YEARLY
WORKED SOLUTIONS
LEVEL
EXAM
PAPERS
Mathematics
PAPER 2
2 nd edition
 Actual exam papers
 Clear answers and
methods
Compiled and Solved
by
Mr.Mununga. J
2016 - 2019
Level
Contacts: 0762486410/0978934334
CONTENTS
1. Algebra………………………………………………………………………………….1
2. Matrices……………………………………………………………………….…...……2
3. Sets.……………………………………………………………………...………..……3
4. Quadratic equations….........................................................................................7
5. Sequences and series……………………………………………….……….…….…8
6. Probability……………………………………………………………………………..10
7. Vector geometry……………………………………………………………….……..12
8. Pseudo codes and flow charts………………………………………………..…….16
9. Mensuration…………………………………………………………………….…….19
10. Calculus…………………………………………………………………………….…22
11. Loci and construction………………………………………………………….……..23
12. Earth geometry……………………………………………………………………….26
13. Trigonometry………………………………………………………………………….30
14. Statistics…………………………………………………………………………........33
15. Linear programming……………………………………………………………........38
16. Functions………………………………………………………………………………41
17. Geometric transformations…………………………………………………………..46
18. Answers…………………………………………………………………………….....47
© 2020 All rights Reserved
TOPIC 1: ALGEBRA
Page |1
1. 2019 OCTOBER/NOVEMBER EXAMS, Q2 (a), 4 (a) & 12 (c) RESPECTIVELY
(a) Simplify
6𝑥 2 −24
𝑥−2
.
5
4
(b) Express 2𝑥−4 − 3𝑥+5 as a single fraction in its simplest form.
(c) Simplify
25𝑝4
7𝑞 2
5𝑝6
𝑝
÷ 21𝑞4 × 15𝑞 .
2. 2019 JULY/AUGUST EXAMS, Q1 (a), 3 (a) & 8 (c) RESPECTIVELY
10𝑥 3 𝑦 2
2𝑥 2 𝑦 2
(a) Simplify 35𝑥 5 𝑦 4 ÷ 7𝑥 4 𝑦 2 .
6
5
(b) Express 𝑛−3 − 𝑛−2 as a single fraction in its simplest form.
(c) Simplify
2𝑥 2 −18
𝑥+3
.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q5 (a), 7 (b) & 8 (c) RESPECTIVELY
𝑏−𝑎
(a) Simplify𝑎2 −𝑏2 .
3
2
(b) Express 𝑥+1 − 𝑥−1 as a single fraction in its lowest terms.
12𝑑𝑛3
9𝑐 3 𝑛
(c) Simplify 15𝑐𝑑3 ÷ 10𝑐 2 𝑑2 .
4. 2018 JULY/AUGUST EXAMS, Q2 (a) & 12 (a) RESPECTIVELY
7𝑠𝑡 3
5𝑢3 𝑣
(a) Simplify 15𝑢3 𝑣 2 × 28𝑠3 𝑡 2 .
3
4
(b) Express 2𝑥−5 − 𝑥−3 as a single fraction in its lowest terms.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q5 (b), 7 (c) & 10 (b) RESPECTIVELY
(a) Simplify
(b) Simplify
14𝑥 3
9𝑦 2
7𝑥 4
÷ 18𝑦 3 .
2𝑥 2 −8
𝑥+2
.
1
2
(c) Express 𝑥−4 − 5𝑥−1 as a single fraction in its lowest terms.
6. 2017 JULY/AUGUST EXAMS, Q2 (a), 4 (a) & 10 (c) RESPECTIVELY
𝑚2 −1
(a) Simplify 𝑚2 −𝑚 .
3
2
(b) Express 5𝑥−2 − 𝑥+3 as a single fraction in its simplest form.
(c) Simplify
𝑝2 𝑞3
4
8
× 𝑝𝑞 ÷ 2𝑝2 𝑞 .
Compiled and solved by Mr Mununga J
Page |2
7.
2016 OCTOBER/NOVEMBER EXAMS Q 5 (a), 10 (c) & 12 (b) RESPECTIVELY
𝑥−1
(a) Simplify 𝑥 2 −1 .
17𝑘 2
(b) Simplify 20𝑎2 ÷
51𝑘 2
5𝑎
2
.
1
(c) Express 2𝑥−1 − 3𝑥+1 as a single fraction in its simplest form.
8. 2016 JULY/AUGUST EXAMS 1 (a), Q 2 (a), & 2 (b) RESPECTIVELY
(a) Factorise completely 4𝑥 2 − 16𝑦 2 .
4
3
3𝑎
10𝑐 2
(b) Express 3𝑟−2 − 𝑟+5 as a single fraction in its simplest form.
(c) Simplify 5𝑐 2 ×
𝑎2
.
TOPIC 2: MATRICES
1. 2019 OCTOBER/NOVEMBER EXAMS Q1 (a)
6
Given that matrix A= (
2
𝑥
),
3
(i) find the value of x for which the determinant of A is 36,
(ii) hence, find the inverse of A.
2. 2019 JULY/AUGUST EXAMS Q 2 (a)
8
12
) is 8. Find
𝑥−4 𝑥
The determinant of matrix Q= (
(i) the value of x,
(ii) the inverse of Q.
3. 2018 OCTOBER/NOVEMBER EXAMS Q1 (a)
8 𝑦
4 −5
) and B= (
),
1
2
3 5
Given that matrix A= (
(i) find the value of y for which the determinant of A and B are equal,
(ii) hence find the inverse of B.
4. 2018 JULY/AUGUST EXAMS Q1 (a)
Given that matrix A= (
2𝑥
3
2
),
𝑥
(i) find the positive value of x for which the determinant of A is 12,
(ii) hence or otherwise, write 𝐴−1 .
Compiled and solved by Mr Mununga J
Page |3
5. 2017 OCTOBER/NOVEMBER EXAMS Q1 (a)
3
5
−2
),
𝑥
Given that matrix M= (
(i) find the value of x for which the determinant of M is 22,
(ii) hence find the inverse of M.
6. 2017 JULY/AUGUST EXAMS Q1 (a)
Given that matrix K= (
10 −2
), find
11 −2
(i) the determinant of K,
(ii) the inverse Of K.
7. 2016 OCTOBER/NOVEMBER EXAMS, Q1 (a)
3
Given that matrix Q= (
𝑥
−2
), find the
4
(i) value of x, given that the determinant of Q is 2,
(ii) inverse of Q.
8. 2016 JULY/AUGUST EXAMS, Q2 (c)
𝑥−2 𝑥
) is 4,
2
1
Given that the determinant of matrix A= (
(i) find the value of x,
(ii) write the inverse of the matrix A.
TOPIC 3: SETS
1.
2019 OCTOBER/NOVEMBER EXAMS Q3 (b)
The Venn diagram below shows the number of elements in sets A, B and C.
E
B
A
7
C
𝑥−4
8
5
10
Compiled and solved by Mr Mununga J
2𝑦
Page |4
Find
(i) x, such that 𝑛(𝐵) = 𝑛(𝐵 ∪ 𝐶)′,
(ii) y, such that 𝑛(𝐶) = 𝑛(𝐴),
(iii) 𝑛(𝐸),
(iv) 𝑛(𝐵 ′ ).
2. 2019 JULY/AUGUST EXAMS, Q2 (b)
The Venn diagram below shows the optional subjects that all the Grade 10
Learners at Kusambilila Secondary school took, in a particular year.
E
History
59
Music Geography
𝑥 − 3 𝑥+2 𝑥 −2
43
(i) Given that 12 learners took music, find the value of x.
(ii) How many learners were in Grade 10 this particular year?
(iii) find the number of learners who took
(a) one optional subject only,
(b) two optional subjects only.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q2 (b)
At Sambileni College, 20 students study at least one of the three subjects;
Mathematics (M), Chemistry (C) and Physics (P). all those who study Chemistry
Also study Mathematics. 3 students study all the three subjects. 4 students
Study Mathematics only, 8 students study Chemistry and 14 students study
Mathematics.
(i) draw a venn diagram to illustrate this information.
(ii) how many students study
(a) Physics only,
(b) two subjects only,
(c) Mathematics and Physics but not Chemistry?
Compiled and solved by Mr Mununga J
Page |5
4. 2018 JULY/AUGUST EXAMS, Q (a)
The diagram below shows how learners in a grade 12 class at Twaenda
School travel to school. The learners use either buses (B), cars (C) or
Walk (W) to school.
E
B
C
2
14
X 3
4
W
7
7
(i) if 22 learners walk to school, find the value of x.
(ii) how many learners use
(a) only one mode of transport,
(b) two different modes of transport?
5. 2017 OCTOBER/NOVEMBER EXAMS, Q1 (b)
A survey carried out at Kamulima Farming Block showed that 44 farmers
Planted maize, 32 planted sweet potatoes, 37 planted cassava, 14 planted
Both maize and sweet potatoes, 24 planted both sweet potatoes and
cassava,20 planted both maize and cassava, 9 planted all the three crops
and 6 did not plant any of these crops.
(i) Illustrate this information on a Venn diagram.
(ii) How many farmers
(a) were at this farming block,
(b) planted maize only,
(c) planted 2 different crops?
Work hard stay consistent be patient
Compiled and solved by Mr Mununga J
Page |6
6. 2017 JULY/AUGUST EXAMS, Q3 (b)
The Venn diagram below shows tourist attractions visited by students in a
Certain week.
Victoria falls
Mambilima falls
2
6
2y+1
10
1
4
8
Gonya falls
(i) Find the value of y, if 7 students visited Mambilima falls only.
(ii) How many students visited
(a) Victoria falls but not Gonya falls,
(b) two tourist attractions only,
(c) one tourist attraction only?
7. 2016 OCTOBER/NOVEMBER EXAMS, Q2 (a)
Of the 50 villagers who can tune in to Kambani Radio Station, 29 listen to news,
25 listen to sports, 22 listen to music, 11 listen to both news and sports, 9 listen to
Both sports and music, 12 listen to both news and music, 4 listen to all the three
Programs, and 2 do not listen to any programme.
(i) Draw a Venn diagram to illustrate this information.
(ii) How many villagers
(a) listen to music only,
(b) Listen to one type of programme only,
(c) listen to two types of programmes only?
Compiled and solved by Mr Mununga J
Page |7
8. 2016 JULY/AUGUST EXAMS, Q5 (a)
The Venn diagram below shows the results of a survey conducted at Mayuka
clinic on patients who were attended to on a particular day. Set W represents
Those who complained of body weakness, set H those who complained of
Headache and set F those who complained of fever.
E
W
H
18
13 14
F
6
5
(i) Use the information in the Venn diagram to find the number of people who
Complained of
(a) body weakness only,
(b) body weakness and fever only,
(c) headache.
(ii) Calculate the percentage of those who complained of all the three ailments.
TOPIC 4: QUADRATIC EQUATIONS
1. 2019 OCTOBER/NOVEMBER EXAMS, Q3 (a)
Solve the equation 𝑝2 − 𝑝 = 4, giving your answers correct to 2 decimal places.
2. 2019 JULY/AUGUST EXAMS, Q5 (a)
Solve the equation 13 − 9𝑥 − 5𝑥 2 = 0, giving your answers correct to 2 decimal
Places.
Compiled and solved by Mr Mununga J
Page |8
3. 2018 OCTOBER/NOVEMBER EXAMS, Q2 (a)
Solve the equation 3𝑥 2 − 𝑥 − 5 = 0, giving your answers correct to 2 decimal
places.
4. 2018 JULY/AUGUST EXAMS, Q1 (b)
Solve the equation 𝑥 2 − 4𝑥 − 2 = 0, giving your answers correct to 2 decimal
Places.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q4 (a)
Solve the equation 2𝑥 2 = 6𝑥 + 3, giving your answers correct to 2 decimal places.
6. 2017 JULY/AUGUST EXAMS, Q 1(b)
Solve the equation 3𝑧 2 = 7𝑧 − 1, giving your answers correct to 2 decimal places.
7. 2016 OCTOBER/NOVEMBER EXAMS, Q1 (b)
Solve the equation 𝑥 2 + 2𝑥 = 7, giving your answers correct to 2 decimal places.
8. 2016 JULY/AUGUST EXAMS, Q3 (b)
Solve the equation 𝑥 2 + 2𝑥 = 5, giving your answers correct to 2 decimal places.
TOPIC 5: SEQUENCES AND SERIES
1. 2019 OCTOBER/NOVEMBER EXAMS, Q2 (b)
Given the geometric progression 4, 8, 16, …,
find
(i) the geometric mean of 256 and 1024,
(ii) the 11th term,
(iii) the sum of the first 11 terms.
The foundation is the determiner. Justin Mununga
Compiled and solved by Mr Mununga J
Page |9
2. 2019 JULY/AUGUST EXAMS, Q1 (b)
In a geometric progression, the third term is 16 and the fifth term is 4. Calculate
(i) the first term and the common ratio,
(ii) the tenth term,
(iii) the sum to infinity.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q5 (b)
The first three terms of a geometric progression are 𝑘 + 4, 𝑘 and 2𝑘 − 15 where 𝑘
is a positive constant.
(i) Find 𝑘.
(ii) List the first three terms of the progression.
(iii) Calculate the sum to infinity.
4. 2018 JULY/AUGUST EXAMS, Q2 (b)
2
2
In a geometric progression, the third term is 9 and the fourth term is 27 . find
(i) the first term and the common ration,
(ii) the sum of the first 5 terms of the geometric progression,
(iii) the sum to infinity.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q5 (a)
1
For the geometric progression 20, 5, 1 4 , …, find
(i) the common ratio,
(ii) the nth term,
(iii) the sum of the first 8 terms.
It takes good people to see the goodness. Justin Mununga
Compiled and solved by Mr Mununga J
P a g e | 10
6. 2017 JULY/AUGUST EXAMS, Q2 (b)
The first three terms of a geometric progression are 6 + 𝑛, 10 + 𝑛 and 15 + 𝑛.
find
(i) the value of 𝑛,
(ii) the common ratio,
(iii) the sum of the first 6 terms of this sequence.
7. 2016 OCTOBER/NOVEMBER EXAMS, Q5 (b)
The first three terms of a geometric progression are 𝑥 + 1, 𝑥 − 3 and 𝑥 − 1. Find
(i) the value of 𝑥,
(ii) the first term,
(iii) the sum to infinity.
TOPIC 6: PROBABILITY
1. 2019 OCTOBER/NOVEMBER EXAMS, Q1 (b)
A box contains 4 red pens and 5 green pens. A pen is picked at random from
the box without replacement and a second pen is then picked.
(i) Draw a tree diagram to illustrate the outcomes.
(ii) What is the probability of picking one red pen and one green pen?
2. 2019 JULY/AUGUST EXAMS, Q5 (b)
Thirteen cubes of the same size numbered 1 to 13 are placed in a bag. If two
cubes are drawn at random from the bag one after the other and not replaced,
what is the probability that
(i) both cubes are old numbered,
(ii) only one is even numbered.
Compiled and solved by Mr Mununga J
P a g e | 11
3. 2018 OCTOBER/NOVEMBER EXAMS, Q1 (b)
A small bag contains 6 black and 9 green pens of the same type. Two pens are
taken at random one after the other from the bag without replacement. Calculate
the probability that both pens
(i) are black,
(ii) are of different colours.
4. 2018 JULY/AUGUST EXAMS, Q5 (a)
A box contains identical buttons of different colours. There are 20 black, 12 red
and 4 white buttons in the box. Two buttons are picked at random one after
another and not replaced in the box.
(i) Draw a tree diagram to show all the possible outcomes.
(ii) What is the probability that both buttons are white?
5. 2017 OCTOBER/NOVEMBER EXAMS, Q2 (a)
A box of chalk contains 5 white, 4 blue and 3 yellow pieces of chalk. A piece of
chalk is selected at random from the box and not replaced. A second piece
of chalk is then selected.
(i) Draw a tree diagram to show all the possible outcomes.
(ii) Find the probability of selecting pieces of chalk of the same colour.
6. 2017 JULY/AUGUST EXAMS, Q3 (a)
In a box of 10 bulbs, 3 are faulty. If two bulbs are drawn at random one after the
Other, find the probability that
(i) both are good,
(ii) one is faulty and the other is good.
Success is the sum of small repeated efforts everyday
Compiled and solved by Mr Mununga J
P a g e | 12
7.
2016 OCTOBER/NOVEMBER EXAMS, Q2 (b)
A survey carried out at a certain hospital indicates that the probability that a
patient tested positive for malaria is 0.6. What is the probability that two patients
Selected at random
(i) one tested negative while the other positive,
(ii) both patients tested negative.
8.
2016 JULY/AUGUST EXAMS,Q9 (b)
A bag contains 3 black balls and 2 white balls. Two balls are taken from the bag
at random, one after another, without replacement.
(i) Draw a tree diagram to represent this information.
(ii) calculate the probability that the two balls taken at random are of the same
colour.
TOPIC 7: VECTOR GEOMETRY
1. 2019 OCTOBER/NOVEMBER EXAMS, Q6 (a)
⃗⃗⃗⃗⃗ = 4𝑂𝐴
⃗⃗⃗⃗⃗ and ⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗ . M is the midpoint of BC, ⃗⃗⃗⃗⃗
In the diagram below, 𝑂𝐵
𝐴𝐶 = 5𝐴𝑋
𝑂𝐴 = 𝑎
⃗⃗⃗⃗⃗⃗ = 𝑏.
and 𝐵𝑀
C
M
𝑏
X
O
𝑎
A
B
(i) Express in terms of 𝑎 and/or 𝑏.
⃗⃗⃗⃗⃗ ,
(a) 𝐴𝐵
⃗⃗⃗⃗⃗ ,
(b) 𝐴𝐶
2
(ii) Show that ⃗⃗⃗⃗⃗
𝑂𝑋 = 5 (4𝑎 + 𝑏).
Compiled and solved by Mr Mununga J
⃗⃗⃗⃗⃗⃗ .
(c) 𝑂𝑀
P a g e | 13
2. 2019 JULY/AUGUST EXAMS, Q3 (b)
⃗⃗⃗⃗⃗ = 𝑏 and 𝐴𝐶 = 1 .
In the diagram below, ⃗⃗⃗⃗⃗
𝑂𝐴 = 𝑎 , 𝑂𝐵
𝐶𝐵
2
B
C
𝑏
M
A
𝑎
O
(i) Express in terms of 𝑎 and/or 𝑏
(a) ⃗⃗⃗⃗⃗
𝐴𝐵 ,
(b) ⃗⃗⃗⃗⃗
𝐴𝐶 ,
⃗⃗⃗⃗⃗ .
(c) 𝑂𝐶
1
⃗⃗⃗⃗⃗⃗ = (𝑏 − 4𝑎).
(ii) Given that M is the midpoint of OC, show that 𝐴𝑀
6
3. 2018 OCTOBER/NOVEMBER EXAMS, Q6 (a)
⃗⃗⃗⃗⃗ = 𝑎, 𝐴𝐷
⃗⃗⃗⃗⃗ = 𝑏, 𝐵𝐶
⃗⃗⃗⃗⃗ = 2𝑏 and 𝐴𝐸: 𝐴𝐶 = 1: 3.
In the quadrilateral ABCD below, 𝐴𝐵
C
2𝑏
D
E
𝑏
A
𝑎
B
(i) Find in terms of 𝑎 and/or 𝑏
(a) ⃗⃗⃗⃗⃗
𝐴𝐸 ,
⃗⃗⃗⃗⃗ ,
(b) 𝐵𝐸
⃗⃗⃗⃗⃗⃗ .
(c) 𝐵𝐷
(ii) Hence or otherwise, show that the points B, E and D are collinear.
4. 2018 JULY/AUGUST EXAMS, Q3 (b)
Show that the points 𝐿(−2, −10), 𝑀(2, 2) and 𝑁(5, 11) are collinear.
Compiled and solved by Mr Mununga J
P a g e | 14
5. 2017 OCTOBER/NOVEMBER EXAMS, Q2 (b)
⃗⃗⃗⃗⃗ = 2𝑝,𝑂𝑄
⃗⃗⃗⃗⃗⃗ = 4𝑞 and 𝑃𝑋: 𝑋𝑄 = 1: 2.
In the diagram below, 𝑂𝑃
P
C
2𝑝
X
O
Q
4𝑞
(i) Express in terms of 𝑝 and/or 𝑞
⃗⃗⃗⃗⃗⃗
(a) 𝑃𝑄,
(b) ⃗⃗⃗⃗⃗
𝑃𝑋,
(c) ⃗⃗⃗⃗⃗
𝑂𝑋.
⃗⃗⃗⃗⃗ = ℎ𝑂𝑋
⃗⃗⃗⃗⃗ , show that 𝐶𝑄
⃗⃗⃗⃗⃗ = 4 (1 − ℎ) 𝑞 − 4ℎ 𝑝.
(ii) Given that 𝑂𝐶
3
3
6. 2017 JULY/AUGUST EXAMS, Q6 (a)
In the diagram below, OABC is a parallelogram in which ⃗⃗⃗⃗⃗
𝑂𝐴 = 𝑎 and ⃗⃗⃗⃗⃗
𝐴𝐵 = 2𝑏.
OB and AC intersect at D. E is the midpoint of CD.
2𝑏
A
𝑎
B
D
E
O
C
Express in terms of, 𝑎 and/or 𝑏.
(i)
⃗⃗⃗⃗⃗ ,
𝑂𝐵
(ii)
⃗⃗⃗⃗⃗
𝑂𝐸 ,
(iii)
⃗⃗⃗⃗⃗
𝐶𝐷.
The activity you are avoiding contains your biggest opportunity. Robin Sharma
Compiled and solved by Mr Mununga J
P a g e | 15
7. 2016 OCTOBER/NOVEMBER EXAMS, Q3 (b)
⃗⃗⃗⃗⃗ = 3𝑎 and 𝑂𝐵
⃗⃗⃗⃗⃗ = 6𝑏.
In the diagram below, OAB is a triangle in which 𝑂𝐴
𝑂𝐶: 𝐶𝐴 = 2: 3 and 𝐴𝐷: 𝐷𝐵 = 1: 2. OD meets CB at E.
A
3𝑎
C
D
E
O
B
6𝑏
(i) Express each of the following in terms of 𝑎 and/or 𝑏
(a) ⃗⃗⃗⃗⃗
𝐴𝐵 ,
⃗⃗⃗⃗⃗⃗ ,
(b) 𝑂𝐷
⃗⃗⃗⃗⃗ .
(c) 𝐵𝐶
⃗⃗⃗⃗⃗ , express 𝐵𝐸
⃗⃗⃗⃗⃗ = ℎ𝐵𝐶
⃗⃗⃗⃗⃗ in terms of h, 𝑎 and 𝑏.
(ii) Given that 𝐵𝐸
8. 2016 JULY/AUGUST EXAMS, Q6 (a)
⃗⃗⃗⃗⃗ = 𝑏. C on AB is such that 𝐴𝐶: 𝐶𝐵 = 2: 1
In the diagram below, ⃗⃗⃗⃗⃗
𝑂𝐴 = 𝑎 and 𝑂𝐵
and B on OD is such that 𝑂𝐵: 𝑂𝐷 = 1: 2.
A
𝑎
O
𝑏
B
D
Express as simply as possible in terms of 𝑎 and/or 𝑏.
(i) ⃗⃗⃗⃗⃗
𝐴𝐵 ,
⃗⃗⃗⃗⃗ ,
(ii) 𝐴𝐷
(iii) ⃗⃗⃗⃗⃗
𝐶𝐷.
Compiled and solved by Mr Mununga J
TOPIC 8: PSEUDO CODES & FLOW CHARTS
P a g e | 16
1. 2019 OCTOBER/NOVEMBER EXAMS, Q4 (b)
The program below is given in the form of a pseudocode.
Begin
Enter length
If length< 0
The display “error message and re-enter positive length
Else enter height
If height < 0
Then display “error message” and re-enter positive height
1
Else volume= 3 ∗ 𝑙 ∗ 𝑙 ∗ ℎ
End if
Display volume
End
Draw the corresponding flowchart for the information given above.
2. 2019 JULY/AUGUST EXAMS, Q6 (b)
The flow chart below shows the steps in calculating the volume of a solid given
the base area (A) and height (h).
Start
Enter A
𝐼𝑠 𝐴 < 0
Yes
“error message”
A must be positive
No
Enter h
𝐼𝑠 ℎ < 0
Yes
“error message”
h must be positive
No
𝑣 =𝐴∗ℎ
Display v
Stop
Write the corresponding pseudocode for the flow chart given above.
Compiled and solved by Mr Mununga J
P a g e | 17
3. 2018 OCTOBER/NOVEMBER EXAMS, Q6 (b)
The program below is given in pseudo code.
Start
Enter x, y
Let 𝑀 = 𝑠𝑞𝑢𝑎𝑟𝑒 𝑟𝑜𝑜𝑡𝑡(𝑥 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 + 𝑦 𝑠𝑞𝑢𝑎𝑟𝑒𝑑)
IF 𝑀 < 0
THEN display error message “M must be positive”
ELSE
END IF
Display M
Stop
Draw the corresponding flow chart for the information given above.
4. 2018 JULY/AUGUST EXAMS, Q5 (b)
Study the pseudo code below.
Start
Enter a, r, n
𝑅 =1−𝑟
IF 𝑅 = 0 THEN
Print “the value of r is not valid”
Else 𝑆𝑛 =
𝑎(1−𝑟 𝑛 )
𝑅
End if
Print 𝑆𝑛
Stop
Construct a flow chart corresponding to the pseudo code above.
Failure is the opportunity to begin again more intelligently. Henry Ford
Compiled and solved by Mr Mununga J
P a g e | 18
5. 2017 OCTOBER/NOVEMBER EXAMS, Q6
Study the flow chart below.
Start
Enter r
Is
Yes
𝑟 < 0?
Error “r must be positive”
No
𝐴=
1
∗ 𝑟 ∗ 𝑟 ∗ 𝑠𝑖𝑛𝜃
2
Display Area
Stop
Write a pseudo code corresponding to the flow chart program above.
6. 2017 JULY/AUGUST EXAMS, Q6 (b)
The program below is given in the form of a flow chart.
Start
Enter a, r
Is
No
|𝑟| < 1?
Yes
𝑎
𝑆∞ =
1−𝑟
Display sum to infinity
Stop
Write a pseudo code corresponding to the flow chart program above.
Compiled and solved by Mr Mununga J
P a g e | 19
7. 2016 OCTOBER/NOVEMBER EXAMS, Q3 (a)
The program below is given in the form of a pseudocode.
Start
Enter radius
If radius < 0
Then display “error message” and re-enter positive radius
Else enter height
If height < 0
Then display “error message” and re-enter positive height
1
Else Volume = 3 ∗ 𝜋 ∗ 𝑠𝑞𝑢𝑎𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 ∗ ℎ𝑒𝑖𝑔ℎ𝑡
End if
Display volume
Stop
Draw the corresponding flowchart for the information given above.
TOPIC 9: MENSURATION
1. 2019 OCTOBER/NOVEMBER EXAMS, Q11 (b)
The figure below shows a right pyramid with vertex O and a square base ABCD
of side 8cm. 𝐴𝑃̂ 𝐷 = 𝑂𝑃̂ 𝐶 = 90°.
O
10cm
A
B
P
8cm
D
C
Given that 𝑂𝐴 = 𝑂𝐵 = 𝑂𝐶 = 𝑂𝐷 = 10𝑐𝑚, calculate
(i)
The height OP,
(ii)
The angle between the edge OC and the base PC.
Compiled and solved by Mr Mununga J
P a g e | 20
2. 2019 JULY/AUGUST EXAMS, Q10 (a)
The diagram below shows a frustum TQRS of a cone. [𝑡𝑎𝑘𝑒 𝜋 𝑎𝑠 3.142]
T
U 3cm
S
10cm
Q
V
R
8cm
Given that US= 3𝑐𝑚, 𝑈𝑉 = 10𝑐𝑚 and 𝑅𝑉 = 8𝑐𝑚, calculate its volume.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q12 (a)
The diagram below is a frustum of a rectangular pyramid with a base 14cm long
and 10cm wide. The top of the frustum is 8cm long and 4cm wide.
8cm
4cm
10cm
14cm
Given that the height of the frustum is 11.4cm, calculate its volume.
4. 2018 JULY/AUGUST EXAMS, Q6
The diagram below shows a bin in the form of a frustum with square ends of
sides 4cm and 10cm respectively. The height of the bin is 9cm.
10cm
9cm
4cm
Find the volume of the bin.
MATHEMATICS is not about numbers, equations, computations or
algorithms: it is about UNDERSTANDING.
Compiled and solved by Mr Mununga J
P a g e | 21
5. 2017 OCTOBER/NOVEMBER EXAMS, Q4 (b)
The figure below is a frustum of a cone. The base diameter and top diameter are
42cm and 14cm respectively, while the height is 20cm. (𝑇𝑎𝑘𝑒 𝜋 𝑎𝑠 3.142)
14cm
20cm
42cm
Calculate its volume.
6. 2017 JULY/AUGUST EXAMS, Q12 (a)
The figure below is a cone ABC from which BCXY remained after the small cone
AXY was cut off. [𝑇𝑎𝑘𝑒 𝜋 𝑎𝑠 3.142]
A
Y
E
X
D
12cm
15cm
C
B
Given that 𝐸𝑋 = 4𝑐𝑚, 𝐷𝐵 = 12𝑐𝑚 and 𝐷𝐸 = 15𝑐𝑚, calculate
(i)
The height AE, of the smaller cone AXY.
(ii)
The volume of XBCY, the shape that remained.
7. 2016 OCTOBER/NOVEMBER EXAMS, 9 (b & c) RESPECTIVELY
(a) The cross section of a rectangular tank measures 1.2m by 0.9m. if it contains
fuel to a depth of 10m, find the number of litres of fuel in the tank.
(1𝑚3 = 1000 𝑙𝑖𝑡𝑟𝑒𝑠).
(b) A cone has a perpendicular height of 12cm and slant height of 13cm.
calculate its total surface area. (Take 𝜋 = 3.142)
Compiled and solved by Mr Mununga J
P a g e | 22
TOPIC 10: CALCULUS
1. 2019 OCTOBER/NOVEMBER EXAMS, Q6 (b) & 10 (b) RESPECTIVELY
(a) Find the equation of the normal to the curve 𝑦 = 5𝑥 3 − 6𝑥 2 + 2𝑥 + 5 at the
point (1, 2).
3
(b) Evaluate ∫1 (3𝑥 2 + 4𝑥) 𝑑𝑥.
2. 2019 JULY/AUGUST EXAMS, Q6 (a) & 12 (b) RESPECTIVELY
(a) The gradient function of a curve is 𝑦 = 6𝑥 + 8. Find the equation of the curve
passing through the point (1, 2).
(b) Find the equation of the tangent to the curve 𝑦 = (2𝑥 + 3)3 at the point
where 𝑥 = −1.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q3
2
(a) Evaluate∫−1(2 + 𝑥 − 𝑥 2 )𝑑𝑥.
4
(b) Find the equation of the normal to the curve 𝑦 = 𝑥 + 𝑥 at the point where
𝑥 = 4.
4. 2018 JULY/AUGUST EXAMS, Q7 (b)
(a) Determine the equation of the normal to the curve 𝑦 = 2𝑥 2 − 3𝑥 − 2 that
passes through the point (3, 7).
1
(b) Evaluate∫0 (𝑥 2 − 2𝑥 − 3)𝑑𝑥.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q9 (b & c) RESPECTIVELY
(a) Find the coordinates of the points on the curve 𝑦 = 2𝑥 3 − 3𝑥 2 − 36𝑥 − 3
where the gradient is zero.
3
(b) Evaluate ∫−1(3𝑥 2 − 2𝑥)𝑑𝑥.
6. 2017 JULY/AUGUST EXAMS, Q4 (b) & 9 (b)
5
(a) Evaluate ∫2 (3𝑥 2 + 2)𝑑𝑥.
(b) Find the equation of the tangent to the curve𝑦 = 𝑥 2 − 3𝑥 − 4 at the point
where 𝑥 = 2.
Compiled and solved by Mr Mununga J
P a g e | 23
7. 2016 OCTOBER/NOVEMBER EXAMS, Q6
3
The equation of a curve is 𝑦 = 𝑥 3 − 2 𝑥 2 . Find
(a) The equation of the normal where 𝑥 = 2,
(b) The coordinates of the stationary points.
TOPIC 11: LOCI AND CONSTRUCTION
1. 2019 OCTOBER/NOVEMBER EXAMS, Q5
(a) (i) Construct triangle ABC in which 𝐴𝐵 = 8𝑐𝑚, 𝐵𝐴̂𝐶 = 110° and 𝐴𝐵̂ 𝐶 = 35°.
(ii) Measure and write the length of BC.
(b) Within the triangle ABC, construct the locus of points which are
(i)
3cm from AB,
(ii)
Equidistant from AC and BC,
(iii)
4cm from A.
(c) A point Q inside triangle ABC is greater than or equal to 3cm from AB, less
than or equal to 4cm from A and nearer to AC than BC. Indicate clearly, by
shading, the region in which Q must lie.
2. 2019 JULY/AUGUST EXAMS, Q4
(a) (i) Construct a triangle JKL in which 𝐾𝐿 = 8𝑐𝑚, 𝐾𝐽 = 6𝑐𝑚 and 𝐽𝐿 = 10𝑐𝑚.
(ii) Measure and write angle JLK.
(b) Within the triangle JKL, draw the locus of points which are
(i)
5cm from J,
(ii)
3cm from JL,
(iii)
Equidistant from JK and JL.
(c) A point Q, within triangle JKL, is such that it is greater than or equal to 5cm
from J, less than or equal to 3cm from JL and nearer to JK than to JL.
Indicate by shading the region in which Q must lie.
Compiled and solved by Mr Mununga J
P a g e | 24
3. 2018 OCTOBER/NOVEMBER, Q4
(a) (i) Construct a triangle XYZ in which XY= 9𝑐𝑚, 𝑌𝑍 = 7𝑐𝑚 and angle
XYZ= 38°.
(ii) Measure and write the length of XZ.
(b) On your diagram, within triangle XYZ, construct the locus of points which are
(i)
6cm from Y,
(ii)
Equidistant from XZ and XY.
(c) Mark clearly with the letter P, within triangle XYZ, a point which is 6cm from Y
and equidistant from XZ and XY.
(d) A point T, within triangle XYZ, is such that its distance from Y is less than or
equal to 6 cm and it is nearer XZ than XY. Indicate clearly, by shading, the
region in which T must lie.
4. 2018 JULY/AUGUST EXAMS, Q4
̂ 𝑹 = 50°.
(a) (i) Construct triangle PQR in which 𝑷𝑸 = 10𝑐𝑚, 𝑸𝑹 = 8𝑐𝑚 and 𝑷𝑸
(iii)
Measure and write the length of PR.
(b) On your diagram, within triangle PQR, construct the locus of points which are
(i)
Equidistant from P and Q,
(ii)
Equidistant from PR and PQ,
(iii)
5cm from R.
(c) A point T within triangle PQR is such that it is 5cm from R and equidistant
from P and Q. label the point T.
(d) Another point X is such that it is less than or equal to 5cm from R, nearer to Q
than P and nearer to PQ than PR. Indicate clearly, by shading, the region in
which X must lie.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q3
(a) Construct a quadrilateral ABCD in which 𝐴𝐵 = 10𝑐𝑚, angle 𝐴𝐵𝐶 = 120°,
angle 𝐵𝐴𝐷 = 60°, 𝐵𝐶 = 7𝑐𝑚 and 𝐴𝐷 = 11𝑐𝑚.
(b) Measure and write the length of CD.
(c) Within the quadrilateral ABCD, draw the locus of points which are
(i)
8cm from A,
(ii)
Equidistant from BC and CD.
Compiled and solved by Mr Mununga J
P a g e | 25
(d) A point P, within the quadrilateral ABCD, is such that it is 8cm from A and
equidistant from BC and CD. Label point P.
(e) Another point Q, within the quadrilateral ABCD, is such that it is nearer to CD
than BC and greater than or equal to 8cm from A. indicate, by shading, the
region in which Q must lie.
6. 2017 JULY/AUGUST EXAMS, Q5
(a) (i) construct triangle PQR in which PQ is 9cm, angle 𝑃𝑄𝑅 = 60° and
𝑄𝑅 = 10𝑐𝑚.
(i)
Measure and write the length of PR.
(b) On your diagram, draw the locus of points within triangle PQR which are
(i)
3cm from PQ,
(ii)
7cm from R,
(iii)
Equidistant from P and R.
(c) A point M, within triangle PQR, is such that it is nearer to R than P, less than
or equal to 7cm from R and less than or equal to 3cm from PQ. Shade the
region in which M must lie.
7. 2016 OCTOBER/NOVEMBER EXAMS, Q4
(a) (i) Construct a triangle ABC where 𝐴𝐵 = 𝐵𝐶 = 𝐶𝐴 = 7𝑐𝑚.
(ii)
Measure and write the size of CAB.
(b) Within the triangle ABC, construct the locus of points
(i)
Equidistant from AB and BC,
(ii)
4cm from B,
(iii)
3cm from AB.
(c) A point R, within triangle ABC, is such that it is nearer to BC than AB, less
than 3cm from AB and less than 4cm from B. shade the region in which R
must lie.
Compiled and solved by Mr Mununga J
P a g e | 26
8. 2016 JULY/AUGUST EXAMS, Q4
(a) Construct triangle PQR in which PQ=10cm, PR=8.5cm and QR=9cm.
̂ 𝑸.
(b) Measure and write the size of 𝑷𝑹
(c) On your diagram, draw the locus of points which are
(i)
5.5cm from P,
(ii)
Equidistant from P and R,
(iii)
Equidistant from PR and PQ.
(d) A point S inside triangle PQR is such that S is: less than or equal to 5.5cm
from P, nearer to P than to R, nearer to PR than to PQ. Indicate clearly, by
shading, the region in which S must lie
TOPIC 12: EARTH GEOMETRY
1. 2019 OCTOBER/NOVEMBER EXAMS, Q11 (a)
The points P, Q, R and T are on the surface of the earth as shown in the
diagram below. [𝑇𝑎𝑘𝑒 𝜋 𝑎𝑠 3.142 𝑎𝑛𝑑 𝑅 = 3437𝑛𝑚]
N
P
Q
90°W
65°N
45°E
R
T
55°S
S
(i)
Find the difference in longitude between the points T and R.
(ii)
Find, in nautical miles, the distance between
(a) P and Q along the latitude 65°N,
(b) P and T along the longitude 90°W.
Life is the most difficult exam. Many people fail because they try to copy
others, not realizing that everyone has a different question paper.
Compiled and solved by Mr Mununga J
P a g e | 27
2. 2019 JULY/AUGUST EXAMS, Q10 (b)
The points K, L and M are on the surface of the earth as shown in the
diagram below. [𝑇𝑎𝑘𝑒 𝜋 𝑎𝑠 3.142 𝑎𝑛𝑑 𝑅 = 6370𝑘𝑚]
N
K
L
50°N
60°E
30°W
M
45°S
S
(i) Find the difference in longitude between points K and L.
(ii) Find, in kilometres, the distance
(a) LM,
(b) KL.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q12 (b)
The points 𝐴(15°𝑁, 40°𝐸), 𝐵(35°𝑆, 70°𝐸) and𝐶(35°𝑆, 40°𝐸) are on the surface
of the earth. [𝑈𝑠𝑒 𝜋 = 3.142 𝑎𝑛𝑑 𝑅 = 6370𝑘𝑚]
(i) Calculate the distance AC in kilometres.
(ii) An aeroplane takes off from point B and flies due west on the same
latitude covering a distance of 900 km to a point Q.
(a) Calculate the difference in longitudes between B and Q.
(b) Find the position of Q.
Your level of success is determined by your level of discipline and
perseverance.
Compiled and solved by Mr Mununga J
P a g e | 28
4. 2018 JULY/AUGUST EXAMS, Q7 (a)
In the diagram below, A and B are points on latitude 60°N while C and D are
points on latitude 60°S. [𝜋 = 3.142 𝑎𝑛𝑑 𝑅 = 3437𝑛𝑚]
N
60°N
B
A
60°W
60°E
60°S
D
C
S
(i)
Calculate the distance BC along the longitude 60°E in nautical miles.
(ii)
A ship sails from C to D in 12 hours. Find its speed in knots.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q9 (b)
W, X, Y and Z are four points on the surface of the earth as shown in the
diagram below.(𝑇𝑎𝑘𝑒 𝜋 𝑎𝑠 3.142 𝑎𝑛𝑑 𝑅 = 3437𝑛𝑚)
N
W
X
80°N
105°E
15°W
Y
Z
E
30°S
S
(i)
Calculate the difference in latitude between W and Y.
(ii)
Calculate the distance in nautical miles between
(a) X and Z along the longitude 105°E,
(b) Y and Z along the circle of latitude 30°S.
6. 2017 JULY/AUGUST EXAMS, Q12 (b)
P(80°N, 10°E), Q(80°N, 70°E), R(85°S, 70°E) and S(85°S, 10°E) and four
points on the surface of the earth.
(i)
Show these points on a clearly labelled sketch of the surface of the
earth.
(ii)
Find in nautical miles
Compiled and solved by Mr Mununga J
P a g e | 29
(a) The distance QR along the longitude,
(b) The circumference of the circle of latitude85°S.
7. 2016 OCTOBER/NOVEMBER EXAMS, Q9 (a)
The points A, B, C and D are on the surface of the earth.
(𝑇𝑎𝑘𝑒 𝜋 = 3.142 𝑎𝑛𝑑 𝑅 = 3437𝑛𝑚)
N
50°N
A
B
30°E
75°W
70°S
D
C
S
(i)
Find the difference in latitude between points C and B.
(ii)
Calculate the length of the circle of latitude 50°N in nautical miles.
(iii)
Find the distance AD in nautical miles.
8. 2016 JULY/AUGUST EXAMS, Q12 (b)
In the diagram below, A(65°N, 5°E), B(65°N, 45°W) and C are three points on
the surface of the model of the earth and O is the centre of the model. The
̂ 𝑪 = 82°.[𝜋 = 3.142, 𝑅 = 3437𝑛𝑚]
point C, due south of A, is such that 𝑨𝑶
A
B
O 82°
45°W
65°N
0°
C
5°E
(i)
State the longitude of A.
(ii)
Calculate the latitude of C.
(iii)
Calculate, in nautical miles, the shortest distance
(a) Between A and C measured along the common longitude,
(b) Between A and B measured along the circle of latitude.
Compiled and solved by Mr Mununga J
P a g e | 30
TOPIC 13: TRIGONOMETRY
1. 2019 OCTOBER/NOVEMBER EXAMS, Q12 (a & b) RESPECTIVELY
(a) The diagram below shows a triangle KMN in which KM=8km, MN=10km and
̂ 𝑁 = 92°.
𝐾𝑀
N
K
10km
8km
92°
M
Calculate
(i)
KN,
(ii)
The area of triangle KMN,
(iii)
The shortest distance from M to KN.
(b) Solve the equation 2 tan 𝜃 = −3 𝑓𝑜𝑟 0° ≤ 𝜃 ≤ 180°.
2. 2019 JULY/AUGUST EXAMS, Q8 (a & b) RESPECTIVELY
(a) In triangle ABC below, AC=275km, angle BAC=125° and angle ACB=40°.
B
40°
Calculate
125°
A
C
275km
(i)
The distance BC,
(ii)
The area of triangle ABC,
(iii)
The shortest distance from A to BC.
(b) Solve the equation13 cos 𝜃 = 5 𝑓𝑜𝑟 0° ≤ 𝜃 ≤ 360°.
Dream Big. Start small. Act now. Robin Sharma
Compiled and solved by Mr Mununga J
P a g e | 31
3. 2018 OCTOBER/NOVEMBER EXAMS, Q8 (a & b) RESPECTIVELY
(a) In the diagram below, K, N, B and R are places on horizontal surface.
̂ 𝑅 = 60° and 𝐾𝑅̂ 𝑁 = 52°.
KN=80m, NB=50m, 𝐾𝑁
80 m
K
N
60°
50 m
B
52°
(i)
Calculate
R
(a) KR,
(b) The area of triangle KNB.
(ii)
Given that the area of triangle KNR is equal to 3260cm 2, calculate
the shortest distance from R to KN.
(b) Sketch the graph of 𝑦 = cos 𝜃 𝑓𝑜𝑟 0° ≤ 𝜃 ≤ 360°.
4. 2018 JULY/AUGUST EXAMS Q8
(a) Three villages A, B and C are connected by straight paths as shown in the
diagram below.
A
15km
B 79°
40°
C
Given that AB=15km, angle ABC=79° and angle ACB=40°, calculate the
(i)
Distance AC,
(ii)
Area of triangle ABC,
(iii)
Shortest distance from B to AC.
(b) Solve the equation cos 𝜃 = 0.937 𝑓𝑜𝑟 0° ≤ 𝜃 ≤ 360°.
(c) Sketch the graph of 𝑦 = sin 𝜃 𝑓𝑜𝑟 0° ≤ 𝜃 ≤ 360°.
Compiled and solved by Mr Mununga J
P a g e | 32
5. 2017 OCTOBER/NOVEMBER EXAMS, Q7 (a & b) RESPECTIVELY
(a) The diagram below shows the location of houses for a village Headman (H),
his Secretary (S) and a Trustee (T). H is 1.3km from S, T is 1.9km from H and
̂ 𝑆 = 130°
𝑇𝐻
H
130°
1.9km
1.3km
T
S
Calculate
(i)
The area of triangle THS,
(ii)
The distance TS,
(iii)
The shortest distance from H to TS.
2
(b) Find the angle between 0°and 90° which satisfies the equation cos 𝜃 = 3 .
6. 2017 JULY/AUGUST EXAMS, Q10 (a & b) RESPECTIVELY
(a) In triangle PQR below, QR=36.5m, angle PQR=36° and angle QPR=46°.
P
46°
R
Calculate
36.5m
36°
Q
(i)
PQ,
(ii)
The area of triangle PQR,
(iii)
The shortest distance from R to PQ.
(b) Solve the equation sin 𝜃 = 0.6792 𝑓𝑜𝑟 0° ≤ 𝜃 ≤ 360°.
Every pain gives a lesson and every lesson changes a person
Compiled and solved by Mr Mununga J
P a g e | 33
7. 2016 OCTOBER/NOVEMBER EXAMS, Q10 (a & b) RESPECTIVELY
(a) The diagram below shows the location of three secondary schools, namely
Kamubala (K), Belengani (B) and Pendeni (P) in a district. P is 5km from K, B
̂ 𝐵 = 110°.
is 3km from K and 𝑃𝐾
K
110°
3km
5km
B
P
Calculate
(i)
BP,
(ii)
The area of triangle BKP,
(iii)
The shortest distance from K to BP.
(b) Solve the equation tan 0.7 𝑓𝑜𝑟 0° ≤ 𝜃 ≤ 180° .
TOPIC 14: STATISTICS
1. 2019 OCTOBER/NOVEMBER EXAMS, Q8
The table below shows the expenditure of 90 farmers in a particular farming
season
Amount
0 < 𝑥 ≤ 100 100 < 𝑥 ≤ 200 200 < 𝑥 ≤ 300 300 < 𝑥 ≤ 400 400 < 𝑥 ≤ 500 500 < 𝑥 ≤ 600 600 < 𝑥 ≤ 700 700 < 𝑥 ≤ 800
(K)
No. of
5
16
17
17
14
12
7
2
Farmers
(a) Calculate the standard deviation.
(b) Answer this part of the question on a sheet of graph paper.
(i)
Using the table above, copy and complete the cumulative frequency
table below.
Amount
≤0
≤ 100 ≤ 200 ≤ 300 ≤ 400 ≤ 500 ≤ 600 ≤ 700 ≤ 800
(K)
Frequency
0
5
Compiled and solved by Mr Mununga J
21
38
55
69
P a g e | 34
(ii)
Using a scale of 2cm to represent 100 units on the horizontal axis and
2cm to represent 10 units on the vertical axis, draw a smooth
cumulative frequency curve.
(iii)
Showing your method clearly, use your graph to estimate the
interquartile range.
2. 2019 JULY/AUGUST EXAMS, Q9
(a) The table below shows the distribution of the ages of 30 football players at a
school.
Age (x) years
10
11
12
13
14
15
16
Frequency
0
2
5
7
8
6
2
Calculate the standard deviation.
(b) Answer this part of the question on a sheet of graph paper.
(i)
Using the table above, copy and complete the relative cumulative
frequency table below
Age (x) years
≤ 10
≤ 11
≤ 12
Cumulative frequency
0
2
7
0.00
0.07
0.23
Relative cumulative
Frequency
(ii)
≤ 13
14
≤ 14
≤ 15
22
28
≤ 16
30
1.00
Using a scale of 2cm to represent 1 unit on the x-axis for 10 ≤ 𝑥 ≤ 16
and a scale of 2cm to represent 0.1 units on the y-axis for
0.0 ≤ 𝑦 ≤ 1.0, draw a smooth relative cumulative frequency curve.
(iii)
Showing your method clearly, use your graph to estimate the 90 th
percentile.
Don’t talk, act. Don’t say, show. Don’t promise, prove.
Compiled and solved by Mr Mununga J
P a g e | 35
3. 2018 OCTOBER/NOVEMBER EXAMS, Q9
The frequency table below shows the distribution of marks obtained by 90
learners on a test.
Marks (x)
10 < 𝑥 ≤ 20 20 < 𝑥 ≤ 30 30 < 𝑥 ≤ 40 40 < 𝑥 ≤ 50 50 < 𝑥 ≤ 60 60 < 𝑥 ≤ 70
Frequency
2
10
15
23
30
10
(a) Calculate the standard deviation.
(b) Answer this part of the question on a sheet of graph paper.
(i)
(ii)
Copy and complete the relative cumulative frequency table below.
Marks (x)
≤ 10 ≤ 20 ≤ 30 ≤ 40 ≤ 50 ≤ 60 ≤ 70
Cumulative frequency
0
2
12
27
Relative Cumulative frequency
0
0.02
0.13
0.3
50
80
90
Using a scale of 2cm to represent 10 units on the x-axis for 0 ≤ 𝑥 ≤ 70
and 2 cm to represent 0.1 units on the y-axis for 0 ≤ 𝑦 ≤ 1, draw a
smooth relative cumulative frequency curve.
(iii)
Showing your method clearly, use your graph to estimate the 65 th
percentile.
4. 2018 JULY/AUGUST EXAMS, Q11
A farmer planted 60 fruit trees. In a certain month, the number of fruits per tree
was recorded and the results were as shown in the table below.
Fruits per tree
2
3
4
5
6
7
8
Frequency
1
5
4
6
10
16
18
(a) Calculate the standard deviation.
(b) Answer this part of the question on a sheet of graph paper.
(i)
Using the table above, copy and complete the relative cumulative
frequency table below.
Fruits per tree
2
3
4
5
6
Cumulative frequency
1
6
10
16
26 42
Relative cumulative frequency
0.02
0.1
0.17
0.27
Compiled and solved by Mr Mununga J
7
8
60
P a g e | 36
(ii)
Using a scale of 1cm to represent 1 unit on the x-axis for 0 ≤ 𝑥 ≤ 8
and 2 cm to represent 0.1 units on the y-axis for 0 ≤ 𝑦 ≤ 1, draw a
smooth relative cumulative frequency curve.
(iii)
Showing your method clearly, use your graph to estimate the 70 th
percentile.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q8
The table below shows the amount of money spent by 100 learners at school on
a particular day.
Amount in kwacha 0 < 𝑥 ≤ 5 5 < 𝑥 ≤ 10
10 < 𝑥 ≤ 15 15 < 𝑥 ≤ 20 20 < 𝑥 ≤ 25 25 < 𝑥 ≤ 30
Frequency
13
27
35
16
7
2
(a) Calculate the standard deviation.
(b) Answer this part of the question on a sheet of graph paper.
(i)
Using the table above, copy and complete the cumulative frequency
table below.
Amount in
≤0
≤5
≤ 10
≤ 15
≤ 20
≤ 25
≤ 30
Kwacha
Frequency
(ii)
0
13
40
100
Using a scale of 2cm to represent 5 units on the horizontal axis and
2cm to represent 10 units on the vertical axis, draw a smooth
cumulative frequency curve.
(iii)
Showing your method clearly, use your graph to estimate the semiinterquartile range.
6. 2017 JULY/AUGUST EXAMS, Q8
The frequency table below shows the number of copies of newspapers allocated
to 48 newspaper vendors.
Copies of newspaper
Number of vendors
25 < 𝑥 ≤ 30 30 < 𝑥 ≤ 35 35 < 𝑥 ≤ 40 40 < 𝑥 ≤ 45 45 < 𝑥 ≤ 50 50 < 𝑥 ≤ 55
5
4
(a) Calculate the standard deviation.
Compiled and solved by Mr Mununga J
7
11
12
8
55 < 𝑥 ≤ 60
1
P a g e | 37
(b) Answer this part of the question on a sheet of graph paper
(i)
Using the information in the table above, copy and complete the
cumulative frequency table below.
(ii)
Copies of newspaper
≤ 25
≤ 30
≤ 35
≤ 40
≤ 45
Number of vendors
0
5
9
16
27
≤ 50
≤ 55
≤ 60
Using a horizontal scale of 2cm to represent 10 newspapers on the xaxis for 0 ≤ 𝑥 ≤ 60 and a vertical scale of 4cm to represent 10 vendors
on the y-axis for 0 ≤ 𝑦 ≤ 50, draw a smooth cumulative frequency
curve.
(iii)
Showing your method clearly, use your graph to estimate the 50 th
percentile.
7. 2016 OCTOBER/NOVEMBER EXAMS, Q7
The ages of people living at Pamodzi village are recorded in the frequency table
below.
Ages
0 < 𝑥 ≤ 10 10 < 𝑥 ≤ 20 20 < 𝑥 ≤ 30 30 < 𝑥 ≤ 40 40 < 𝑥 ≤ 50 50 < 𝑥 ≤ 60
Number of people 7
22
28
23
15
5
(a) Calculate the standard deviation.
(b) Answer this part of the question on a sheet of graph paper.
(i)
Using the information in the table above, copy and complete the
cumulative frequency table below.
(ii)
Age
≤ 10
≤ 20
Number of people
7
29
≤ 30
≤ 40
≤ 50
≤ 60
100
Using a scale of 2cm to represent 10 units on both axes, draw a smooth
cumulative frequency curve where 0 ≤ 𝑥 ≤ 60 and 0 ≤ 𝑦 ≤ 100.
(iii)
Showing your method clearly, use your graph to estimate the semiinterquartile range.
Compiled and solved by Mr Mununga J
TOPIC 15: LINEAR PROGRAMMING
P a g e | 38
1. 2019 OCTOBER/NOVEMBER EXAMS, Q9
Kuunika wishes to build a lodge with single and double rooms. He needs to
decide the number of each room type he should build to maximize profit.
Let x represent the number of single rooms and y the number of double rooms.
(a) Write the inequalities which represent each of the following conditions:
(i)
There must be at least one single room.
(ii)
There must be at least 10 rooms altogether.
(iii)
The total number of rooms should not exceed 15.
(iv)
The number of double rooms must be at least twice the number of
single rooms.
(v)
The number of double rooms should not be more than 12.
(b) Using a scale of 2cm to 5 units on both axes, draw x and y axes for
0 ≤ 𝑥 ≤ 16 and 0 ≤ 𝑦 ≤ 16 respectively and shade the unwanted region to
indicate clearly the region where the solution of the inequalities lie.
(c) The rate for a single rooms is K600.00 and K900.00 for a double room. How
many rooms of each type should Kuunika build to maximize the income?
2. 2019 JULY/AUGUST EXAMS, Q7
Mipando makes two types of chairs for sale; dining and garden. He intends to
make at least 10 dining chairs and at least 20 garden chairs. He wants to make
not more than 80 chairs altogether. The number of garden chairs must not be
more than three times the number of dining chairs.
(a) Let x be the number of dining chairs and y the number of garden chairs. Write
four inequalities to represent the information above.
(b) Using a scale of 2cm to represent 10 chairs on each axis, draw x and y axes
for 0 ≤ 𝑥 ≤ 80 and 0 ≤ 𝑦 ≤ 80 respectively and shade the unwanted region to
indicate clearly the region where the solution of the inequalities lie.
(c) Given that the profit on the sale of a dining chair is K80.00 and profit on a
garden chair is K50.00, how many chairs of each type should Mipando make
in order to maximize the profit?
(d) What is this maximum profit?
Compiled and solved by Mr Mununga J
P a g e | 39
3. 2018 OCTOBER/NOVEMBER EXAMS, Q11
A hired bus is used to take learners and teachers on a trip. The number of
learners and teachers must not be more 60. There must be at least 35 people on
the trip. There must be at least 6 teachers on the trip. The number of teachers on
the trip should not be more than 14.
Let x be the number of learners and y the number of teachers.
(a) Write four inequalities which represent the information above.
(b) Using a scale of 2cm to represent 10 units on both axes, draw the x and y
axes for 0 ≤ 𝑥 ≤ 70 and 0 ≤ 𝑦 ≤ 70 respectively and shade the unwanted
region to indicate clearly the region where the solution of the inequalities lie.
(c) (i) if the group has 25 learner, what is the minimum number of teachers that
Must accompany them?
(ii) if 8 teachers go on this trip, what is the maximum number of learners that
can be accommodated on the bus?
(d) If T is the amount in Kwacha paid by the whole group, what is the cost per
learner if 𝑇 = 30𝑥 + 50𝑦?
4. 2018 JULY/AUGUST EXAMS, Q9
A tailor at a certain market intends to make dresses and suits for sale.
(a) Let x represent the number of dresses and y the number of suits. Write the
inequalities which represent each of the conditions below.
(i)
The number of dresses should not exceed 50.
(ii)
The number of dresses should not be less than the number of suits.
(iii)
The cost of making a dress is K140.00 and that of a suit is K210.00.
the total cost should be at least K10500.00.
(b) Using a scale of 2cm to represent 10 units on both axes, draw x and y axes
for 0 ≤ 𝑥 ≤ 60 and 0 ≤ 𝑦 ≤ 80. Shade the unwanted region to indicate clearly
the region where (x, y) must lie.
(c) (i) the profit on a dress is K160.00 and on a suit it is K270.00. Find the
number
of dresses and suits the tailor must make for maximum profit.
(ii) Calculate this maximum profit.
Compiled and solved by Mr Mununga J
P a g e | 40
5. 2017 OCTOBER/NOVEMBER EXAMS, Q11
Himakwebo orders maize and groundnuts for sale. The order price of a bag of
maize is K75.00 and that of a bag of groundnuts is K150.00. He is prepared to
spend up to K7500.00 altogether. He intends to order at least 5 bags of maize
and at least 10 bags of groundnuts. He does not want to order more than 70
bags altogether.
(a) If x and y are the number of bags of maize and groundnuts respectively, write
four inequalities which represent these conditions.
(b) Using a scale of 2cm to represent 10 bags on each axis, draw the x and y
axes for 0 ≤ 𝑥 ≤ 70 and 0 ≤ 𝑦 ≤ 70 respectively and shade the unwanted
region to show clearly the region where the solution of the inequalities lie.
(c) Given that the profit on a bag of maize is K25.00 and on a bag of groundnuts
is K50.0, how many bags of each type should he order to have maximum
profit?
(d) What is this estimate of the maximum profit?
6. 2017 JULY/AUGUST EXAMS Q11
Makwebo prepares two types of sausages, Hungarian and beef, daily for sale.
She prepares at least 40 hungarian and at least 10 beef sausages. She prepares
not more than 160 sausages altogether. The number of beef sausages prepared
are not more than the number of hungarian sausages.
(a) Given that x represents the number of hungarian sausages and y the number
of beef sausages, write four inequalities which represent these conditions.
(b) Using a scale of 2cmto represent 20 sausages on both axes, draw the x and y
axes for 0 ≤ 𝑥 ≤ 160 and 0 ≤ 𝑦 ≤ 160 respectively and shade the unwanted
region to show clearly the region where the solution of the inequalities lie.
(c) The profit on the sale of each hungarian sausages is K3.00 and on each beef
sausages is K2.00. How many of each type of sausages are required to be
prepared to make maximum profit?
(d) Calculate this maximum profit.
Compiled and solved by Mr Mununga J
P a g e | 41
7. 2016 OCTOBER/NOVEMBER EXAMS, Q11 (a)
A health Lobby Group produced a guide to encourage healthy living among the
local community. The group produced the guide in two formats: a short video and
a printed book. The group needed to decide the number of each format to
produce for sale to maximise profit.
Let x represent the number of videos produced and y the number of printed
books produced.
(i) Write the inequalities which represent each of the following conditions:
(a) The total number of copies produced should not be more than 800,
(b) The number of video copies to be at least 100,
(c) The number of printed books to be at least 200.
(ii)
Using a scale of 2cm to represent 100 copies on both axes, draw the x
and y axes for 0 ≤ 𝑥 ≤ 800 and 0 ≤ 𝑦 ≤ 800 respectively and shade the
unwanted region to indicate clearly the region where the solution of the
inequalities lie.
(iii)
The profit on the sale of each video copy is K15.00 while profit on each
printed book is K8.00. How many of each type were produced to make
maximum profit?
TOPIC 16: FUNCTIONS
1. 2019 OCTOBER/NOVEMBER EXAMS, Q10 (a)
The diagram below shows part of the graphs of 𝑦 = 𝑥 3 + 2𝑥 − 1 and 𝑦 = 10𝑥.
y
40
𝑦 = 𝑥 3 + 2𝑥 − 1
30
𝑦 = 10𝑥
20
10
-2
-1
0
-10
-20
Compiled and solved by Mr Mununga J
1
2
3
4
x
P a g e | 42
(i)
Use the graphs to solve the equations
(a) 𝑥 3 + 2𝑥 = 6,
(b) 𝑥 3 + 2𝑥 − 1 = 10𝑥.
(ii)
Calculate an estimate of
(a) The gradient of the curve at the point (2, 11),
(b) The area bounded by the curve, 𝑦 = 10𝑥, 𝑦 = 0 and 𝑥 = 2.
2. 2019 JULY/AUGUST EXAMS, Q12 (a)
The values of x and y are connected by the equation 𝑦 = 𝑥 3 − 5𝑥 + 3. Some
corresponding values of x and y are given in the table below.
x
-3
-2
-1
0
1
2
3
y
k
5
7
3
-1
1
15
(i)
Calculate the value of k.
(ii)
Using a scale of 2cm to 1 unit on the x-axis for −3 ≤ 𝑥 ≤ 3 and 2cm to
represent 5 units on the y-axis for −10 ≤ 𝑦 ≤ 20, draw the graph of
𝑦 = 𝑥 3 − 5𝑥 + 3.
(iii)
Use your graph to
(a) Solve the equation 𝑥 3 − 5𝑥 = 0,
(b) Estimate the area bounded by the curve, 𝑦 = 3 and 𝑥 = −2.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q7 (a)
The values of x and y are connected by the equation 𝑦 = 2𝑥 3 − 3𝑥 2 + 5. Some
corresponding values of x and y are given in the table below.
X
-2
-1.5
-1
-0.5 0
0.5
1
1.5
2
Y
P
-8.5
0
4
4.5
4
5
9
5
(i)
Calculate the value of p.
(ii)
Using a scale of 4cm to represent 1 unit on the x-axis for −2 ≤ 𝑥 ≤ 2 and
2cm to represent 5 units on the y-axis for −25 ≤ 𝑦 ≤ 10, draw the graph of
𝑦 = 2𝑥 3 − 3𝑥 2 + 5.
(iii)
Use your graph to solve the equation 2𝑥 3 − 3𝑥 2 + 5 = 𝑥.
(iv)
Calculate an estimate of the gradient of the curve at the point where x=1.5.
Compiled and solved by Mr Mununga J
P a g e | 43
4. 2018 JULY/AUGUST EXAMS, Q12 (b)
The diagram below shows the graph of 𝑦 = 𝑥 3 + 𝑥 2 − 12𝑥.
(i)
Use the graph to solve the equations
(a) 𝑥 3 + 𝑥 2 − 12𝑥 = 0,
(b) 𝑥 3 + 𝑥 2 − 12𝑥 = 𝑥 + 10.
(ii)
Calculate an estimate of the
(a) Gradient of the curve at the point where 𝑥 = −3,
(b) Area bounded by the curve, 𝑥 = −3, 𝑥 = −1 and 𝑦 = −10.
Compiled and solved by Mr Mununga J
P a g e | 44
5. 2017 OCTOBER/NOVEMBER EXAMS, Q10 (a)
The diagram below shows the graph of 𝑦 = 𝑥 3 + 3𝑥 2 − 𝑥 − 3.
(i)
Use the graph to find the solutions of the equations
(a) 𝑥 3 + 3𝑥 2 − 𝑥 − 3 = 0,
(b) 𝑥 3 + 3𝑥 2 − 𝑥 = 5.
(ii)
Calculate an estimate of
(a) The gradient of the curve at the point (-3, 0),
(b) The area bounded by the curve, 𝑥 = 0, 𝑦 = 0 and 𝑦 = 20.
You can change anything in your life today by changing your perceptions
and changing your actions. Tony Robbins
Compiled and solved by Mr Mununga J
P a g e | 45
6. 2017 JULY/AUGUST EXAMS, Q9 (a)
The diagram below shows the graph of 𝑦 = 𝑥 3 + 𝑥 2 − 5𝑥 + 3.
Use the graph
(i)
To calculate an estimate of the gradient of the curve at the point (2, 5).
(ii) To solve the equations
(a) 𝑥 3 + 𝑥 2 − 5𝑥 + 3 = 0,
(b) 𝑥 3 + 𝑥 2 − 5𝑥 + 3 = 5𝑥.
(iii) To calculate an estimate of the area bounded by the curve, 𝑥 = 0, 𝑦 = 0
and 𝑥 = −2.
Compiled and solved by Mr Mununga J
P a g e | 46
7. OCTOBER/NOVEMBER EXAMS, Q12 (a)
The values of x and y are connected by the equation 𝑦 = 𝑥(𝑥 − 2)(𝑥 + 2). Some
corresponding values of x and y are given in the table below.
x
-3
-2
-1
0
1
2
3
y
-15
0
3
0
-3
0
K
(i)
Calculate the value of k.
(ii)
Using a scale of 2cm to 1 unit on the x-axis for −3 ≤ 𝑥 ≤ 3 and 2cm to
represent 5 units on the y-axis for −16 ≤ 𝑦 ≤ 16. Draw the graph of
𝑦 = 𝑥(𝑥 − 2)(𝑥 + 2).
(iii)
Use your graph to solve the equations
(a) 𝑥(𝑥 − 2)(𝑥 + 2) = 0
(b) 𝑥(𝑥 − 2)(𝑥 + 2) = 𝑥 + 2.
TOPIC 17: GEOMETRIC TRANSFORMATIONS
1. 2019 OCTOBER/NOVEMBER EXAMS, Q7
The vertices of triangle ABC are A(1, 1), B(1, 3) and C(3, 3). The vertices of
triangle A1B1C1 are A1(-1, 1), B1(-3, 1) and C1(-3, 3).
(a) Using a scale of 1cm to represent 1 unit on each axis on each axis, draw the
x and y axes for −6 ≤ 𝑥 ≤ 6 and −6 ≤ 𝑦 ≤ 6. Draw and label triangles ABC
and A1B1C1.
(b) Describe fully a single transformation that maps triangle ABC onto triangle
A1B1C1.
(c) An enlargement maps triangle A2B2C2 with vertices A2(-2, -2), B2(-2, -6) and
C2(-6, -6).
(i) Draw and label triangle A2B2C2.
(ii) Find the scale factor.
2 0
) maps triangle ABC onto
0 1
(d) The transformation represented by the matrix (
triangle A3B3C3.
(i) Find the coordinates of the vertices A3, B3 and C3.
Compiled and solved by Mr Mununga J
P a g e | 47
(ii) Draw and label triangle A3B3C3.
(e) Triangle ABC is mapped onto triangle A4B4C4 with vertices A4(1, -2), B4(1, 0)
and C4(3, -6).
(i) Draw and label triangle A4B4C4.
(ii) Find the matrix representing this transformation.
2. 2019 JULY/AUGUST EXAMS, Q11
Study the diagram below and answer the questions that follow.
A
2
A3
C3
1
C
B3
B-4
1
-3
-2
-1
C2
1
0
B
2
-1
C1
-2
B2
A2
-3
-4
A1
(a) An enlargement maps triangle ABC onto triangle A1B1C1. Find
(i)
The centre of enlargement,
(ii)
The scale factor.
Compiled and solved by Mr Mununga J
P a g e | 48
(b) Triangle ABC is mapped onto triangle A2B2C2 by a single transformation.
Describe fully this transformation.
(c) Triangle ABC is mapped onto triangle A3B3C3 by a stretch. Find
(i)
The matrix which represents this transformation.
(ii)
Find the area scale factor.
1
2
(d) A transformation matrix (
0
) maps triangle ABC onto triangle A4B4C4, not
1
drawn on the diagram. Find the coordinates of A4, B4 and C4.
3. 2018 OCTOBER/NOVEMBER EXAMS, Q10
Study the diagram below and answer the questions that follow.
Compiled and solved by Mr Mununga J
P a g e | 49
(a) Triangle R is the image of triangle P under a rotation. Find the coordinates of
the centre, angle and direction of rotation.
(b) A single transformation maps triangle P onto triangle M. describe fully this
transformation.
(c) Triangle P maps onto triangle V by a stretch. Find the matrix of this
transformation.
(d) If triangle P is mapped onto triangle S by a shear represented by the matrix
1 0
), find the coordinates of triangle S.
−2 1
(
4. 2018 JULY/AUGUST EXAMS, Q10
Using a scale of 1cm to represent 1 unit on both axes, draw x and y axes for
−8 ≤ 𝑥 ≤ 12 and −6 ≤ 𝑦 ≤ 14.
(a) Draw and label triangle X with vertices (2, 4), (4, 4) and (4, 1).
(b) Triangle X is mapped onto triangle U with vertices (6, 12), (12, 12) and (12, 3)
by a single transformation.
(i)
Draw and label triangle U.
(ii)
Describe fully this transformation.
(c) A 90° clockwise rotation about the origin maps triangle X onto triangle W.
Draw and label triangle W.
(d) A shear with x-axis as the invariant line and shear factor -2 maps triangle X
onto triangle S. draw and label triangle S.
(e) Triangle X is mapped onto triangle M with vertices (4, 4), (8, 4) and (8, 1).
(i)
Draw and label M.
(ii)
Find the matrix which represents this transformation.
5. 2017 OCTOBER/NOVEMBER EXAMS, Q12
Using a scale of 1cm to represent 1 unit on each axis, draw x and y axes for
−6 ≤ 𝑥 ≤ 10 and −10 ≤ 𝑦 ≤ 8.
(a) A quadrilateral ABCD has vertices A(-5, 7), B(-4, 8), C(-3, 7) and D(-4, 4)
while its image has vertices A1(-5, -3), B1(-6, -2), C1(-5, -1) and D1(-2, -2).
(i)
Draw and label the quadrilateral ABCD and its image A 1B1C1D1
Compiled and solved by Mr Mununga J
P a g e | 50
(ii)
Describe fully the transformation which maps quadrilateral ABCD onto
quadrilateral A1B1C1D1.
−2 0
) maps the quadrilateral ABCD onto the quadrilateral
0 1
(b) The matrix (
A2B2C2D2.
(i)
Find the coordinates of the vertices of the quadrilateral A2B2C2D2.
(ii)
Draw and label the quadrilateral A2B2C2D2.
(c) The quadrilateral ABCD is mapped onto the quadrilateral A 3B3C3D3 where A3
is (4, -8), B3 is (2, -10), C3 is (0, -8) and D3 is (2, -2). Describe fully this
transformation.
6. JULY/AUGUST EXAMS, Q7
Using a scale of 1cm to represent 1 unit on each axis, draw x and y axes for
−6 ≤ 𝑥 ≤ 10 and −6 ≤ 𝑦 ≤ 12.
(a) Quadrilateral ABCD has vertices A(1, 2), B(2, 1), C(3, 2) and D(2, 3).
Quadrilateral A1B1C1D1 has vertices A1(3, 2), B1(6, 1), C1(9, 2) and D1(6, 3).
(i)
Draw and label quadrilaterals ABCD and A1B1C1D1.
(ii)
Describe fully a single transformation which maps quadrilateral ABCD
onto quadrilateral A1B1C1D1.
1
3
(b) The matrix (
0
), maps quadrilateral ABCD onto quadrilateral A2B2C2D2.
1
(i)
Find the coordinates of quadrilateral A2B2C2D2.
(ii)
Draw and label quadrilateral A2B2C2D2.
(c) Quadrilateral A3B3C3D3 has vertices A3(-2, -4), B3(-4, -2), C3(-6, -4) and
D3(-4, -6). Describe fully the transformation which maps quadrilateral ABCD
onto quadrilateral A3B3C3D3.
If you want the things you’ve never had, you’ve to do the things
you’ve never done.
Compiled and solved by Mr Mununga J
P a g e | 51
7. 2016 OCTOBER/NOVEMBER EXAMS, Q8
Study the diagram below to answer the questions that follow.
(a) An enlargement maps triangle ABC onto triangle A1B1C1. Find
(i)
The centre of enlargement,
(ii)
The scale factor.
(b) Triangle ABC is mapped onto triangle A2B2C2 by a shear. Find the matrix
which represents this transformation.
(c) Triangle ABC is mapped onto triangle A3B3C3 by a single transformation.
Describe this transformation fully.
−3 0
) maps triangle ABC onto triangle A4B4C4
0 1
(d) A transformation with matrix (
not drawn on the diagram. Find
(i)
The scale factor of this transformation,
(ii)
The coordinates of A4, B4 and C4.
End of questions, answers next
Compiled and solved by Mr Mununga J