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MINISTRY OF SECONDARY EDUCATION COBIPERO DOUALA

********* P.O Box 5321-Douala-Cameroon**

Littoral Regional Delegatio n for Secondary Education School year : 2025 / 2026

********* Discipline – Knowledge - Success**

0770 Pure maths with Stats 1

DEC 2025 ADVANCED LEVEL

PRE-MOCK 1 G.C.E EXAMINATION 2025

Centre Number

Centre Name

Candidate Number

Candidate Name

Mobile phones are NOT allowed in the examination room.

MULTIPLE CHOICE QUESTION PAPER

One and half hours

INSTRUCTIONS TO CANDIDATES

Read the following instructions carefully before you start answering the questions in this paper. Make sure you have a soft HB

pencil and an eraser for this examination.

1. USE A SOFT HB PENCIL THROUGHOUT THIS EXAMINTION. 2. DO NOT OPEN THIS BOOKLET UNTIL YOU ARE TOLD TO DO SO****.

Before this examination begins:

3. Check that this question booklet is headed “0770 Pure Maths with Stats 1- Advanced level ”

4. Fill in the information required in the spaces above.
5. Fill in the information required in the spaces provided on the answer sheet using your HB pencil:

Candidate Name, Exam Session, Subject Code and Candidate Identification Number.

Take care that you do not crease or fold the answer sheet or make any marks on it other than those asked for in

these instructions_._

How to answer questions from this Examination.

6. Answer all the 50 questions in this Examination. All questions carry equal marks.
7. Non-programmable calculators are allowed.
8. Each question has four suggested answers: A, B, C and D. Decide on which answer is appropriate. Find the

number of the question on the Answer Sheet and draw a horizontal line across the letter to join the square brackets

for the answer you have chosen.

For example, if C is your correct answer, mark C as shown below:

[A] [B] [C] [D]

9. Mark only one answer for each question. If you mark more than one answer, you will score a zero for that

question. If you change your mind about an answer, erase the first mark carefully, then mark your new answer.

10. Avoid spending too much time on any one question. If you find a question difficult, move on to the next question.

You can come back to this question later.

11. Do all rough work in this booklet using the blank spaces in the question booklet. 12. At the end of the examination, the invigilator shall collect first the answer sheet and then the question booklet. DO

NOT ATTEMPT TO LEAVE THE EXAMINATION HALL WITH ANY.

SECTION A: PURE MATHEMATICS

1. The partial fraction equivalence of

4 𝑥+ 1

2 𝑥

2

+𝑥− 3

is:

A.

2

2 𝑥+ 3

1

𝑥− 1

B.

7

5 ( 2 𝑥+ 3 )

4

( 5 𝑥− 1 )

C.

2

2 𝑥+ 3

1

𝑥− 1

D.

2 𝑥

2 𝑥+ 3

1

𝑥− 1

2. There are 12 contestants in a competition, the

number of ways in which the first three places

can be filled is:

A. 220

B. 1320

C. 12

D. 132

2

in the form 𝑎 + 𝑏√ 2 ,

A. 11 − 3 √ 2

B. 11 + 6 √ 2

C. 13 + 6 √ 2

D. 8 + 6

4. The number of ways in which three books can

be selected from five books is:

A. 120

B. 20

C. 15

D. 10

5. The number of ways in which the letters of

the word MOTOMBOLOMBO can be

arranged is?

A.

12!

5! 3! 2!

B.

12!

5!

C.

11!

5! 2! 3!

D.

12!

10!

6. Given that 4

( 2 𝑥+ 1 )

(𝑥− 1 )

the value of 𝑥 is:

A. − 1

B.

− 2

3

C. 1

D.

− 3

2

7. Given that the vector i + αj + βk is

perpendicular to i + j + k and to

−3i + 2j + 3k, then

A. 𝛼 = − 6 , β = 5

B. α = − 2 , β = 1

C. α = 5 , β = − 6

D. α = 2 , β = − 1

8. lim

𝑥→ 0

3 𝑥

2

−𝑥

3

2 𝑥

2

A. 0

B. 3

C. ∞

D.

3

2

9. An equation of the line L

1

is 3 𝑥 + 4 𝑦 = 5.

Another line L

2

passes through the point

( 1 , 2 ) and is perpendicular to L 1. Then the

equation of L

2

is:

A. 4 𝑥 − 3 𝑦 = − 2

B. 3 𝑥 − 4 𝑦 = 2

C. 4 𝑥 − 3 𝑦 = 2

D. 3 𝑥 − 4 𝑦 = − 2

10. If the matrix A= (

) has no inverse,

then the value of 𝑘 is

A. 0

B. 1

C.

4

3

D. − 1

11. Given 𝑓

𝑥

2

− 1

𝑥+ 1

is continuous

at 𝑥 = − 1. The value of 𝑎 is:

A. 2

24. The 20

th

term of the sequence defined by

𝑛

cos

1

2

𝑛𝜋

𝑛

is

A. 0

B. −

1

20

C.

1

10

D.

1

20

25. Given that 𝑒

3 𝑥

𝑥

−𝑥

= 0 the real

value of 𝑥 is:

A.

1

2

ln 2

B. ln 4

C.

1

2

ln 4

D.

1

4

ln 4

26. Given that ( 2 , 5 ) is the midpoint of the line

joining the points (𝑘, 3 ) and ( 6 , 7 ), then the

value of 𝑘 is:

A. − 2

B. 2

C. 6

D. 4

27. The tangent of the acute angle between the

lines 𝑦 = 4 𝑥 − 3 and 𝑦 = 𝑥 − 5 is:

A.

5

2

B.

3

5

C.

5

3

D.

2

5

28. The arc length of a circle of radius 2cm is

4cm. The area of a sector is:

A. 2 cm

2

B. 4 cm

2

C. 4 cm

D. 8 πcm

2

29. The functions f and g are real valued functions.

Given that g(𝑥) =

𝑥− 1

𝑥+ 2

and gof(𝑥) =

7

3 𝑥− 5

, then

f(𝑥) =

A.

𝑥− 3

𝑥− 4

B.

𝑥+ 3

𝑥+ 4

C.

𝑥+ 3

𝑥− 4

D.

𝑥− 3

𝑥+ 4

30. The line segment PQ, where P is the point

( 7 , 7 ) and Q the point (− 1 , 3 ), is the diameter of a

circle. the equation of the circle is

A.

B.

C.

D. (𝑥 + 7 )(𝑥 + 1 ) + (𝑦 − 7 )(𝑦 + 3 ) = 0

31. The In the set 𝐴 = {1,2,3,4,5, }, a relation 𝑅 is

defined by 𝑅 = {(𝑥, 𝑦): 𝑥, 𝑦 𝜖 𝐴 and 𝑥 < 𝑦 }, Then

R is

A. Reflexive

B. Transitive

C. Symmetric

D. Anti-symmetric

32. The quadratic equation whose one root is 3 + √ 2

A. 𝑥

2

B. 𝑥

2

C. 𝑥

2

D. 𝑥

2

33. Suppose that log 2 = a and log 5 = b. Using the

properties of logarithms to write log 20 in terms

of 𝑎 and 𝑏 is Maps to the null vector

A. 2a + b

B. 4b

C. 2a + 2b

D. a + b

𝑛

𝑟= 1

A. 𝑛(𝑛 − 2 )

B.

1

2

C. 𝑛(𝑛 + 1 ) − 3

D. 𝑛(𝑛 − 5 )

35. Given Given that 6 and 150 are two terms of a

geometric progression, separated by only one

term, this term is

A. 900

B. 144

C. 30

D. 25

36. The value of the constant 𝜆, for which the plane

𝜆𝑥 − 3 𝑦 + 4 𝑧 = 5 and the line

𝑟 = i − 2j − 3k + t(2i + 6j + 3k) are parallel is

A. 3

B. 5

C. 6

D. 9

37. The periodic function f of period 4 is defined as

follows:

2

The value of f( 11 ) is

A. 17

B. − 2

C. 1

D. − 3

38. The image of the line 𝑦 = 2 𝑥 under the

transformation matrix 𝑀 = (

) is

A. 𝑥 + 2 𝑦 = 0

B. 𝑥 − 2 𝑦 = 0

C. 2 𝑥 + 𝑦 = 0

D. 𝑥 + 2 𝑦 = 0

39. The invariant line under the transformation N,

where N = (

A. 2 𝑥 − 𝑦 = 0

B. 2 𝑥 − 𝑦 = 0

C. 3 𝑥 + 𝑦 = 0

D. 2 𝑥 + 2 𝑦 = 0

40. Let ℎ(𝑥) = 3 𝑥 + 1 and g(𝑥) = √

𝑥 − 1 , then ℎ ∘

g( 5 ) =

A. 0

B. √ 15

C. 4

D. 7

SECTION B : STATISTICS

41. Given that the events A and B are mutually

exclusive and that P(A) = 0. 50 and P(B) = 0. 30 ,

P(A ∪ B ) =

A. 0. 80

B. 0. 65

C. 0. 15

D. 0. 95

42. The mean of a set of number is 15. If 3 is added

to each of the number, the mean of the resulting

set is

A. 18

B. 45

C. 15

D. 5

43. Given that A and B are two independent events

such that P(A) =

1

3

and P(B) =

3

4

. Then

P(A ∩ B

′

A.

1

12

B.

7

12

C.

1

3

D.

1

4

44. A set of bivariate data has the following summary

statistics: 𝑛 = 7 ,

2

2

𝑥𝑦 = 119. 36. the

covariance of this data is

A. 3. 8514

B. 3. 1429

C. 4. 8200

D. 3. 5814

𝑋 1 2 3 4

𝑌 1 4 9 16

The Kendall’s coefficient of rank correlation for the

above data is

A. 𝑟

𝑘

B. 𝑟

𝑘

1

2

C. 𝑟

𝑘

7

6

D. 𝑟

𝑘

46. The grouped distribution of the heights, 𝑥cm of

some young plants is as shown in the table below