GRADE 10 MIDYEAR EXAMINATIONS
Mathematics
4024/2
Paper 2
TERM TWO (2) - JUNE 2025
Time: 1 hours 20 minutes
Instructionsto
toCandidates
Candidates
Instructions
1
Write your name and Class on the Answer Booklet.
2
Write your answers and working in the Answer Booklet provided.
4
Omission of essential working will result in loss of marks.
Information for Candidates
1.
The number of marks is given in brackets [ ] at the end of each question or
part question.
2.
The total marks for this paper is 40.
3.
If the degree of accuracy is not specified in the question, and if the answer is
not exact, give the answer to three significant figures. Give answers in
degrees to one decimal place.
©RPS/G10/CAT/2025
This question paper consists of 3 printed pages
2|Page
Answer all the questions in this paper.
1.
𝑦−1
(a)
Simplify
(b)
Given that the determinant of matrix Q = (
𝑥𝑦 3 −𝑥𝑦
.
[2]
2𝑏 − 1 4
) is 15,
−3𝑏
−5
Find the
2.
(a)
(i)
the value of b,
[2]
(ii)
inverse of matrix Q.
[2]
Some students were interviewed to find out which of the following three
sports they liked: Football, boxing and volleyball. 70% of the students liked
football, 60% boxing and 45% volleyball, 45% liked football and boxing, 15%
boxing and volleyball, 25% football and volleyball and 5% liked all three
sports.
3
(i)
Draw a Venn diagram to illustrate this information.
(ii)
Use your diagram to find the percentage of students who liked
[2]
(a)
football or boxing but not volleyball,
[1]
(b)
exactly two sports,
[1]
(c)
none of the three sports.
[1]
𝑥 2 −𝑦 2
.
(a)
Simplify
(b)
Given that matrix K =
3𝑥 + 3𝑦
[2]
5 −3
,
4 −2
find
(i)
the determinant of K
[2]
(ii) the inverse of matrix K.
[2]
(c) Simplify
𝑎2 𝑥 2 −𝑏2 𝑦 2
𝑎𝑥+𝑏𝑦
.
[2]
3|Page
3. (a)
Express as
2
3𝑚−2
3𝑑 2 −27
−
1
2𝑚−3
as a single fraction in its lowest terms.
[3]
(b)
Simplify
.
[2]
(c)
Factorise completely 3𝑥 3 − 27𝑥.
[2]
𝑑+3
(d) The Universal set E ={0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, set ={Prime numbers}
and set B = {3, 6, 9}.
List A ∪ 𝐵 ′
[1]
_____________________________________________________________________
c
2 −1 0 1
9
4. (a)
Given that (
) ( ) = ( ), find all the possible values of 𝑐 and 𝑑.
0 2 𝑑 𝑑
11
[2]
1 𝑥
(b)
The matrix A= (
),
−1 2
(i)
Given that the determinant of A is 5, calculate the value of 𝑥,
[2]
−1
(ii)
Write down A
[2]
5. (a)
(b)
Factorize completely 𝑥 2 + 3m + m𝑥 + 3𝑥.
Given that B = (
𝑥 − 10 −6
). For what values of 𝑥 would the matrix B
4
𝑥+1
have no inverse?
(c)
Simplify
(d) Solve
[2]
[2]
16m4 n5
8m3 n5
m n
m6 n 7
÷
2 4
.
[2]
[2]