How do you evaluate 1 − 1/3 of 24?

First find one-third of 24 which is 24 ÷ 3 = 8. Then subtract: 24 − 8 = 16.

What is a digit in a number?

A digit is any single number from 0 to 9 used to form larger numbers.

How do you solve 6x = 45?

Divide both sides by 6 to isolate x. So x = 45 ÷ 6 = 7.5.

How do you arrange fractions in descending order?

Convert fractions to decimals or use a common denominator, then arrange from largest to smallest.

How do you calculate temperature increase over time?

Multiply the increase per interval by the number of intervals, then add to the initial value.

How do you convert a decimal to a fraction?

Write the decimal over 100 or a power of 10, then simplify the fraction.

What are significant figures?

Significant figures are digits that carry meaning contributing to the precision of a number.

How do you convert between time zones?

Add or subtract the time difference between the two locations.

How do you calculate original price after discount?

Divide the discounted price by (1 minus the discount rate expressed as a decimal).

How do you divide money in a ratio?

Add all ratio parts, divide total amount by the sum, then multiply by each ratio part.

How do you convert meters to kilometers?

Divide the number of meters by 1000.

How do you find perimeter of a composite figure?

Add all outer sides, including curved parts such as arcs if present.

How do you find volume of a cylinder?

Volume = base area × height. If half full, divide the result by 2.

What does intersection of sets mean?

Intersection means elements common to both sets.

What defines a function in mapping?

Each input must correspond to exactly one output.

How do you find common multiples in sets?

Identify numbers that satisfy both conditions simultaneously.

How do you simplify algebraic expressions?

Combine like terms by adding or subtracting coefficients.

How do you factorize quadratic expressions?

Find two numbers that multiply to give the constant term and add to give the coefficient of x.

How do you simplify algebraic fractions?

Factor numerator and denominator, then cancel common factors.

How do you evaluate expressions with given values?

Substitute the value into the expression and simplify step by step.

How do you solve exponential equations?

Rewrite both sides with the same base and equate the exponents.

What is a geometric progression?

A sequence where each term is obtained by multiplying the previous term by a constant ratio.

What does inverse variation mean?

One variable decreases as the other increases such that their product is constant.

How do you solve inequalities?

Solve like equations but reverse the inequality sign when multiplying or dividing by a negative number.

How do you make a variable the subject of a formula?

Rearrange the equation so the desired variable is isolated.

How do you identify a function from a diagram?

Ensure each input maps to only one output.

How do you find composite functions?

Substitute one function into another.

How do you find a vector between two points?

Subtract coordinates of the starting point from the ending point.

How do you find midpoint of a line segment?

Average the x-coordinates and y-coordinates separately.

How do you find intersection of graphs?

Set the equations equal and solve simultaneously.

How do you solve simultaneous equations?

Use substitution or elimination methods.

What are complementary angles?

Angles that add up to 90 degrees.

What are vertically opposite angles?

Angles opposite each other when two lines intersect, and they are equal.

What is a parallelogram?

A quadrilateral with both pairs of opposite sides parallel.

How do you find missing angles in triangles?

Use the fact that the sum of angles in a triangle is 180 degrees.

How do you use similarity to find areas?

Area ratio equals the square of the scale factor.

What is a cyclic quadrilateral?

A quadrilateral with all vertices on a circle; opposite angles sum to 180 degrees.

What is reflection in transformation?

A flip of a shape across a line of symmetry.

How do bearings work?

Measured clockwise from north using three digits.

How do you add vectors?

Add corresponding components of each vector.

How do you find median from cumulative graph?

Locate halfway point on frequency axis and read corresponding value.

What is mode in statistics?

The value that appears most frequently.

How do you find probability of selecting a prime number?

Number of prime outcomes divided by total outcomes.

How do tree diagrams work in probability?

Multiply probabilities along branches and add where necessary.

0570 Mathematics 2014 Solution Paper 1

Question 1

Evaluate: 1 − 1/3 of 24

A. 7

B. 8

C. 16

D. 17

Show Answer

Answer: 17

Explanation: First calculate 1/3 of 24 = 8. Then 1 − 8 = -7? Wait carefully: the question is interpreted as 24 − (1/3 × 24). So 24 − 8 = 16 OR if written as 1 − (1/3 of 24) → 1 − 8 = -7 (not in options). Correct interpretation from exam is 24 − 1/3 of 24 = 16.

Question 2

In the number 57, 5 is called the

A. Base

B. Exponent

C. Digit

D. Index

Show Answer

Answer: Digit

Explanation: A digit is any single number (0–9) used in writing numbers.

Question 3

Given that 6x = 45, find x

A. 6

B. 7.5

C. 8

D. 10

Show Answer

Answer: 7.5

Explanation: Divide both sides by 6: x = 45 ÷ 6 = 7.5.

Question 4

Arrange the fractions in descending order

A. 3/4, 2/3, 1/2

B. 1/2, 2/3, 3/4

C. 2/3, 3/4, 1/2

D. 3/4, 1/2, 2/3

Show Answer

Answer: 3/4, 2/3, 1/2

Explanation: Convert to decimals: 3/4 = 0.75, 2/3 ≈ 0.67, 1/2 = 0.5. Largest to smallest gives correct order.

Question 5

A temperature increases by 5°C every 30 minutes. Find temperature after 1 hour if initial is 23°C

A. 28°C

B. 30°C

C. 33°C

D. 43°C

Show Answer

Answer: 33°C

Explanation: 1 hour = 2 intervals of 30 minutes. Increase = 2 × 5 = 10. Final = 23 + 10 = 33°C.

Question 6

Express 0.36 as a fraction

A. 9/25

B. 36/100

C. 18/25

D. 4/9

Show Answer

Answer: 9/25

Explanation: 0.36 = 36/100. Simplify by dividing by 4 → 9/25.

Question 7

0.678 correct to two significant figures is

A. 0.67

B. 0.68

C. 0.70

D. 0.69

Show Answer

Answer: 0.68

Explanation: First two digits: 6 and 7. Next digit is 8 → round up → 0.68.

Question 8

Cameroon time is 1 hour ahead of GMT. If it is 17:50 in Cameroon, find GMT

A. 16:50

B. 18:50

C. 15:50

D. 6:50

Show Answer

Answer: 16:50

Explanation: GMT is 1 hour behind → 17:50 − 1 hour = 16:50.

Question 9

An item sold for 1,800,000 FCFA after 10% discount. Find original price

A. 2,000,000

B. 1,980,000

C. 1,620,000

D. 2,200,000

Show Answer

Answer: 2,000,000

Explanation: Selling price = 90% of original. Original = 1,800,000 ÷ 0.9 = 2,000,000.

Question 10

240,000 FCFA shared in ratio 2:3:7. Largest share is

A. 160,000

B. 140,000

C. 120,000

D. 100,000

Show Answer

Answer: 140,000

Explanation: Total ratio = 12. Largest = 7/12 × 240,000 = 140,000.

Question 11

A car travels 12,000 m between towns. Distance in km is

A. 120

B. 12

C. 1.2

D. 0.12

Show Answer

Answer: 12

Explanation: 1 km = 1000 m → 12000 ÷ 1000 = 12 km.

Question 12

Find the perimeter of the composite figure (rectangle + semicircle)

A. 76 cm

B. 68 cm

C. 98 cm

D. 88 cm

Show Answer

Answer: 88 cm

Explanation: Perimeter = straight edges + semicircle arc. Arc = πr. Add all lengths carefully.

Question 13

A cylinder base area = 75 cm², height = 10 cm. Volume when half full

A. 750

B. 375

C. 250

D. 150

Show Answer

Answer: 375

Explanation: Volume = base × height = 75 × 10 = 750. Half = 375.

Question 14

The shaded region represents

A. P ∩ Q

B. P ∪ Q

C. P ∩ Q ∩ R

D. P ∩ Q'

Show Answer

Answer: P ∩ Q

Explanation: Overlapping region of P and Q.

Question 15

Select correct Venn diagram

Show Answer

Answer: D

Explanation: Diagram must satisfy given set conditions.

Question 16

Universal set multiples of 3 and even numbers. Find intersection

A. 6

B. 3

C. 9

D. 12

Show Answer

Answer: 6

Explanation: Common number divisible by 2 and 3.

Question 17

Simplify 2x + 3x − x

A. 4x

B. 5x

C. 6x

D. 3x

Show Answer

Answer: 4x

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

Question 18

Factorize expression

A. (x+3)(x−3)

B. (x−3)(x+1)

C. (x+1)(x+3)

D. (x−1)(x−3)

Show Answer

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

Explanation: Find factors that multiply and add correctly.

Question 19

Simplify algebraic fraction

Show Answer

Answer: B

Explanation: Factor numerator and denominator then cancel common terms.

Question 20

Evaluate expression for given x

A. 48

B. 40

C. 24

D. 28

Show Answer

Answer: 48

Explanation: Substitute value and simplify step-by-step.

Question 21

Given that 2^(x+1) = 8, find x

A. 2

B. 3

C. 4

D. 1

Show Answer

Answer: 2

Explanation: 8 = 2³. So 2^(x+1) = 2³ ⇒ x + 1 = 3 ⇒ x = 2.

Question 22

The geometric progression is

A. 1, 2, 3, 4

B. 2, 4, 8, 16

C. 1, 3, 6, 10

D. 2, 3, 5, 7

Show Answer

Answer: 2, 4, 8, 16

Explanation: A geometric progression has a constant ratio. Here ratio = 2.

Question 23

y varies inversely as x. If y = 4 when x = 2, find y when x = 4

A. 1

B. 2

C. 4

D. 8

Show Answer

Answer: 2

Explanation: y = k/x. When x=2, y=4 ⇒ k=8. When x=4 ⇒ y=8/4=2.

Question 24

Solve inequality: 5 − 2x ≥ 11

A. x ≤ -3

B. x ≥ 3

C. x ≤ 3

D. x ≥ -3

Show Answer

Answer: x ≤ -3

Explanation: 5 − 2x ≥ 11 ⇒ -2x ≥ 6 ⇒ divide by -2 (reverse sign) ⇒ x ≤ -3.

Question 25

Make y the subject of: 3x + y = 9

A. y = 9 − 3x

B. y = 3x − 9

C. y = 9 + 3x

D. y = x − 3

Show Answer

Answer: y = 9 − 3x

Explanation: Rearrange: y = 9 − 3x.

Question 26

Identify the function in the arrow diagram

Show Answer

Answer: B

Explanation: A function assigns exactly one output to each input.

Question 27

If 3x = 12, express x

A. 2

B. 3

C. 4

D. 6

Show Answer

Answer: 4

Explanation: Divide both sides by 3: x = 12 ÷ 3 = 4.

Question 28

Given f(x) = 3x − 2 and g(x) = 2x + 3, find f(g(x))

A. 6x + 7

B. 6x − 1

C. 3x + 1

D. 5x + 3

Show Answer

Answer: 6x + 7

Explanation: f(g(x)) = 3(2x+3) − 2 = 6x + 9 − 2 = 6x + 7.

Question 29

Given P = (1,2) and Q = (3,4), find PQ

A. (2,2)

B. (4,6)

C. (1,1)

D. (3,2)

Show Answer

Answer: (2,2)

Explanation: PQ = (3−1, 4−2) = (2,2).

Question 30

M is midpoint of PQ where P(2,4) and Q(6,8). Find M

A. (4,6)

B. (3,6)

C. (5,7)

D. (2,6)

Show Answer

Answer: (4,6)

Explanation: Midpoint = ((2+6)/2 , (4+8)/2) = (4,6).

Question 31

Find x-coordinate of intersection of graphs

A. 1

B. 2

C. 3

D. 4

Show Answer

Answer: 2

Explanation: Intersection occurs where equations are equal.

Question 32

Solve simultaneous equations

A. 3

B. 6

C. -2

D. 1

Show Answer

Answer: 3

Explanation: Substitute or eliminate variables.

Question 33

Two angles sum to 90°. They are

A. Complementary

B. Supplementary

C. Vertical

D. Adjacent

Show Answer

Answer: Complementary

Explanation: Complementary angles sum to 90°.

Question 34

Find angle in diagram

A. 135°

B. 90°

C. 120°

D. 60°

Show Answer

Answer: 120°

Explanation: Use straight line and vertically opposite angles.

Question 35

Figure represents

A. Parallelogram

B. Kite

C. Tetrahedron

D. Trapezium

Show Answer

Answer: Parallelogram

Explanation: Opposite sides parallel.

Question 36

Find angle x

A. 40°

B. 50°

C. 70°

D. 30°

Show Answer

Answer: 50°

Explanation: Use triangle angle sum = 180°.

Question 37

Area of larger triangle

A. 16

B. 25

C. 36

D. 20

Show Answer

Answer: 36

Explanation: Use scale factor for similar triangles.

Question 38

Find angle in cyclic quadrilateral

A. 50°

B. 90°

C. 110°

D. 120°

Show Answer

Answer: 110°

Explanation: Opposite angles sum to 180°.

Question 39

Angle in circle diagram

A. 45°

B. 60°

C. 30°

D. 90°

Show Answer

Answer: 45°

Explanation: Use angle in semicircle theorem.

Question 40

Transformation shown is

A. Rotation

B. Reflection

C. Translation

D. Enlargement

Show Answer

Answer: Reflection

Explanation: Image flipped across axis.

Question 41

In a right triangle, find sinθ

A. 3/5

B. 4/5

C. 5/3

D. 5/4

Show Answer

Answer: 3/5

Explanation: sinθ = opposite / hypotenuse.

Question 42

Find bearing of Q from P

A. 043°

B. 223°

C. 047°

D. 227°

Show Answer

Answer: 223°

Explanation: Reverse bearing = original + 180°.

Question 43

Given sin(90° − A) = cos A, find sin25°

A. cos65°

B. sin65°

C. cos25°

D. sin75°

Show Answer

Answer: cos65°

Explanation: sinθ = cos(90° − θ).

Question 44

Given vectors, find result

A. p + q

B. p − q

C. q − p

D. 2p

Show Answer

Answer: p + q

Explanation: Add corresponding components.

Question 45

In trapezium, find length

A. q − p

B. p + q

C. 2p

D. q

Show Answer

Answer: q − p

Explanation: Use parallel sides relationship.

Question 46

Find modulus of vector

A. √25

B. √29

C. √41

D. √50

Show Answer

Answer: √41

Explanation: √(x² + y²).

Question 47

From cumulative frequency graph, find median

A. 45

B. 50

C. 48

D. 60

Show Answer

Answer: 48

Explanation: Median = middle value on graph.

Question 48

From frequency table, find mode

A. 3

B. 4

C. 4.5

D. 5

Show Answer

Answer: 5

Explanation: Mode = highest frequency value.

Question 49

Probability of selecting a prime number from 1–10

A. 1/2

B. 2/5

C. 3/10

D. 4/10

Show Answer

Answer: 2/5

Explanation: Primes: 2,3,5,7 → 4 out of 10 → 4/10 = 2/5.

Question 50

Find probability from tree diagram

A. 7/15

B. 3/10

C. 7/30

D. 1/5

Show Answer

Answer: 7/30

Explanation: Multiply probabilities along branches.

0570 Mathematics 2014 Solution Paper 1

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Question 29

Question 30

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50

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