0570 Mathematics Paper 1 June 2024 Questions & Answers + Solutions (GCE O Level)

0570 Mathematics Paper 1 June 2024 Questions and Answers

Practice Cameroon GCE O Level Mathematics (0570) Paper 1 June 2024 with complete answers and detailed step-by-step explanations. This page helps students prepare effectively for the GCE examination.

Topics Covered

• Number and Standard Form
• Algebra and Functions
• Geometry and Trigonometry
• Statistics and Probability

Question 1

Given that 36 ÷ 9 = 4, 4 is known as the

• A. Remainder
• B. Divisor
• C. Quotient
• D. Dividend

Answer: Quotient

Explanation: In division, Dividend ÷ Divisor = Quotient. Therefore 4 is the quotient.

Question 2

The next prime number greater than 23 is

• A. 31
• B. 25
• C. 27
• D. 29

Answer: 29

Explanation: A prime number has only two factors. 29 is the next such number.

Question 3

The absolute value of -1 - 9 is

• A. -10
• B. 10
• C. -8
• D. 8

Answer: 10

Explanation: -1 - 9 = -10 and the absolute value is 10.

Question 4

Converting 0.15 to a fraction in simplest form gives

• A. 3/20
• B. 15/100
• C. 3/100
• D. 15/20

Answer: 3/20

Explanation: 0.15 = 15/100 = 3/20 after simplification.

Question 5

Expressing 0.0597 in standard form gives

• A. 5.97 × 10²
• B. 5.97 × 10⁻²
• C. 6.0 × 10⁻²
• D. 6.0 × 10²

Answer: 5.97 × 10⁻²

Explanation: Move decimal 2 places → multiply by 10⁻².

Question 6

The number of significant figures in 14.501 is

• A. 5
• B. 2
• C. 4
• D. 3

Answer: 5

Explanation: All digits are significant.

Question 7

Mary went to bed at 11:20 pm and woke after 2 hours. What time?

• A. 13:20 pm
• B. 1:20 pm
• C. 1:20
• D. 13:20

Answer: 1:20

Explanation: 11:20 pm + 2 hours = 1:20 am.

Question 8

An article sold at 10% loss for 7200 FCFA. Find cost price.

• A. 7,920
• B. 6,480
• C. 8,800
• D. 8,000

Answer: 8,000

Explanation: SP = 90% of CP → CP = 7200 ÷ 0.9 = 8000.

Question 9

Six textbooks cost 30,000 FCFA. Cost of three?

• A. 5,000
• B. 15,000
• C. 90,000
• D. 25,000

Answer: 15,000

Explanation: Half of 6 → half of 30,000.

Question 10

Map scale 1:50,000. 4 cm represents

• A. 2 km
• B. 20 km
• C. 2.5 km
• D. 25 km

Answer: 2 km

Explanation: 4 × 50,000 = 200,000 cm = 2 km.

Question 11

Given A = {1,2,3,4} and B = {2,4,6,8}. The sets A and B are

• A. Equal sets
• B. Power sets
• C. Equivalent sets
• D. Subsets

Answer: Equivalent sets

Explanation: Equivalent sets have the same number of elements. Both sets contain 4 elements.

Question 12

If P and Q are disjoint sets then

• A. P ∪ Q = Ø
• B. n(P ∩ Q) = 0
• C. P ∩ Q = Ø
• D. P = Q

Answer: n(P ∩ Q) = 0

Explanation: Disjoint sets have no common elements, so their intersection contains zero elements.

Question 13

The shaded region in the diagram represents

• A. A ∪ B
• B. (A ∩ B)'
• C. (A ∪ B)'
• D. A' ∪ B'

Answer: (A ∪ B)'

Explanation: The shaded region lies outside both sets A and B, which is the complement of their union.

Question 14

The negation of “Some students will pass the examination” is

• A. No student will pass the examination
• B. No student will not pass the examination
• C. All students will not pass the examination
• D. All students will pass the examination

Answer: No student will pass the examination

Explanation: The negation of “some” is “none”.

Question 15

The range of the relation in the diagram is

• A. {2,5}
• B. {1,2,3,4,5}
• C. {a,b,c}
• D. {1,3,4}

Answer: {1,3,4}

Explanation: The range consists of all output values that have arrows pointing to them in the mapping diagram.

Question 16

If f(x) = 1 − x, find f(-3)

• A. -7
• B. 7
• C. -5
• D. 5

Answer: 4

Explanation: f(-3) = 1 - (-3) = 1 + 3 = 4.

Question 17

If A = {3,4} and B = {x,y}, then A × B is

• A. {(3,x),(4,y)}
• B. (3x,4y)
• C. {(3,x),(3,y),(4,x),(4,y)}
• D. (3,x),(3,y),(4,x),(4,y)

Answer: {(3,x),(3,y),(4,x),(4,y)}

Explanation: The Cartesian product includes all possible ordered pairs between elements of A and B.

Question 18

If f(x) = 3x − 2 then f⁻¹(x) is

• A. (x+2)/3
• B. (x-2)/3
• C. (x+3)/2
• D. (x-3)/2

Answer: (x+2)/3

Explanation: Replace f(x) with y, swap x and y, and solve → inverse = (x+2)/3.

Question 19

A polygon with nine sides is called

• A. Octagon
• B. Decagon
• C. Nonagon
• D. Heptagon

Answer: Nonagon

Explanation: A polygon with 9 sides is called a nonagon.

Question 20

The sum of the interior angles of a triangle is

• A. 90°
• B. 270°
• C. 360°
• D. 180°

Answer: 180°

Explanation: The sum of interior angles in any triangle is always 180°.

Question 21

The number of lines of symmetry in a rhombus is

• A. 8
• B. 4
• C. 1
• D. 2

Answer: 2

Explanation: A rhombus has two lines of symmetry along its diagonals.

Question 22

In the circle shown, find θ

• A. 35°
• B. 70°
• C. 55°
• D. 20°

Answer: 70°

Explanation: Using circle theorems, the angle at the center is twice the angle at the circumference.

Question 23

The net shown represents

• A. a rectangle
• B. a cylinder
• C. a square
• D. an open cylinder

Answer: a cylinder

Explanation: The rectangle forms the curved surface and circles form the ends → cylinder.

Question 24

The number of edges in the rectangular pyramid shown is

• A. 5
• B. 4
• C. 8
• D. 9

Answer: 8

Explanation: 4 edges on base + 4 edges to apex = 8.

Question 25

The shaded region in the circle is called a

• A. Segment
• B. Sector
• C. Chord
• D. Secant

Answer: Sector

Explanation: A sector is formed by two radii and the arc between them.

Question 26

The perimeter of a rectangle of length x and width y is

• A. 2xy
• B. x+y
• C. xy
• D. 2(x+y)

Answer: 2(x+y)

Explanation: Perimeter = 2(length + width).

Question 27

In the triangle shown find x

• A. 8
• B. 4
• C. 2
• D. 18

Answer: 8

Explanation: Using Pythagoras: x² = 10² − 6² = 64 → x = 8.

Question 28

The volume of a cone with radius 6 cm and height 10 cm is

• A. 60π
• B. 360π
• C. 120π
• D. 180π

Answer: 120π

Explanation: Volume = (1/3)πr²h = (1/3) × π × 36 × 10 = 120π.

Question 29

The y-intercept of y = 2x + 4 is

• A. -4
• B. 2
• C. -2
• D. 4

Answer: 4

Explanation: At x = 0, y = 4.

Question 30

The gradient of 3y = 6x − 3 is

• A. -1
• B. 6
• C. -2
• D. 2

Answer: 2

Explanation: Divide by 3 → y = 2x − 1, gradient = 2.

Question 31

The equation of the line shown in the figure is

• A. y = 4
• B. x = 4
• C. y = 4x
• D. 4y = x

Answer: y = 4

Explanation: A horizontal line has equation y = constant.

Question 32

Subtracting (2 + b) from (2a + b) gives

• A. 2 − 2a
• B. 2a + 2
• C. 2a − 2
• D. 2a + 2b − 2

Answer: 2a − 2

Explanation: (2a + b) − (2 + b) = 2a + b − 2 − b = 2a − 2.

Question 33

Find the value of x² − y when x = 3 and y = 2

• A. 1
• B. 7
• C. 11
• D. 4

Answer: 7

Explanation: 3² − 2 = 9 − 2 = 7.

Question 34

Solve the inequality 7 − 2x ≤ 19

• A. x ≥ -6
• B. x ≤ -6
• C. x ≤ 6
• D. x ≥ 6

Answer: x ≥ -6

Explanation: 7 − 2x ≤ 19 → -2x ≤ 12 → x ≥ -6 (inequality reverses when dividing by negative).

Question 35

Factorize x² + 4x + 3

• A. (x + 4)(x + 3)
• B. (x + 1)(x − 3)
• C. (x − 1)(x + 4)
• D. (x + 1)(x + 3)

Answer: (x + 1)(x + 3)

Explanation: Factors of 3 that add to 4 are 1 and 3.

Question 36

Simplify 2⁻³

• A. -1/8
• B. 1/8
• C. 1/6
• D. -1/6

Answer: 1/8

Explanation: Negative exponent means reciprocal → 2⁻³ = 1/2³ = 1/8.

Question 37

The next term in the sequence −3, 1, 5, ... is

• A. 11
• B. 14
• C. 9
• D. 10

Answer: 9

Explanation: Common difference = +4 → next term = 5 + 4 = 9.

Question 38

The number of even nodes in the network is

• A. 3
• B. 2
• C. 5
• D. 7

Answer: 5

Explanation: Even nodes are vertices with even number of edges connected to them.

Question 39

The relationship between sinθ, cosθ and tanθ is

• A. tanθ = cosθ / sinθ
• B. tanθ = sinθ / cosθ
• C. tanθ = sinθ + cosθ
• D. tanθ = sinθ − cosθ

Answer: tanθ = sinθ / cosθ

Explanation: By definition, tanθ = sinθ ÷ cosθ.

Question 40

In the right-angled triangle shown find n

• A. 14
• B. 6
• C. 8
• D. 10

Answer: 10

Explanation: Using Pythagoras or trigonometry, the correct value is 10.

Question 41

The bearing of R from S is

• A. 026°
• B. 154°
• C. 206°
• D. 116°

Answer: 206°

Explanation: Bearings are measured clockwise from North.

Question 42

Given vectors r = [-3,6] and p = [1,-1], find r + p

• A. [2,5]
• B. [4,5]
• C. [-2,5]
• D. [-4,5]

Answer: [-2,5]

Explanation: Add components: (-3+1, 6-1) = (-2,5).

Question 43

If OP = −4i + 3j then |OP| is

• A. 5
• B. 7
• C. 1
• D. 25

Answer: 5

Explanation: Magnitude = √((-4)² + 3²) = √25 = 5.

Question 44

The direction of the vector −3i − 3j is

• A. 315°
• B. 135°
• C. 45°
• D. 225°

Answer: 225°

Explanation: Vector lies in the third quadrant → 225°.

Question 45

The order of the matrix (-1 0 3) is

• A. 3 × 1
• B. 1 × 3
• C. 2 × 1
• D. 2 × 3

Answer: 1 × 3

Explanation: One row and three columns.

Question 46

Find the transpose of the matrix shown

• A. A
• B. B
• C. C
• D. D

Answer: A

Explanation: Transpose swaps rows and columns.

Question 47

Find the range of the distribution 2,4,2,6,3,7,-1

• A. 2
• B. 7
• C. 8
• D. 23

Answer: 8

Explanation: Range = max − min = 7 − (−1) = 8.

Question 48

The median of 7,3,1,1,4,7,0 is

• A. 7
• B. 1
• C. 0
• D. 3

Answer: 3

Explanation: Sorted data → middle value is 3.

Question 49

The mode of 8,9,6,8,15,8,11,7 is

• A. 8
• B. 9
• C. 6
• D. 15

Answer: 8

Explanation: 8 appears most frequently.

Question 50

If the probability that Susan goes to the farm is 2/5, the probability that she does NOT go is

• A. 3/5
• B. 6/25
• C. 2/5
• D. 1/5

Answer: 3/5

Explanation: P(not going) = 1 − 2/5 = 3/5.

0570 Mathematics Paper 1 June 2024 Questions & Answers

Practice all questions with answers and explanations. Click “Show Answer”.

Question 1: What is 36 ÷ 9?

• Remainder
• Divisor
• Quotient
• Dividend

Answer: Quotient

Explanation: 36 ÷ 9 = 4, so 4 is the quotient.