Topic 6: Revision Activities

Activity 2

(a) Write down the place value of each digit in the following numbers;

i) 1202, three ii) 45123 seven

(b) Using the results in (a), express the following:

i) 1202, in Base Ten. three ii) 45123 in Base Five. seven iii) AB4 in Base Four. thirteen iii) AB4 thirteen

Activity 3

(a) Design and complete addition and multiplication tables for different number bases.

(b) Perform the following operations:

i) 101, two + 111two ii) 543six-34six iii) 26 seven 31 seven iv) 127 ÷ 35 eight eight

Activity 4

Find the value of n if,

(a) 12n = 20 three,

(c) 56n = 99 ten (b) 184n= 101 six (d) 103 four = 33

Activity 5

(a) With examples, discuss and differentiate the following categories of numbers:

(i) Natural and whole numbers

(ii) Odd and even numbers

(iii). Prime and composite numbers

(b) Amuge has four number cards: 6 7 3 0

She can arrange the cards to form different numbers.

i) What is the greatest even number that she can form using all the four cards?

ii) What is the least odd number that she can form using all the four cards?

Activity 6

(a) Study the following number cards: 70 246 3578 3578 120090 3497602824

(b) Identify the place value of each digit in the numbers in (a).

Activity 7

(a) Write the following figures in words:

i) 796,900 ii) 32,442,008 iii) 124,984,492

iv) 46,598,767,450 v) 7,568,823,496,500

(b) Write the following in figures:

i) Thirty four million two hundred forty five thousand

ii) Seven hundred eighty seven million three hundred two thousand four hundred fifty

iii) Six trillion four hundred forty six billion nine hundred eighty million five hundred twenty five thousand one hundred fifty five

Activity 8

Work out the following using a number line:

(a) -4+7 (b) 9–2 (b) -8-3 (c) -4 × -4 (d) -10 + 7 (e) -2 x -7 (f) 3× -5

Activity 9

Express the following numbers as products of their prime factors.

(a) 625 (b) 1,200 (d) 1,024 (f) 3,969 (g) 6,936 (h) 9,000

Activity 10

Five small containers of capacities; 12, 16, 24, 56, and 72 litres are to be used to fill a bigger container. What is the capacity of the bigger container which can be filled up by each of the above containers exactly without a remainder when used separately?

Activity 11

In groups, discuss and summarise the divisibility tests of different numbers.

Activity 12

1)Mayom is a businessman dealing in ropes. He has a long rope measuring 120 m, which he intends to cut into short pieces of 72 m. How many short ropes can he make from the long rope?

2) How many 31 kg are there in 179 kg?

3) Opiku and Legu own a rabbit farm, from which they make an average profit of UGX 750,000 monthly. They re-invest three-eighths of the profit and share the rest of the money between themselves. If Opiku receives of the profits, determine how much Legu receives.

Activity 13

(a) Plot the points (4, 0), Q(0, 4), and R(4, 0) on the Cartesian Plane: P.

(b) Join the above points to form a shape and name it.

(c) What are the coordinates for the midpoint of side PQ?

Activity 14

(a) From your experience, differentiate between perpendicular and parallel lines.

(b) Imagine that you were very deep in a village and that you did not have a geometry set there. How, most accurately, would you draw four parallel lines on a ground?

Activity 15

(a) Construct the angle of 1/822°.

(b) Describe how you have constructed the angle above.

Activity 16

A point G moves in the Cartesian Plane such that its distance from the origin (0, 0) is always g units.

(a) What do you expect to be the locus of G?

(b) Briefly explain why you expect so.

Activity 17

(c) Are there triangles in real life? If yes, where?

(d) What shapes can be obtained from (joining) a given number of triangles?

Activity 18

1) Write the next four terms in the -1, -3, -6, -10, 15, 21, 28, …, …

2) Your Class Monitor forgot the password, a four-digit number, to your classroom electronic lock. But luckily, he remembered some hints on how o recall this password. These are: to

i) the first digit is half of the second.

ii) the sum of the second and third digits is 10.

iii) the fourth digit is 1 more than the second.

iv) the sum of all the digits is 23. What is the password?

Activity 19

(a) State four uses of a compass in your community.

(b) When you directly face the chalkboard (or whiteboard) in your classroom, what is its compass direction from you?

Activity 20

(a) At a certain school, the kitchen and the dining hall are such that the bearing of the dining hall from the kitchen is 60° East of South. The distance between the kitchen and the dining hall is 60 m.

i) Draw a sketch for the above information.

ii) Represent the above information on a scale drawing.

iii) Calculate the bearing of the kitchen from the dining hall.

(b) If you were facing West-North-West, what would be your bearing after turning anticlockwise through 360°?

(c) If you were facing South-South-East, what would be your bearing after turning clockwise through 540°?

Activity 21

At a certain polling station, ten candidates, who were contesting for the same position, were voted as follows:

(a) Present the above data on a tally chart.

(b) If the candidate who polls the highest number of votes wins the race, which of the candidates won the position?

(c) i) In case the candidate whom you have named in (b) left the race just after counting of the votes, is there a candidate who would be declared the winner of the race? If yes, which candidate is it?

ii) Explain your answer in c(i) above.

(d) How many votes did Candidate C13 get?

Activity 22

(a) Suggest two uses of reflection in your community.

(b) After a reflection along the line y = 4, the image of a point was (0, 0). What was the object point?

(c) Find the images of the following points under reflection in the given lines:

i) (0, 2), (-4, 6), (2, 3), and (6, 0); y = 2 – x

ii) (4, 4), (2, -7), and (2, 19); 2y = 3x + 8

Activity 23

(a) Draw an arrow diagram to show the relation, “is an odd divisor of” using the sets: T = {3, 5, 7, 11, 13} and R = {18, 45, 21, 33, 26, 11}.

(b) What type of relation is exhibited in Part (a) above?

Activity 27

(a) A car moves steadily at an increasing speed of 20 km/hr every after an hour. If the car started the journey at 8 a.m. at a speed of 0 km/hr, draw a table of values for its journey up to 6 hours.

(b) Use the tabulated information to plot a graph. 1

(c) From the graph, find the speed of the car after 34 hours of steady movement.

Activity 28

A motorcyclist started a journey from rest and rode for 3 hours at a steady speed of 30 km/hr, then maintained that speed for 5 hours, and then started decreasing the speed steadily for the next 3 hours to rest.

(a) Draw a graph to illustrate the information above.

(b) Use the graph to find the:

i) total distance travelled.

ii) average speed for the whole journey.

(c) If the motorcyclist started at 9:00 a.m., at what time was the journey completed?

Activity 30

(a)Represent the following inequalities on a number line:

i) x>2

ii) x > 2

iii) x<5

v) -2x> 5

(b) Interpret the information below and represent it on a number line:

i) X vi) -2<x<5 less than or equal to -1 and greater than or equal to 4

ii) y is between 2 and -5

iii) x is at most -2

iv) y is at least 2

Activity 31

1) Margarine is three times as expensive as Blue Band, and the sum of their prices is not less than UGX 5,000. Calculate their least possible prices.

2) Solve the following inequalities and represent their solution sets on a number line:

(a) 1/2= x < 4

(b) 6-3y <-3

(c) 82x < -12 4

Activity 32

Given a triangle, with Vertices A (1, 1), B (2, -3) and C (3, 5), that is enlarged under a linear scale factor k to give an image A'(2, 2), B'(4, -6), and C'(6, 10):

(a) determine the value of k.

(b) considering A’B’C’ as the object and ABC as the image, state the corresponding linear scale factor.

Activity 34

1) Draw diagrams to represent the following:

(a) a half turn (b) a quarter turn (d) a revolution 74 (c) a three quarter turns do you determine: (e) an anticlockwise half turn (f) a clockwise half turn

2) When Triangle PQR is mapped onto its image P’Q’R’ under a rotation, how

(a) the centre of rotation? (b) the angle of rotation?

3)In a Mathematics quiz, Adumo was asked: Under a rotation as a transformation, the size and shape of the object and its image are the same. Is it true or false? She replied that it was false. Was she correct? Defend your opinion.

.Activity 37

(a) Draw a rectangular box with dimensions of your choice.

(b) Measure and record the length of the diagonal of your box.

(c) Calculate the length of the diagonal. Compare your results in (b) and (c). What do you conclude? (d) When is it possible to use Pythagoras’ Theorem?

Activity 38

(a) Draw a composite shape that is made up of at least four regular figures with different dimensions.

(b) Work out the total area of your composite shape.

(c) Explain how you obtained the area in (b).

Activity 39 (Work in groups)

Using an internet-enabled device, go to the link; mathisfun.com/definitions/net.html

(a) Sstudy the different nets of solids provided by this link.

(b) draw the different nets of common solids.

(c) compare your work with other groups.

Activity 41

1) Pulkol plans to set up a milk storage tank of volume 6,000 litres. How deep should the tank be, if it is three metres long and two metres wide?

2) The Director of Studies wants to ascertain the number of small cubic boxes of chalk of Side Length 20 cm that can fit into a big cubic shelf of Side Length 1.2 metres. As a Senior Four Mathematics learner, help him or her to determine the number of small boxes that can fit into the big cubic shelf when the small boxes are arranged, end to end.

Activity 42

1) Identify the unlike surds from the following sets:

(a) √80, √117, 17√5, √320, and √496

(b) √92, 2√7, √207, and 11√23

2) From the fact that yx – zx = x(y-z), find (13√29-16√29)

3) How many threes would you need to multiply by the square root of 3 to obtain the square of 3?

4) Simplify the following;

(a) 3√11 + 2 – √πT + 5(√TT)(VIT) + 4√11 1

(b) -6√11 x 60 √10 5) a) Determine the result of adding 5 to itself four times.

b) Determine the result of adding 4 to itself five times.

c) Comment on your answers in (a) and (b). Relate your comment to the multiplication of 5 by 4 and that of 4 by 5.

d) In your own words, prepare short notes that you would present to pupils in Primary Three about what the multiplication of two numbers means.

Activity 43

(a) i) List the activities that you do when you just wake up in the morning.

ii) List the activities that a 4-year old child would do (or does) if you can actually relate with such a child, It could be your younger brother / sister) when he/she just wakes up in the morning.

(b) i) Are there activities that are common to you and him / her?

ii) List the members of set C, defined as: Set C = {activities that my younger brother/sister and I share in common). (c) Share your findings with other members in the class.

Activity 44 (Work in pairs)

Name the following sets:

(a) X = {1, 3, 5, 7, 9, 11, 13, 15}

(b) Y = {wash your hands, maintain a social distance from your neighbour, always wear a face mask}.

(c) Z = {0} Discuss the names that you have written, with other groups.

Activity 45 (Work in pairs)

(a) i) Is it possible to fail to collect and group a given list of objects into one set? If yes, when is it so?

(b) What is the greatest number of elements that any given set can have?

(c) Share your answers with other groups.

Activity 46

(a) When are two or more sets said to be equivalent?

(b) Given that sets: A = {1, 5}; B = {0, 4, 8}; C = {0,0 }; D = {a, b, c), and E = {}

i) state the pairs of sets which are equivalent.

ii) is E an infinite set? Explain.

Activity 47

(a) List the elements in each of the sets below:

i) M = {planets in the solar system}

ii) N = {even prime numbers}

iii) P = {odd multiples of 10}

(b) Are any of the above sets equal? Explain.

Activity 48

a) Is it false that an empty set is not a subset of itself? Explain.

b) of the sets A = {T, μ, B}, and B = {T, μ, B}, which one is the subset of the other? Explain

Activity 49 (Work in pairs)

(a) Let, in each pair, every member randomly write down ten multiples of 2, which are between 14 and 44. This should be done individually.

(b) Exchange your book or paper (where you have written your random multiples) with your colleague in the pair and let him / her note the multiples that you have written into a set.

(c) Compare your colleague’s set with yours.

(d) What do you observe about the elements in each of the sets, in your pair?

(e) Form the set R = {multiples which are common to the two sets, in your pair).

(f) What name is given to R, as far as your two sets in the pair are concerned?

(g) Discuss your findings with members in other pairs.

Activity 50

Given a universal set = {February, April, August, December} and a set T, given by: T = {February, April, August, December), what is the complement of T?

Activity 51

Consider the sets below:

W = {the first six triangle numbers}

X = {all prime numbers which are divisible by 8}

Y = {even positive multiples of 7 which are less than 10}

Z= {odd factors of 2} By listing the members of these sets, find: (a) n (YUZ)

Activity 53 (Work in pairs)

In Atero Village, there are 215 homes. Of these, 133 rear poultry, 115 rear cattle, and 140 rear goats. 85 homes rear poultry and goats, 107 homes rear cows and goats while 77 homes rear poultry and cattle. Given that the number of homes that keep all the three kinds of animals is three times that of the homes that do not rear any of the three:

(a) Represent this information on a Venn Diagram.

(b) Find the number of homes that rear all the three kinds of animals.

(c) Find the probability of visiting a home that rears:

i) only poultry.

ii) poultry and goats but not cattle.

Activity 54 (Work in pairs)

At Nabiswa High School, an A-level class has 180 students; 90 of them study Economics, 54 study Physics, and 77 study Biology. 21 students study Economics and Physics, 39 students study Physics and Biology, and 47 students study Economics and Biology. 45 students do not study any of the above subjects.

(a) Represent this information on a Venn dDiagram.

(b) Find the number of students who study all the three subjects.

(c) If a student was selected at random from the class, find the probability that one studies: i) only Economics

ii) Biology but not Physics

iii) only one of the subjects.

Activity 55 (Work in groups)

A village has 160 homes. 74 of the homes grow groundnuts, 82 of them grow maize, and 63 of them grow sorghum. No home grows only sorghum. 64 homes do not have any garden. 60 homes grow groundnuts and maize, while 45 homes grow sorghum and groundnuts. The number of homes that grow groundnuts only is one more than that of the homes that grow maize only.

(a) Draw a Venn Diagram to show this information.

(b) Determine the number of homes that grow:

i) maize and sorghum only.

ii) all the three types of crops.

(c) Determine the probability that a home visited at random in that village grows:

i) at most two types of crops.

ii) at least two types of crops.

Activity 56 (Work in groups)

At Kajoko Trading Centre, there are 65 shops. 48 shops sell foodstuffs, 30 shops sell household utensils, while 31 shops sell stationery. Out of these, 17 shops sell foodstuffs and household utensils while 18 shops sell foodstuffs and stationery. Each shop sells at least one of the items.

(a) Draw a Venn Diagram to show this information.

(b) Determine the:

i) number of shops that sell all the three items.

ii) probability of picking a shop that sells only one of the items.

iii) probability of selecting a shop that sells two or more of the items.

Activity 57 (Work in groups)

Study the following set of Points M = {(-4, -8), (2, 2), (0, 4), (2, 10)}

(a) Plot any one point in the set on a graph paper. Is it possible to draw a straight line through all the points in M using only this point? Explain.

(b) Plot any two points in the set on the same graph paper. Join them using a blue ink pen to form a line.

(c) Plot any three points in the set on the same grid paper. Join them using a black ink pen to form a straight line.

(d) Plot all the points in the set on the same graph paper. Join them using a pencil to form a straight line.

(e) State the least number of points that need to be plotted in order to draw a straight line.

Activity 58 (Work in groups)

(a) Plot the Points A(-3, -2), B(-1, 2) and C(2, 8) on a graph paper.

(b) Join the points you have plotted above to form a straight line.

(c) Find the change in x-values and change in y-values from Point:

i) A to Point C. ii) A to Point B. iii) B to Point C.

(d) Find the ratio of the change in y-values to the change in the x-values in c) i, ii and iii. Comment on your results.

(e) State the gradient of the straight line formed.

Activity 59

(a) Plot the following points on a graph paper. Use a scale of 1cm: 1 unit: i) A(1, 1), B(2, 4) and C(-1, -5). ii) R(0, 6), S(2, 12) and T(-2, 0).

(b) Join the Points A, B and C to form a straight line. Find its gradient and linear equation.

(c) Join the Points R, S, and T to form a straight line. Find its gradient and linear equation. (d) Classify the lines drawn and comment on their gradients.

Activity 60 (Work in groups)

Read the following case: Your school is to hire a bus for a trip from a bus company that charges a fee of UGX 300,000 for bus hire and an additional fee of UGX 10,000 for every kilometre covered. Given that x kilometres are covered to cost the trip y shillings altogether, write down the cost equation.

Activity 61

(a) Draw the graph y= sin 2x for; 0°< x < 180°.

(b) Use your graph to estimate:

i) sin 30°. ii) sin 210°. iii) the value of x when sin x = 0.2. iv) the value of x when sin x = -0.5 7)

(a) Draw the graph of y = cos 3x for 0°< x < 120°:

(b) Use your graph to estimate:

i) cos 75. ii) cos 225. X 812 iii) the value of x when cos = 0.4. iv) the value of x for when cos x = -0.2. 8) (a) Draw the graph y= tan for; 0°< x < 720°:

(b) Use your graph to estimate:

i) tan 90°. X iii) the value of x when tan = 0.7. ii) tan 220°. 2 iv) the value of x when tan = 0.3. X

Activity 62 (Work in groups)

1) (a) List down your favourite games at your school. 2)

(b) Compare the games you have listed in (a) with those of other groups.

(c) Identify the most popular game(s) at your school.

2) The masses of babies weighed at Aketa Health Centre on a certain day were recorded as 2.5 kg, 4.6 kg, 4.6 kg, 3.5 kg, 3.9 kg, 3.6 kg, 3.5 kg, m kg, and 4.3 kg, 2.9 kg. Given that the modal mass was 3.5 kg, find the value of m.

Activity 70 (Work in groups)

Read the text below:

Mr. Mugisha bought land at UGX 19,000,000. After 5 years, he opted to venture into transport but had only UGX 4,000,000 with him. He approached a car bond which accepted to sell to him a truck valued at UGX 35,000,000 in exchange for the land and UGX 4,000,000 cash.

(a) Give a reason why the car bond offered the truck to Mr. Mugisha on these terms.

(b) Discuss and list other examples of assets that appreciate.

(c) Discuss and write down your own definition of the term “appreciation”.

Activity 71

A civil servant wants to buy a house which costs 80 million Ugandan shillings cash. His monthly income is 1.5 million Ugandan shillings and he has so far saved 60 million Ugandan shillings, for the years he has worked. On 1st January, 2021, he decided to negotiate with a property agency on how to pay for this house. The agency manager accepted to sell to him the house at a cash deposit of 60 million Ugandan shillings and a monthly payment of 1 million Ugandan shillings for 5 years.

Task: If the civil servant decides to buy the house now, determine how much money he will have paid by the end of the 5 years.

Activity 72 (Work in groups)

Solve the following:

(a) tan 0 = 1,0°≤ 0≤720° (b) tan = 2, -180°≤ 0≤180° (c) tan 0 = -3, -360° 0≤360° (d) 3tan 0= -1.5, -180°≤ 0≤ 270°

Activity 73

(a) You are given matrices; A = = 12 2 3 and B = -5 2 2 Find the matrix; I = 4 5 2 -1 AB and, hence, AI, IA, BI, and IB.

(b) What do you conclude about Matrices A and B?

Activity 74 (Work in groups)

(a) Find the matrix corresponding to the reflections below, by considering the images of the points (1, 0) and J(0, 1):

(i) Reflection along the line x = 0

(ii) Reflection along the line y -x = 0

(iii) Reflection along the line x + y = 0

(b) What do you notice about the determinants of the transformation matrices?

Activity 75 (Work in groups)

(a) Plot the following triangles on a graph paper: T: (-1, -1), (5, 1), (-5, -3) T: (1, 1), (5, 1), (5, 3) T: (1, 1), (5, 1), (5, 3) Describe the transformation matrix that maps:

(b) i) T, onto T1 3 2 ii) T, onto T, 1 iii) T, onto T2 2

Activity 76 (Work in groups)

Given that a transformation Matrix A maps Object P onto P’, show that P = A P’.

Activity 77

A quadrilateral ABCD has vertices A(1, 1), B(4, 1), C(4, 4), and D(1, 4). If ABCD is transformed by Matrix M = 2 2 1 2 to give Image A’B’C’D’.

(a) Find the coordinates of A’B’C’D’.

(b) Plot ABCD and A’B’C’D’ on the same graph.

(c) By counting squares, estimate the areas of ABCD and A’B’C’D’.

(d) Find the ratio k = (area of A’B’C’D’) (area of ABCD)

(e) Compute the determinant of Matrix M.

(f) Identify the relationship between the determinant of Matrix M and the ratio in (d).

Activity 78 (Work in groups)

(a) Eliminate x from the given pairs of linear equations:

i) x + y = 2 -x + 2y = 1 ii) 2x-3y = 1 2x + 2y = 6

(b) Eliminate y from the given pairs of linear equations i) x + 2y = 3 2x + y = 3 ii) 3x-2y= 1 2x+5y= 7 What do you conclude about the coefficients of the unknown to be eliminated? Explain views with the rest of the class.

Activity 79 (Work in groups)

(a) Write down three pairs of equivalent quadratic expressions:

(b) Expand the following algebraic expressions: i) (2m – n) (m + 2n) ii) (3x + 2)2 iii) (5k-4)2 iv) (4x-5y)(4x+5y)

(c) Give two examples of algebraic perfect squares.

(d) Factorise the following quadratic expressions: (i) xy2 – xy (ii) 5h2 – 12h+7 (iii) 1-2d-3d2

(e) Use factorization to solve the following quadratic equations: i) 9×2 -64 = 0 ii) x2 + 8x + 12 = 0 iii) 7×2-2x-3=0

(f) Share with other groups.

Activity 80 (Work in groups)

Summarise all the circle properties you learnt in Senior Three.

Activity 81 (Work in groups)

(a) Discuss and write short notes on the following:

i) a relation ii) a mapping iii) a function mapping iv) a non-function mapping

(b) Draw an arrow diagram to show the relation “is a multiple of” using sets A = {2, 3, 5, 7} and B = {4, 6, 15, 21).

(c) What type of mapping is the relation in b)?

(d) Identify the domain and range of the relation in b).

(e) Is the relation in b) a function or a non-function mapping? Explain.

Activity 82 (Work in groups)

(a) Write the Pythagoras’ Theorem.

(b) Give examples of plane figures.

(c) Make a discussion on perimeters of plane figures.

(d) Draw the net for each of the following solids.

(i) cube (ii) cuboid (e) Discuss the volume of a: (i) cube