0570 Mathematics 2025 Solution Paper 1

GCE O Level Mahthematics P1 Solution June 2025

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Mathematics 1

0570

GENERAL CERTIFICATE OF EDUCATION BOARD

General Certificate of Education Examination

JUNE  2025 ORDINARY LEVEL

Centre Number
Centre Name	GCE Panel
Candidate Identification Number
Candidate Name

Source: Cameroon GCE Board | Compiled by GCE Panel

Question 1

The value of the digit 7 in the number 5.074 is

A. 70

B. 7

C. 5.07

D. 0.07

Show Answer

Answer: 0.07

Explanation: The 7 is in the hundredths place → value = 0.07.

Question 2

The Highest Common Factor (HCF) of x³, x², x is

A. x

B. x²

C. x³

D. x⁰

Show Answer

Answer: x

Explanation: HCF takes the smallest power → x¹.

Question 3

Arranging the decimals 0.33, 0.42, 0.25 in ascending order gives

A. 0.25, 0.33, 0.42

B. 0.42, 0.33, 0.25

C. 0.25, 0.42, 0.33

D. 0.33, 0.42, 0.25

Show Answer

Answer: 0.25, 0.33, 0.42

Explanation: Arrange from smallest to largest.

Question 4

The number line that represents the set T = {x : 0 ≤ x ≤ 5} is

A. Open ends

B. Closed at both ends

C. Half open

D. Only 0 included

Show Answer

Answer: Closed at both ends

Explanation: ≤ includes endpoints.

Question 5

The number −5 belongs to the set

A. Natural numbers

B. Rational numbers

C. Irrational numbers

D. Integers

Show Answer

Answer: Integers

Explanation: −5 is a negative integer.

Question 6

The fraction “two and one fifth” in figures gives

A. 2 1/5

B. 2/5

C. 1 2/5

D. 2 2/5

Show Answer

Answer: 2 1/5

Explanation: Two wholes plus one-fifth.

Question 7

The number 234.5 × 10³ written in standard form is

A. 2.345 × 10⁴

B. 2.345 × 10⁵

C. 2.345 × 10²

D. 2.345 × 10³

Show Answer

Answer: 2.345 × 10⁵

Explanation: Move decimal 2 places left → increase power to 10⁵.

Question 8

The number 17.561 correct to the nearest whole number is

A. 18

B. 16

C. 17

D. 17.60

Show Answer

Answer: 18

Explanation: Since 0.561 ≥ 0.5, round up.

Question 9

In a class of 105 students, there are 60 girls. The ratio of boys to girls is

A. 4:3

B. 7:4

C. 3:4

D. 4:7

Show Answer

Answer: 3:4

Explanation: Boys = 45 → 45:60 simplifies to 3:4.

Question 10

The rate at which 2,000,000 FCFA is invested for 2 years to yield interest of 200,000 FCFA is

A. 2%

B. 4%

C. 10%

D. 5%

Show Answer

Answer: 5%

Explanation: Using I = PRT → R = 200000 / (2000000 × 2) = 5%.

Question 11

An empty set is represented as

A. {∅}

B. { }

C. {0}

D. 0

Show Answer

Answer: { }

Explanation: An empty set has no elements.

Question 12

Given the set M = {prime factors of 25}, M is

A. {1,5,25}

B. {5,25}

C. {5}

D. {1,5,10,25}

Show Answer

Answer: {5}

Explanation: The only prime factor of 25 is 5.

Question 13

In set notation, the number of elements in P and not in Q is

A. n(P ∩ Q)

B. n(P ∪ Q)

C. n(P ∩ Q′)

D. n(P ∩ Q)

Show Answer

Answer: n(P ∩ Q′)

Explanation: Elements in P but not in Q → intersection with complement of Q.

Question 14

If p: John is a Cameroonian and q: John is bilingual, the statement “If John is bilingual then he is Cameroonian” is

A. p → q

B. q → p

C. p ↔ q

D. q → ¬p

Show Answer

Answer: q → p

Explanation: “If bilingual then Cameroonian” corresponds to q → p.

Question 15

A mapping for which maps to 2x + 1 is called

A. one-one

B. many-one

C. many-many

D. one-many

Show Answer

Answer: one-one

Explanation: Each input produces a unique output.

Question 16

Given f(x) = 3 − 2x, then f(-1) gives

A. 5

B. 1

C. -1

D. 6

Show Answer

Answer: 5

Explanation: f(-1) = 3 − 2(-1) = 3 + 2 = 5.

Question 17

Given f(x) = x + 3 and g(x) = x², find g(f(x))

A. (x + 3)²

B. x² + 3

C. x² + 6

D. 6x

Show Answer

Answer: (x + 3)²

Explanation: Substitute f(x) into g(x): g(f(x)) = (x + 3)².

Question 18

The point at which two lines meet is called an

A. angle

B. intercept

C. edge

D. origin

Show Answer

Answer: angle

Explanation: Two lines intersect to form an angle.

Question 19

Given the interior angle of a polygon is 76°, its exterior angle is

A. 104°

B. 14°

C. 76°

D. 38°

Show Answer

Answer: 104°

Explanation: Interior + exterior = 180° → 180 − 76 = 104°.

Question 20

A regular solid with 11 nets is a

A. square

B. cylinder

C. cuboid

D. cube

Show Answer

Answer: cube

Explanation: A cube has 11 distinct nets.

Question 21

In a construction, PQ is a perpendicular bisector of RS. The value of angle PTS is

A. 180°

B. 60°

C. 90°

D. 45°

Show Answer

Answer: 90°

Explanation: A perpendicular bisector forms a right angle (90°).

Question 22

Given parallel lines, find angle a

A. 125°

B. 85°

C. 95°

D. 175°

Show Answer

Answer: 95°

Explanation: Use alternate or corresponding angle rules in parallel lines.

Question 23

The circumference of a circle in terms of π is

A. 3π cm

B. 6π cm

C. 18π cm

D. 9π cm

Show Answer

Answer: 6π cm

Explanation: Circumference = 2πr → here r = 3 → 2π × 3 = 6π.

Question 24

The area of a rectangle 9 cm by 3 cm is

A. 12 cm²

B. 24 cm²

C. 54 cm²

D. 27 cm²

Show Answer

Answer: 27 cm²

Explanation: Area = length × width = 9 × 3 = 27.

Question 25

The volume of a cone with radius 3 cm and height 7 cm (π = 22/7) is

A. 66 cm³

B. 198 cm³

C. 22 cm³

D. 44 cm³

Show Answer

Answer: 66 cm³

Explanation: Volume = (1/3)πr²h = (1/3) × (22/7) × 9 × 7 = 66.

Question 26

The perimeter of a rectangle of length 8 cm and width 5 cm is

A. 13 cm

B. 26 cm

C. 40 cm

D. 16 cm

Show Answer

Answer: 26 cm

Explanation: Perimeter = 2(l + w) = 2(8 + 5) = 26.

Question 27

In a right-angled triangle with hypotenuse 13 cm and one side 5 cm, find the other side

A. 8 cm

B. 12 cm

C. 10 cm

D. 6 cm

Show Answer

Answer: 12 cm

Explanation: By Pythagoras: x² + 5² = 13² → x² = 144 → x = 12.

Question 28

The volume of a cylinder of radius 3 cm and height 7 cm is (π = 22/7)

A. 198 cm³

B. 66 cm³

C. 154 cm³

D. 99 cm³

Show Answer

Answer: 198 cm³

Explanation: Volume = πr²h = (22/7) × 9 × 7 = 198.

Question 29

The gradient of the line joining (1,2) and (3,6) is

A. 1

B. 2

C. 3

D. 4

Show Answer

Answer: 2

Explanation: Gradient = (6 − 2) / (3 − 1) = 4/2 = 2.

Question 30

The y-intercept of the line y = 3x − 5 is

A. 3

B. -5

C. 5

D. -3

Show Answer

Answer: -5

Explanation: At x = 0 → y = -5.

Question 31

Solve: 2x + 5 = 13

A. 4

B. 5

C. 3

D. 6

Show Answer

Answer: 4

Explanation: 2x = 8 → x = 4.

Question 32

Simplify: (x + 2)(x + 3)

A. x² + 5x + 6

B. x² + 6x + 5

C. x² + x + 6

D. x² + 5x

Show Answer

Answer: x² + 5x + 6

Explanation: Expand → x² + 3x + 2x + 6.

Question 33

Factorize: x² − 9

A. (x − 3)(x + 3)

B. (x − 9)(x + 1)

C. (x − 1)(x + 9)

D. x(x − 9)

Show Answer

Answer: (x − 3)(x + 3)

Explanation: Difference of squares.

Question 34

Solve: x² = 49

A. 7

B. -7

C. ±7

D. 49

Show Answer

Answer: ±7

Explanation: Square root gives two solutions.

Question 35

Simplify: 3x + 2x − x

A. 4x

B. 6x

C. 5x

D. x

Show Answer

Answer: 4x

Explanation: Combine like terms: 3x + 2x − x = 4x.

Question 36

The next term in the sequence 2, 4, 8, 16, ... is

A. 18

B. 24

C. 32

D. 30

Show Answer

Answer: 32

Explanation: Each term is multiplied by 2 → 16 × 2 = 32.

Question 37

The mean of 2, 4, 6, 8 is

A. 4

B. 5

C. 6

D. 7

Show Answer

Answer: 5

Explanation: Mean = (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4 = 5.

Question 38

The median of 1, 3, 5, 7, 9 is

A. 3

B. 5

C. 7

D. 9

Show Answer

Answer: 5

Explanation: The middle value in the ordered set is 5.

Question 39

The mode of 2, 3, 3, 5, 6 is

A. 2

B. 3

C. 5

D. 6

Show Answer

Answer: 3

Explanation: The number 3 appears most frequently.

Question 40

The probability of getting a head when tossing a fair coin is

A. 0

B. 1

C. 1/2

D. 2

Show Answer

Answer: 1/2

Explanation: One favorable outcome out of two equally likely outcomes.

Question 41

The probability of rolling a 3 on a fair die is

A. 1/3

B. 1/6

C. 1/2

D. 1/4

Show Answer

Answer: 1/6

Explanation: One favorable outcome out of six possible outcomes.

Question 42

If P(A) = 1/4, then P(not A) is

A. 3/4

B. 1/2

C. 1/4

D. 4/1

Show Answer

Answer: 3/4

Explanation: Complement rule → 1 − 1/4 = 3/4.

Question 43

The magnitude of vector (3,4) is

A. 5

B. 7

C. 4

D. 3

Show Answer

Answer: 5

Explanation: √(3² + 4²) = √25 = 5.

Question 44

The direction of vector (1,1) is

A. 45°

B. 90°

C. 180°

D. 270°

Show Answer

Answer: 45°

Explanation: Equal horizontal and vertical components → 45°.

Question 45

The order of a matrix with 2 rows and 3 columns is

A. 3 × 2

B. 2 × 3

C. 2 × 2

D. 3 × 3

Show Answer

Answer: 2 × 3

Explanation: Order = rows × columns.

Question 46

The transpose of a matrix is obtained by

A. Multiplying rows

B. Swapping rows and columns

C. Adding rows

D. Dividing columns

Show Answer

Answer: Swapping rows and columns

Explanation: Rows become columns and vice versa.

Question 47

The range of 4, 6, 9, 3, 10 is

A. 6

B. 7

C. 10

D. 13

Show Answer

Answer: 7

Explanation: Range = highest − lowest = 10 − 3 = 7.

Question 48

The median of 2, 5, 7, 9, 11 is

A. 5

B. 7

C. 9

D. 11

Show Answer

Answer: 7

Explanation: Middle value in ordered data.

Question 49

The mode of 1, 2, 2, 3, 4 is

A. 1

B. 2

C. 3

D. 4

Show Answer

Answer: 2

Explanation: Most frequent value is 2.

Question 50

The probability of not getting a head when tossing a coin is

A. 1

B. 0

C. 1/2

D. 2

Show Answer

Answer: 1/2

Explanation: Complement of getting a head → 1 − 1/2 = 1/2.