13   D. 43

The table below shows the marks obtained by students in a physics test.

• How many students did the test?     A. 35     B. 34     C. 30     D. 25
• What mark did most students get?    A. 5      B. 9     C. 8      D. 7
• The most frequency used value occurring in a set of data is known as   A. median    B. mean   C. average    D. mode
• The scores of some students in mathematics test were as follows: 1, 0, 7, 7, 8, 6, 1, 0, 8, 8, 9, 6, 5, 9, 9, 8, 8, 5, 5, 1, 0, 9, 9, 8, 9, 7, 5, 9, 7, 1, 0, 8, 6, 7, 7, 8, 1, 0
• Form a frequency table distribution
• How many students wrote the test?
• How many students scored less than seven?
• Which score occurred most often
• The following are the number of goals during inter-house football competition in a certain school.

5 0 4 2 5 1 3

2 4 0 0 3 0 2

1 2 3 3 4 0 5

Draw line graph for the data.

WEEK SEVEN

TOPIC: PICTORIAL PRESENTATION OF DATA USING PICTOGRAM, PIE CHARTS AND BAR CHARTS

CONTENT:   i) The Pictogram

ii) The bar charts

iii) The pie charts

INTRODUCTION

A frequency table is a numerical presentation of data in an organized summary from. Diagrams, symbols and pictures sometimes catch the eye more quickly than the number. They also tell stories more easily than numbers. It is also observed that it is easier to understand frequency table than the raw data, another method of presenting data, which most graphical find easier than table, is observe method. Graphs help us to observe any patterns easily. Examples of these graphs are pictogram, bar chart, line graph and pie chart.

THE PICTOGRAM

This uses pictures to represent statistics information or data. The pictogram is also called an ideograph. A pictogram uses pictures or drawings to give a quick and easy meaning to statistical data. A pictogram is a simple way of representing data in which a number of indentical drawings or pictures and used to show the data. It is useful to use pictures which can easily be divided into halves, quarters and do on. A pictogram must have a key to show that each picture stands for. Also you need to give the diagram a title

Example: The following table shows the favorite sports of 75 students

Represent the data in the form of a pictogram.

Football                                               25

Wrestling                                             10

Boxing                                                5

TableTennis                                         15

Swimming                                           20

Evaluation Question

The following table shows the number of students in JSS 1 in different houses at a certain school.

Represent the data in the form of a pictogram

• Essential mathematics for JSS 1 by AJS Oluwasanmi page 187
• New general mathematics for JSS 1 by AJS Channon other. Page 125
• MAN mathematics for JSS 1 page 211

THE BAR CHARTS

Barchart is very like a pictogram. The bars have the same width and usually have equal spaces between them. Instead of using pictures as in case of the pictogram, we must use a bar to represent the frequency of each of the item. In drawing a bar chart, we must take the following features into consideration.

• The charts consists of bars
• The bars must be of equal width
• The lengths of the bars are in proportion of the frequencies being represented. The bars may be vertical or horizontal

The following figures show the number of children per family in a sample of 40 households

1, 2, 4, 3, 4, 3, 8, 3, 2, 2, 3, 2, 5, 6,

5, 4, 2, 1, 3, 2, 4, 5, 3, 8, 7, 6, 5,

4, 5, 7, 6, 3, 8, 6, 3, 5, 7, 5, 4, 3

• Prepare a frequency table for this data
• Draw a bar chart to illustrate the above data
• Frequency table

The table below shows different colours of cars found in a company’s car park. Draw a bar chart for this data.

Essential Mathematics for JSS 2 by AJS Oluwasanmi page 188

THE PIE CHART

A pie chart is a circle, which is divided into slices (i.e sectors) whose angles are used to display data.

The size of an angle of each sector gives the frequency of each value. The major advantage of a pie chart is that it enables us to see clearly how the size of parts are compared in relation to one another and to the overall total. It is important to label each sector according to the given items and also give pie chart a little.

Example: A student was given N 600.00 in June as a pocket money. He spent the money as follows:

Food                =          N 200.00

Transport         =          N 100.00

Books              =          N 120.00

Rent                =          N 150.00

Miscellaneous  =          N 30.00

Draw a pie chart to illustrate the data.

= 200 x 0.6

= 120 o

120 o + 60 o + 72 o + 90 o + 18 o = 360 o

400 students were asked whether they liked yam, cornflakes, bread, rice or some other type of food for breakfast, the following data was recorded.

Draw a bar and a pie chart to represent this information

Essential Mathematics Bk. 2 pages 303 – 307. Exercise 24.2 No 1 and page 304

• Which of the following is not a pictorial form of presenting data?

A. Bar chart    B. Pie chart    C. Frequency distribution     D. Line graph

The pie chart below shows the course which a group of students are doing. Use the pie chart to answer questions 2 to 5

• What is the value of angle x o ?     A. 20 o       B. 30 o      C. 40 o       D. 35 o
• Which course most students doing?      A. Engineering     B. Accounting     C. Law      D. Medicine
• Which course has the least number of students?    A. Engineering     B. Accounting     C. Law      D. Medicine
• 40 youths who were admitted into a mental hospital due to drug abuse were asked to name the types of drugs they often take. The table shows how they replied.

Indian hemp                            35%

Morphine                                 20%

Heroine                                    15%

Cocaine                                    30%

• Represent this information in a pie chart
• Find the number of youths in each category

WEEK EIGHT

TOPIC: EXPERIMENTAL PROBABILITY

CONTENT:   i. Experimental Probability

ii. Probability as a fraction

EXPERIMENTAL PROBABILITY

When experimental data are used to predict further events, the prediction is called Experimental Probability. The following examples explain it further:

Example 1: A girl writes down the number of males and female children of her mother and father. She also writes down the number of male and female children of her parents’ brothers and sisters. Her results are shown below:

• Find the experimental probability that hen the girl has children of her own; her first born will be a girl.
• If the girl eventually has 5 children, how many are likely to be male?
• In the girl’s family, there are a total of 60 children. 36 of these are female. If the girl’s own children follow the pattern of her family, then the experimental probability that her first born will be a girl is
• A die has its six faces numbered 1 to 6
• Roll the die 50 times
• How many times did you roll a 6?
• What is the experimental probability of obtaining a 6 on the die?
• Write down the numbers of male and female children in your family. Follow the example above; find the experimental probability that your first born child will be a boy.

PROBABILITY AS A FRACTION

Probability is a measure of the likelihood of a required outcome happening. It is usually given as a fraction.

if an outcome is certain to happen, its probability is 1. If an outcome is certain not to happen, its probability is 0 (zero). If the probability of an event happening is P, the probability of the event not happening is 1-p .

Example1: it is known that out of every 1000 new cars, 50 develop a mechanical fault in the first 3 months. What is the probability of buying a car that will develop a mechanical fault within 3 months?

Number of cars developing faults = 50

Number of cars altogether = 1000

Example2: A market trader has 100 oranges for sale. Four of them are bad. What is the probability that an orange chosen at random is good? ‘At random’ means ‘without carefully chosen’.

Four out of 100 oranges are bad, thus 96 out of 100 oranges are good.

Example3: City school enters candidates for the WASSCE. The results for the years 1996 to 2000 are given below:

• Find the school’s success rate as a percentage.
• What is the approximate probability of a student at City School getting a WASSCE pass?
• Total number of passes = 51 + 56 + 57 + 65 + 70 = 299

Total number of candidates = 86 + 93 + 102 + 117 + 116 = 514

Success rate as a percentage = 0.58 x 100% = 58%

• The probability of a student getting a WASSCE pass = 0.58.
• a) The probability of passing an exam is 0.8. What is the probability of falling the examination?

b) The probability that a girl win a race 0.6. What is the probability that she loses?

c) The probability that a pen does not write is 0.05. What is the probability that it writes?

NGMFJSS2. Chapter 121

A bag contains 30 blue pens (B), 10 red pens (R) and 60 white pens (W). If a ball is chosen at random, what is the probability of choosing

(a) a blue pen?             (b) a red pen?              (c) a white pen?           (d)a black pen?

• In a class of 36 students, 20 are boys. What is the probability of choosing at random as the prefect of the class?
• A ludo die is thrown once. Find the probability of obtaining a PRIME number.

Essential Mathematics Bk. 2 pages 257 – 260

Exercise 20.2 No 1a – f page 259

• A fair die is thrown 900 times. Find the number of times you would expect to get a 6?    A. 200     B. 150     C. 250     D. 100
• The probability that it will be cloudy tomorrow is 0.45. What is the probability that it will not be cloudy tomorrow?    A. 0.45      B. 0.35     C. 1.25     D. 0.55
• Out of 10 students, the favourite drink of seven is coke and the favourite drink of the rest is Fanta. One of the students is chosen at random. What is the probability that the favourite drink of the student is
• Neither Coke nor Fanta
• Either Coke or Fanta?
• A trader has 100 mangoes for sale. Twenty of them are unripe. Another five of them are bad. If a mango is picked at random, find the probability that it is

WEEK NINE

TOPIC: PYTHAGORAS THEOREM (SOLUTION OF TRIANGLE)

CONTENT:   i. Pythagoras triple

ii. Pythagoras theorem

iii. Using Pythagoras theorem to solve other related problems.

PYTHAGORAS TRIPLE

The sides of a right-angled triangle can be related to the proof of Pythagoras Triple. A Pythagoras triple is a set of three whole numbers which numbers which gives lengths of the sides of right-angled triangle.

Examples of some common Pythagoras triple are (3, 4, 5), (6, 8, 10). (5, 12, 13), etc.

Worked Example

Which of the following is a Pythagoras triple?

a) (15, 30, 35)              b) (33, 56, 65)

15 2 + 30 2 = 225 + 900

= 1125

But 35 2 = 1225

(15, 30, 35) is not a Pythagoras triple

b) 33 2 + 56 2 = 1089 + 3136     =          4225

65 2 = 4225

Thus, 33 2 + 56 2 = 65 2

(33, 56, 65) is a Pythagoras triple.

Find out which of the following are Pythagoras triples.

a) (12, 16, 20)              b) (27, 36, 45)             c) (14, 24, 28)

• (12, 16, 20)

12 2 + 16 2 = 144 + 256 = 400

Thus, 12 2 + 16 2 = 20

(12, 16, 29) is a Pythagoras triple.

• (27, 36, 45)

27 2 + 36 2 = 729 + 1296 = 2025

45 2 = 2025

Thus, 27 2 + 36 2 = 45 2

(27, 36, 45) is a Pythagoras triple

• (14, 24, 28)

14 2 + 24 2 = 196 + 576 = 772

28 2      772

Thus, 14, 24, 28 is not a Pythagoras triple.

Reference: New General Mathematics Book 2, Chapter 7, Pages 150 – 151

Essential Mathematics for JSS Book 2, Chapter, 21, pages 218 and 219

PYTHAGORAS THEOREM

The Pythagoras’ Theorem states that in any right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the two sides.

/AB/ = hypotenuse, /BC/ and /AC/ are the other two sides, i.e.

/AB/ 2 = /BC/ 2 + /AC/ 2

Since /AB/ = c, /AC/ = b, /BC/ = a

Then, c 2 = a 2 + b 2

Calculate the length of the two sides of each of the triangle below

Solution

• Using Pythagoras rule

C 2 = a 2 + b 2

a = 3, b = 4

c 2 = 3 2 + 4 2 = 9 + 16

c = 5m, the length of the third side is 5m.

c 2 = a 2 + b 2

C = 13, a = a b = 5

13 2 = a 2 + 5 2

a 2 = 169 – 25 = 144

a)                                                         b)                                                         c)

• /AC/ 2 = /AB/ 2 + /BC/ 2

AC = ?,           AB = 8cm,      BC = 6cm

AC 2 = 8 2 + 6 2

• /AC/ 2 = /AB/ 2 – /BC/ 2

100 2 = 80 2 + /BC/ 2

• /AC/ 2 = /AB/ 2 + 7 2

AC = 25,         /AB/ = 7 2

25 2 = /AB/ 2 + 49

/AB/ 2 = 625 – 49 = 576

NGM BK 2, chapter 17, pages 147 – 148

Essential mathematics for JSS BK 2, chapter 21, pages 215 – 218

USING PYTHAGORAS THEOREM TO SOLVE OTHER RELATED PROBLEM INVOLVING TRIANGLES

In some cases, we may have more than one right – angled triangle.

• Calculate the length of the unknown in the following triangle:
• PRS is right angled triangle, PQR is also a right angled triangle

Let PR beycm

In triangle PQR; y 2 = 3 2 + 2 2

= 9 + 4 = 13

Let PS be xcm

In triangle PRS, x 2 = y 2 + 6 2

Substitute 13 for y 2 in the formula

x 2 = 13 + 62

x 2 = 13 + 36

• AD is the right angled ABD. Let AB be ycm.

In triangle ABC, x 2 = y 2 + (8 + 12) 2

Substitute 225 for y 2 in the formula

X 2 = 225 + 20 2

= 225 + 400 = 625

When solving triangle relating to decimal fraction and whole numbers, it is advisable to find the squares and square root from tables or multiplying the decimal by itself.

• A ladder is 7.3m long and the foot of the ladder is 1.8m from the wall. How far up the wall is the ladder?
• The distances between the opposite corner of a rectangular lawn is 30m, of the lawn is 24m. Calculate the breadth of the lawn.
• The distance between the opposite corners of a rectangular plot is 30m. The length of the plot is 24m. Calculate the breadth of the plot.
• A student cycles from home to school, first eastwards to a road junction 12km from home, then southwards to school. If the school is 19km from home, how far is it from the road junction?

REVISION QUESTION:

• A square top lid of a container has a diagonal 150cm. Find the length of one side of the lid.
• ABCD is a rectangle. AB = xcm, BC = 9cm and the diagonal AC = 19cm. Calculate the value of x.

Essential Mathematics for JSS 2 Chapter 21 pages 268 – 271

Exercise 21.1 1a – b, 2a – d, 3a – b, page 270

• The longest side of a right-angled triangle is called  A. hypotenuse    C. hypostasis    C. base    D. adjacent
• Calculate the length of the diagonal of a room 15m by 12m.    A. 9m     B. 81m    C. 19m     D. 12m
• Which of the following are Pythagorean triples?       A. 6, 8. 10      B. 12, 28, 32      C. 9, 12, 20     D. 13, 15, 17
• Calculate the value of x in the diagram below.

A. 25m     B. 15m     C. 5m     D. 11m

• In the diagram below, which of the following gives the value of side x 2 ?

A. x 2 = z 2 + y 2        B. x 2 = z 2 – y 2       C. x 2 = y 2 – z 2       D. x = z 2 – y 2

• A flagpole 5m tall is supported by a wire that is fixed at point 3m from the base of the pole. Calculate to 1 d.p the length of the wire.
• A square top lid of a container has a diagonal of 150cm. Find the length of one side of the lid.

## THIRD TERM SCHEME OF WORK FOR HOME ECONOMICS JSS 3(BASIC 9)

Lesson note on english studies jss 1 first term, ami ohun lori awon faweeli ati oro onisilebu kan, first term scheme of work for cultural and creative arts jss1 (basic 7).

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## JSS2 Third Term Mathematics Junior Secondary School

Presentation of data.

Good  presentation  can make statistical data easy to read, understand and interpret. Therefore it is important to present data clearly.

• There are two main ways of presenting data : presentation of numbers or values in  lists  and  tables;
• Presentation using  graphs,  i.e. picture. We use the following examples to show the various kinds of presentation.

She graded the essays from A (very good), through B, C.D, E to f (very poor). The grades of the students were:

B, C, A, B, A, D, F, E, C, C, A, B, B, E, B

Lists and tables

Rank and order list

Rank order  means in order from highest to lowest. The 15 grades are given in rank order below:

A, A, A, B, B, B, B, C, C, C, E, E, F

Notice that all the grades are put in the list even though most of them appear more than once. The ordered list makes it easier to find the following: the highest and lowest grades; the number of students who got each grades; the most common grade; the number of students above and below each grade; and so on.

Frequency table

Frequency  means the number of times something happens. For example, three students got grade A.

The frequency of grade A is three. A  frequency table,  gives the frequency of each grade.

Graphical Presentation

In most cases, a picture will show the meaning of statistical data more clearly than a list of or table or numbers. The following methods of presentation give the data of the example in picture, or  graph,  form.

A  pictogram  uses pictures or drawings to give a quick and easy meaning to statistical data .

A bar chart represents the data as horizontal or vertical bars. The length of each bar is proportional tothe amount that it represents.

There are 3 main types of bar charts.

Horizontal bar charts, vertical bar chart and double bar charts.

When constructing a bar chart it is important to choose a suitable scale to represent the frequency.

The following table shows the number of visitors to a park for the months January to March.

• a) Construct a vertical and a horizontal bar chart for the table.
• a) If we choose a scale of 1:50 for the frequency then the vertical bar chart and horizontal bar chart will be as shown.

Pie charts  are useful to compare different parts of a whole amount.  They are often used to present financial information.  E.g. A company’s expenditure can be shown to be the sum of its parts including different expense categories such as salaries, borrowing interest, taxation and general running costs (i.e. rent, electricity, heating etc).

A pie chart is a circular chart in which the circle is divided into sectors.  Each sector visually represents an item in a data set to match the amount of the item as a percentage or fraction of the total data set.

A family’s weekly expenditure on its house mortgage, food and fuel is as follows:

Draw a pie chart to display the information.

The total weekly expenditure = N300 + N225 + N75 = N600

We can find what percentage of the total expenditure each item equals.

Percentage of weekly expenditure on:

Mortgage = 300/600 X 100% = 50%

Food = 225/600 X 100% = 37.5%

Fuel = 75/600 X 100% = 12.5% To draw a pie chart, divide the circle into 100 percentage parts.  Then allocate the number of percentage parts required for each item.

It is simple to read a pie chart. Just look at the required sector representing an item (or category) and read off the value. For example, the weekly expenditure of the family on food is 37.5% of the total expenditure measured.

A pie chart is used to compare the different parts that make up a whole amount.

The following is a rank order list of an exam result: 87, 82, 78, 76, 75, 70, 66, 64, 59, 59, 59, 51, 49, 48, 41.

• How many students took the exam?
• What was the highest rank?
• What was the lowest rank?
• What is the mark of the student who came 6th?
• What is the position of the student who got 76 marks?
• Three students got 59 marks. What is their position?
• How many students got less than 75 marks?

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## Bearing and Distances

Back to: MATHEMATICS JSS 2

Welcome to Class !!

In today’s Mathematics class, We will be discussing Bearing and Distances.  We hope you enjoy the class!

i. Compass bearing

ii Three figure bearing

iii. Finding the bearing of a point from another

## COMPASS BEARING

A bearing gives the direction between two points in terms of an angle in degrees. The two types of bearing are compass bearing and three-figure bearings.

The four major compass directions are North (N) South (S) East (E) and West (W)

Apart from the four main points or directions, there are also four main secondary directions i.e. NE (northeast), SE (south-east), SW (south-west), NW (north-west). The angle between each point is 45 o

Worked examples

Draw a sketch to show each of these bearings marketing the angles clearly.

a) N35 o W    (B) N70 o E    (C.) S58 o W

• N35 o W means from N measure 35 o toward the W or 35 o W of N

In a), the direction start from a wrong point (W) instead of N, therefore,

90 – 18 = 72 o

i.e. N72 o W

In b), the direction starts from a wrong point (E) instead of S therefore:

90 – 55 = 35 o i.e. S35 o E

Evaluation: Class Work

Find the compass direction of point A from point O in these diagrams.

NGM BK CHAPTER 23, page 185 – 187

Essential Mathematics for JSS BK 2, CHAPTER 24, pg 246-247

## THREE-FIGURE BEARINGS

Three-figure bearings are given as the number of degrees from north, measured in a clockwise direction. Any direction can be given as a three-figure bearing. Three-digit are always given but angles less than 100 o need extra zero to be written in front of the digits e.g. 008 o , 060 o , 070 o up to 099 o

Worked Example

Find the three-figure bearings of A, B, C, and D from X

• The arrow N shows the direction N, NXA = 63 o . the bearing of A from X is 063 o
• NXB = 180 – 35 = 145 o . The bearing of B from X is 145 o
• NXC clockwise = 180 + 75 = 255 o . The bearing of C from X is 255 o
• NXD clockwise = 360 – 52 = 308 o . The bearing of D from X is 308 o .

Evaluation:

In the figure below, find the bearings of A, B, C and D from X.

NGM Bk. 2 Chapter 23, page 180 – 19

In each diagram below, calculate

i) the bearing of B from A

ii) the bearing of A from B

GENERAL EVALUATION

From a point P, the bearing of a house is 060 o . From a point Q 100m due east of P, the bearing is 330 o .

Draw a labelled sketch to show the positions of P, Q and the house.

REVISION QUESTION

• A girl is facing East. If she turns clockwise through 2 right angles, then the direction she would be facing is ……………………..
• A student is facing South-East. If he turns anticlockwise through 1800, then the direction he would be facing is …………………..

WEEKEND ASSIGNMENT

• The bearing of X from Y is 196 o . The bearing of Y from X is 016 o        B. 074 o       C. 106 o      D. 196 o
• A boat sails on a bearing of 225 o . Using compass bearing, in what direction is the boat sailing? South East     B. North-East     C. South West     D. North West
• The bearing of point A from B is 058 o . Find the bearing of point B from point 058 o      B. 122 o      C. 302 0      D. 238 o
• Which of the following statements is not true when we specify a direction with bearing? Measure the angle from North   B. Measure anticlockwise     C. Measure clockwise     D. Always use three digits
• In the diagram below, which of the following angles is the bearing of P from Q? 065 o     B. 245 0      C. 295 o      D. 115 o

We have come to the end of this class. We do hope you enjoyed the class?

Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.

In our next class, we will be talking about Statistics: Data Presentation.  We are very much eager to meet you there.

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## 7 thoughts on “Bearing and Distances”

I NEED MORE EXAMPLES FOR THREE FIGURE BEARING

i need more examples for compass bearing

i need help. i am lost

I need more explanation on bearing and distance

The bearing of sokoto from Kaduna is 050 what Is the bearing of Kaduna from sokoto

If the bearing is less than 180 degrees, add 180. And if it is more than 180, subtract 180 degrees in other to get the back or reciprocal bearing To your question 050+180 =230. Hence the bearing of Kaduna from sokoto is 230 degrees

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## Mathematics JSS3 Third Term Data Presentation

• Data Presentation

Mathematics J.S.S 3 Third Term

Theme: Measurement and geometry

Sub Theme: Shapes

Performance Objectives

Students should be able to;

• Represent information on Pie chart
• Interpret a pie chart

A pie chart is a circular graph showing a distribution. The pie chart is divided into sectors that are proportional to the frequency or class frequencies of items in a distribution.

The total frequencies of the distribution in a pie chart are equal to 360 0 which is the angle in a circle.

The table below shows grades obtained in an examination. Construct a pir chart to show the information.

• Areas of Plane Figures 1
• Areas of Plane Figures 2
• Measure of central tendency 1
• Measure of central tendency 2
• Construction
• Mathematics JSS3 Third Term Assessment
• Category JSS3
• Author ClassNotes Edu

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Week 2 – start april 29th and end 3rd may, 2024.

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## Mathematics Guides for JSS 2 Data Presentation and Probability

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MATHEMATICS

THEME – EVERYDAY STATISTICS

## TOPIC 1 – DATA PRESENTATION

INSTRUCTIONAL MATERIALS

1. Source information 2. Distance charts 3. Flight schedules, etc.

LEARNING OBJECTIVES

By the end of the lesson, students should be able to: 1. present data in an ordered form. 2. construct frequency tables from any given data. 3. draw pie charts. 4. read information from pie chart. 5. generate and use data for statistical purposes. 6. interpret and use tables, charts, records and schedules.

CONTENTS OF THE LESSON

## FOCUS LESSONS 1

1. Ordered presentation of data 2. Frequency table 3. Pie charts 4. Charts, records and schedules

LESSON PRESENTATION

Teacher’s Activities,  1. Guide students to arrange data in an ordered form. 2. Guides students to display any given data on frequency table. 3. Guides students to draw pie charts. 4. Guides students to read information from pie chart. 5. Leads students to generate and use data for statistical purposes. 6. Guides pupil to interpret and use tables, charts, records and schedules.
Student’s Activities, 1. Arrange data in an ordered form. 2. Display any given data on frequency table. 3. Draw pie charts. 4. Read information from pie chart. 5. Generate and use data for statistical purposes. 6. Interpret and use tables, charts, records and schedules.

LESSON EVALUATION

Students to, 1. present data in ordered form. 2. construct frequency table from a given data. 3. draw a pie chart. 4. read information from given pie charts.

## TOPIC 2 – PROBABILITY

1. Coins 2. Dice 3. Source information sheet on events.
By the end of the lesson, students should be able to: 1. discuss the occurrence of chance events in everyday life. 2. determine the probability of certain events. 3. apply the occurrence of chance events/probabilities in everyday life.

## FOCUS LESSONS 2

1. Occurrence of chance events in everyday life. 2. Probability of chance events.
Teacher’s Activities,  1. Leads students to give examples of chance events in everyday life  e.g The chance or event that rain will fall in December. 2. Leads students to perform experiments using coin and die. 3. Guides students to calculate the probability of the resulting experiments. 4. Guides students to analyze statistical data with the use of probability such as mortality rate etc. 5. Guides students to apply the probability occurrence of chance events in everyday life.   Student’s Activities, List examples of chance events in everyday life. 2. Perform experiments using coin and die. 3. Calculates the probability of the resulting experiments. 4. Analyze statistical data with the use of probability. 5. Mention the application of probability in everyday life.
Students to, 1. Give three occurrence of chance events. 2. Calculate the probability of chance events. 3. Give four examples of the application of probability in everyday life.

Related posts, mathematics guides for jss 2 measurement and geometry, mathematics guides for jss 2 algebraic processes, mathematics guides for jss 2 number and numeration, about the author.

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## Types of Data in Spreadsheets - JSS3 Computer Studies Lesson Note

Text Data: Cells in a spreadsheet can contain text, which is useful for labels, descriptions, or any non-numeric information.

Numeric Data: Spreadsheets excel in handling numeric data, whether it's simple values, currency, percentages, or dates. Numeric data can be easily manipulated and used in calculations.

Formulas: Formulas are expressions that perform calculations using values in cells. They can range from basic arithmetic operations to complex functions, enabling users to automate calculations and update results dynamically.

Charts and Graphs: Spreadsheets allow the representation of data visually through charts and graphs. These visual elements enhance data interpretation and presentation.

Conditional Formatting: This feature allows users to apply formatting based on specific conditions, making it easy to highlight important data points or trends.

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Gdp up by 0.3% in both the euro area and the eu.

In the first quarter of 2024, seasonally adjusted GDP increased by 0.3% in both the euro area and the EU , compared with the previous quarter, according to a preliminary flash estimate published by Eurostat, the statistical office of the European Union . In the fourth quarter of 2023, GDP had declined by 0.1% in the euro area and had remained stable in the EU .

These preliminary GDP flash estimates are based on data sources that are incomplete and subject to further revisions.

Compared with the same quarter of the previous year, seasonally adjusted GDP increased by 0.4% in the euro area and by 0.5% in the EU in the first quarter of 2024, after +0.1% in the euro area and +0.2% in the EU in the previous quarter.

Among the Member States for which data are available for the first quarter of 2024, Ireland (+1.1%) recorded the highest increase compared to the previous quarter, followed by Latvia , Lithuania and Hungary (all +0.8%). Sweden (-0.1%) was the only Member State that recorded a decrease compared to the previous quarter. The year on year growth rates were positive for nine countries and negative for four.

The next estimates for the first quarter of 2024 will be released on 15 May 2024.

## Notes for users

The reliability of GDP flash estimates was tested by dedicated working groups and revisions of subsequent estimates are continuously monitored . Further information can be found on Eurostat website .

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## Release schedule

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This news release presents preliminary flash estimates for euro area and EU after around 30 days.

## Methods and definitions

European quarterly national accounts are compiled in accordance with the European System of Accounts 2010 (ESA 2010).

Gross domestic product (GDP) at market prices measures the production activity of resident production units. Growth rates are based on chain-linked volumes.

Two statistical working papers present the preliminary GDP flash methodology for the European estimates and Member States estimates .

The method used for compilation of European GDP is the same as for previous releases.

## Geographical information

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European Union (EU27): Belgium, Bulgaria, Czechia, Denmark, Germany, Estonia, Ireland, Greece, Spain, France, Croatia, Italy, Cyprus, Latvia, Lithuania, Luxembourg, Hungary, Malta, the Netherlands, Austria, Poland, Portugal, Romania, Slovenia, Slovakia, Finland and Sweden.

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## Share the release

#### IMAGES

1. Data presentation -Part 2 (Mathematics JSS 2)

2. DATA PRESENTATION

3. Lesson Note On Data Presentation.

4. Overview of JSS2 Usage

5. First Term JSS2 Basic Science Scheme of Work

6. MATHEMATICS

#### VIDEO

1. laws of indices

2. Jss2 Kinetic Theory

3. Presentation of Data |Chapter 2 |Statistics

4. SSS1 WELCOME JSS2 FOR THE FIRST SEMI_FINAL OF THE KING'S CHILDREN ACADEMY FOOTBALL TOURNAMENT CUP

5. Jss2 element of art

6. My lesson teacher Live Stream

1. Mathematics Guides for JSS 2 Data Presentation and Probability

By the end of the lesson, students should be able to: 1. present data in an ordered form. 2. construct frequency tables from any given data. 3. draw pie charts. 4. read information from pie chart. 5. generate and use data for statistical purposes. 6. interpret and use tables, charts, records and schedules. CONTENTS OF THE LESSON.

2. Data presentation

JSS2 Mathematics. Data presentation. Overview. Present data in an ordered form Construct frequency tables from any given data Draw pie charts Read information from pie chart Generate and use data for statistical purposes Interpret and use tables, charts, records and schedules.

3. Statistics: Data Presentation

CONTENT: 1. Definition. Method of collecting data. Classification of data. DEFINITION. Statistics: is the branch of the study of data. It involves Gathering (i.e. collecting) data, sorting and tabulating data and presenting data visually by means of diagrams. Data: (SINGULAR DATUM) means information which is usually given in a meaningful form.

4. Lesson Note On Data Presentation.

Subscribe now to gain full access to this lesson note. Take Me There. Click here to gain access to the full notes. Students should be able to;1. Draw pie charts2. Read information from pie charts3. Generate and use data for statistical purposes4. Interpret and use tables, charts, records and schedules.

5. DATA PRESENTATION

This is the explanation of "Data Presentation" in Mathematics for JS2 Week2 according to the curriculum

6. JSS2 Third Term Mathematics Lesson Note

The content is just an excerpt from the complete note for JSS2 Third Term Mathematics Lesson Note - Data Presentation. Check below to download the complete DOCUMENT. WEEK 8. TOPIC: DATA PRESENTATION. CONTENT: Data and Types of Data. Presentation of data. (i) Frequency tables: ungrouped and grouped. (ii) Pie Chart: construction and interpretation.

7. Data Presentation (II)

JSS2 Mathematics. Data Presentation (II) As a guest, you are limited to taking any 3 lessons. Go to your dashboard to take lessons for your class, monitor your progress, join discussions and lots more. Overview. At the end of the lesson, the student should be able to understand more on Data Presentation ...

8. JSS2 Mathematics Lesson Notes- Third Term

JSS2 Mathematics Lesson Notes- Third Term. Here is the Math's scheme and notes for week 1. ... Re-presentation of real situation an graph and the reason(s). Angles and Polygon: (i) definition of angles (ii) Construction of move angles (iii) Definition of polygon with examples ... Statistics: Data Presentation ...

9. PDF NEW GENERAL MATHEMATICS

objectives for JSS1 and JSS2 Week 2 Ch 1 Binary system: Operations and ... Data presentation Find mean, median, mode and range of given data Represent and interpret information in tables and on pie charts, bar charts and pictograms Apply everyday statistics to analysis of information/data and environmental issues. viii JSS 3 Scheme of Work ...

10. JSS 2 Data Presentation II

Discover the world of pie charts and how they make data presentation fun and easy. Learn to construct and interpret pie charts like a pro. Exciting math less...

11. Third term JSS2 Mathematics Lesson note

Worry no more, here is the reviewed and updated version of the JSS2 3 rd TERM Mathematics lesson note available online. The lesson note covers weekly prepared lesson notes and each topic in this lesson note is explained in detail with adequate evaluation at the end of each week. It is based on the latest unified NERDC/UBE curriculum which is ...

12. Lesson Note on Mathematics JSS2 Third Term

The graph of a linear equation is always a straight line. In general, a straight line has an equation in the form y = mx + c, where x and y are variables and m and c are constants. Evaluation: Draw the graph of y = 4x - 7 for values of x from -3 to +3. From your graph find: The value of y when x = 2.5.

13. Free Mathematics Lesson Note JSS 2

19. STATISTICS 2 - PRESENTATION OF DATA 20. PROBABILITY 21. SOLVING EQUATIONS 22. USING CALCULATORS AND TABLES 23. PYTHAGORAS' THEOREM 24. TABLES, TIMES TABLES AND CHARTS. Sample note . Topic: WHOLE NUMBERS. Factors and Prime factors (revision) 40 ÷ 8 = 5 and 40 ÷ 5 = 8. 8 and 5 divide into 40 without remainder. 8 and 5 are factors of 40.

14. Class Notes On Mathematics JSS2 Third Term

06 Mathematics JSS2 Third Term Mid-Term Assessment . View > 07 Bearings . Students should be able to;1. Identify the cardinal points 2. Locate the positions of objects 3. ... 09 Every Statistics Data collection and presentation. Students should be able to;1. present data in an ordered form2. construct frequency table from any given data . View >

15. JSS2 Third Term Mathematics Junior Secondary School → Presentation of

Good presentation can make statistical data easy to read, understand and interpret. Therefore it is important to present data clearly. There are two main ways of presenting data: presentation of numbers or values in lists and tables; Presentation using graphs, i.e. picture. We use the following examples to show the various kinds of presentation.

16. Jss2-Maths-Data Presentation Iii-16.m4v on Vimeo

This is "Jss2-Maths-Data Presentation Iii-16.m4v" by Krystal Digital on Vimeo, the home for high quality videos and the people who love them. Solutions . Video marketing. Power your marketing strategy with perfectly branded videos to drive better ROI. Event marketing. Host virtual events and webinars to increase engagement and generate leads. ...

17. Data presentation -Part 1 (Mathematics JSS 2)

18. Bearing and Distances

NGM Bk. 2 Chapter 23, page 180 - 19. Evaluation. In each diagram below, calculate. i) the bearing of B from A. ii) the bearing of A from B. GENERAL EVALUATION. From a point P, the bearing of a house is 060 o. From a point Q 100m due east of P, the bearing is 330 o. Draw a labelled sketch to show the positions of P, Q and the house.

19. Lesson Note On Data Presentation

The pie chart is divided into sectors that are proportional to the frequency or class frequencies of items in a distribution. The total frequencies of the distribution in a pie chart are equal to 3600 which is the angle in a circle. Example 1. The table below shows grades obtained in an examination. Construct a pir chart to show the information.

20. PDF JSS2 ICT FIRST TERM E-NOTE CLASSIFICATION OF COMPUTER ...

An INPUT consists of data or commands that are entered into the computer usually via an input device such as keyboard, mouse, scanner e.t.c. The role of an input is to provide data for further processing. Processing is the stage where the input data is manipulated to produce meaningful information.

21. Mathematics Guides for JSS 2 Data Presentation and Probability

By the end of the lesson, students should be able to: 1. present data in an ordered form. 2. construct frequency tables from any given data. 3. draw pie charts. 4. read information from pie chart. 5. generate and use data for statistical purposes. 6. interpret and use tables, charts, records and schedules. 1.

22. Types of Data in Spreadsheets

Charts and Graphs: Spreadsheets allow the representation of data visually through charts and graphs. These visual elements enhance data interpretation and presentation. Hyperlinks: Spreadsheets support hyperlinks, enabling users to link to external documents, websites, or other sheets within the same workbook for easy navigation. Conditional Formatting: This feature allows users to apply ...

23. Fact Sheet on FTC's Proposed Final Noncompete Rule

The following outline provides a high-level overview of the FTC's proposed final rule:. The final rule bans new noncompetes with all workers, including senior executives after the effective date.

24. Beautiful Data Science Presentations

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27. PDF Q1 2024 Results

This presentation contains statements about Bristol-Myers Squibb Company's (the "Company") future financial results, plans, business development strategy, anticipated clinical trials, results ... • Data presented as Late Breaker at ASCO GI 2024 • Projected data readout in 2025 for Arm B vs. A in all lines . CT Identifier. NCT04039607 ...

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Using administrative data sources to produce official statistics on refugees, IDPs and(or) stateless persons (Azerbaijan)

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30. GDP up by 0.3% in both the euro area and the EU

Among the Member States for which data are available for the first quarter of 2024, Ireland (+1.1%) recorded the highest increase compared to the previous quarter, followed by Latvia, Lithuania and Hungary (all +0.8%). ... Statistics Explained articles on measuring quarterly GDP and presentation of updated quarterly estimates. Country specific ...