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CIE iGCSE Mathematics Paper 1 Prediction

CIE iGCSE Mathematics Paper 1 Prediction - 2025

CIE iGCSE Prediction Papers - All Subjects

CIE iGCSE Mathematics Paper 1 Prediction – 2025

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Question 1: Distance Calculation and Number Representation

a
Kim takes part in a race that covers a total distance of 20,000 m. She cycles 17,875 m and runs the remaining distance. Work out the distance Kim runs.
▶️Answer/Explanation

Correct answer: 2,125 m

Explanation: Total distance = Distance cycled + Distance run
20,000 m = 17,875 m + Distance run
Distance run = 20,000 m – 17,875 m = 2,125 m

b
Write the number 17,875 in words.
▶️Answer/Explanation

Correct answer: Seventeen thousand eight hundred seventy-five

Note: Accept “seventeen thousand eight hundred and seventy-five”

c
Write the number 17,875 correct to the nearest hundred.
▶️Answer/Explanation

Correct answer: 17,900

Explanation: To round to the nearest hundred:
1. Look at the tens digit (7 in 17,875)
2. Since 7 ≥ 5, we round up the hundreds digit (8 → 9)
3. Replace tens and units digits with zeros → 17,900

Question 2: Solid Geometry

a
The diagram shows the net of a solid. What is the mathematical name of the solid?
 
▶️Answer/Explanation

Correct answer: Square-based pyramid

Explanation: The net consists of:
– 1 square base
– 4 triangular faces meeting at a common vertex (apex)
This forms a pyramid with a square base.

b
For this solid, write down the number of vertices.
▶️Answer/Explanation

Correct answer: 5

Explanation: A square-based pyramid has:
– 4 vertices at the corners of the square base
– 1 vertex at the apex (top point)
Total vertices = 4 + 1 = 5

Question 3: Number Properties

The number N is both a multiple of 12 and a square number. Find the smallest possible value of N.
▶️Answer/Explanation

Correct answer: 36

Explanation: We need the smallest square number that’s divisible by 12.
List square numbers: 1, 4, 9, 16, 25, 36, 49, …
Check multiples of 12: 12, 24, 36, 48, …
The first common number is 36 (6² = 36 and 36 ÷ 12 = 3)

Question 4: Percentage Calculation

A coin is made from a mixture of tin, copper and zinc. The table shows the percentage of each metal used. Work out the value of k.
MetalTinCopperZinc
Percentage0.4%96.5%k%
▶️Answer/Explanation

Correct answer: 3.1

Explanation: Total percentage must equal 100%:
0.4% (tin) + 96.5% (copper) + k% (zinc) = 100%
k = 100 – (0.4 + 96.5) = 100 – 96.9 = 3.1

Question 5: Number Formation

Here are four number cards: 0, 1, 3, 5. Using each card once, write down one number between 3020 and 3200.
▶️Answer/Explanation

Possible correct answers: 3015, 3051, 3105, or 3150

Explanation: To form a 4-digit number between 3020 and 3200 using each digit once:
1. Must start with 3 (to be in 3000 range)
2. Next digit must be 0 or 1 (to stay below 3200)
3. Use remaining two digits for last two places
Valid examples: 3015, 3051, 3105, 3150

Question 6: Ratio Simplification

Write the ratio 90:120 in its simplest form.
▶️Answer/Explanation

Correct answer: 3:4

Explanation: To simplify the ratio:
1. Find the greatest common divisor (GCD) of 90 and 120 → 30
2. Divide both numbers by 30:
90 ÷ 30 = 3
120 ÷ 30 = 4
3. Simplified ratio = 3:4

Question 7: Rotational Symmetry

The diagram shows a shape with five shaded sections. Shade one more section on the diagram so that it has rotational symmetry of order 3.
▶️Answer/Explanation

Correct answer: Shade any one unshaded section that creates three identical 120° rotation positions

Explanation: Rotational symmetry of order 3 means the shape looks identical after 120° rotations (360°/3).
The shape should have 3 identical sectors when rotated. With 5 sections initially shaded, adding 1 more in the correct position will create 3 pairs of identically arranged shaded sections.

Question 8: Scale Drawing and Bearings

The scale drawing shows the position of a rock, R. The scale is 1 centimetre represents 30 metres. A lighthouse, L, is 210 m from R, on a bearing of 125°. On the scale drawing, mark the position of L.
▶️Answer/Explanation

Correct answer: Point marked 7 cm from R at 125° bearing

Explanation: 1. Calculate drawing distance: 210 m ÷ 30 m/cm = 7 cm
2. From point R:
– Draw a north line
– Measure 125° clockwise from north
– Mark point L at 7 cm distance along this bearing
3. The bearing is between 123°-127° and distance 6.8-7.2 cm is acceptable

Question 9: Fraction Calculation

A cake has a mass of 600 g. Joe eats 1/5 of the cake. Find the mass of the cake that is left.
▶️Answer/Explanation

Correct answer: 480 g

Explanation: Method 1:
1. Mass eaten = 1/5 × 600 g = 120 g
2. Mass remaining = 600 g – 120 g = 480 g

Method 2:
1. Fraction remaining = 1 – 1/5 = 4/5
2. Mass remaining = 4/5 × 600 g = 480 g

Question 10: Angle Calculations

a
Find the value of angle a (with AB parallel to CD).
▶️Answer/Explanation

Correct answer: 46°

Reason: Alternate angles are equal (Z-angles)

Explanation: When two lines are parallel (AB ∥ CD):
– Angles formed by a transversal (EF) in matching corners are equal
– Angle a and the given 46° angle are alternate angles
– Therefore, a = 46°

b
Find the value of angle b.
▶️Answer/Explanation

Correct answer: 134°

Reason: Sum of angles at a point on a straight line = 180°

Explanation: 1. From part (a), we know angle a = 46°
2. Angles a and b lie on straight line EG
3. Therefore, a + b = 180°
4. b = 180° – 46° = 134°

c
Find the value of angle c.
▶️Answer/Explanation

Correct answer: 74°

Reason: Angle sum of a triangle = 180°

Explanation: 1. We know angle a = 46° (from part a)
2. The third angle in the triangle is given as 60°
3. Sum of angles in triangle EFG = 180°
4. Therefore, c = 180° – (46° + 60°) = 74°

Question 11: Basic Calculations

a
Work out 7 + 9 × 3
▶️Answer/Explanation

Correct answer: 34

Explanation: Using BIDMAS/BODMAS order of operations:
1. Multiplication first: 9 × 3 = 27
2. Then addition: 7 + 27 = 34

b
Work out -6 – (-12)
▶️Answer/Explanation

Correct answer: 6

Explanation: Subtracting a negative is the same as adding:
-6 – (-12) = -6 + 12 = 6

c
Work out 10⁻²
▶️Answer/Explanation

Correct answer: 0.01 or 1/100

Explanation: Negative exponents mean reciprocal:
10⁻² = 1/10² = 1/100 = 0.01

Question 12: Algebra

a
Factorise 9x + 12
▶️Answer/Explanation

Correct answer: 3(3x + 4)

Explanation: 1. Find the greatest common factor (GCF) of coefficients: GCF(9,12) = 3
2. Divide each term by 3: 9x ÷ 3 = 3x, 12 ÷ 3 = 4
3. Write as product: 3 × (3x + 4)

b
Solve 6x – 5 = 2x + 13
▶️Answer/Explanation

Correct answer: x = 4.5

Explanation: 1. Subtract 2x from both sides: 6x – 2x – 5 = 13 → 4x – 5 = 13
2. Add 5 to both sides: 4x = 18
3. Divide by 4: x = 18/4 = 4.5

Question 13: Time Difference Calculation

A plane flies from London to Colombo. The time in London when the plane leaves is 08:20 on Saturday. The time in Colombo when the plane arrives is 02:15 on Sunday. The flight time is 13 hours 25 minutes. Find the time difference between London and Colombo.
▶️Answer/Explanation

Correct answer: Colombo is 4 hours 30 minutes ahead

Explanation: 1. Calculate total elapsed time:
– From 08:20 Saturday to 02:15 Sunday = 17 hours 55 minutes
2. Subtract flight time: 17h55m – 13h25m = 4h30m
3. Since arrival time is later than departure+flight, Colombo is ahead

Question 14: Area Calculation

The diagram shows a shape made from two different parallelograms with total area 210 cm². Find the value of x.
▶️Answer/Explanation

Correct answer: x = 10

Explanation: 1. Area of first parallelogram = base × height = 15 cm × 4 cm = 60 cm²
2. Remaining area = 210 cm² – 60 cm² = 150 cm²
3. Second parallelogram has same base (15 cm) and height x cm
4. So 15 × x = 150 → x = 150 ÷ 15 = 10 cm

Question 15: Data Analysis

a
Plot points on scatter diagram, identify correlation, draw line of best fit, and estimate running time.
▶️Answer/Explanation

Answers:

  1. Points plotted correctly at (10.20,23.5), (10.86,25.4), (11.04,24.9)
  2. Positive correlation (as running time increases, swimming time increases)
  3. Straight line drawn through center of data points with equal points above/below
  4. Estimated running time ≈10.3s (accept reasonable estimates based on line)
b
Find mode of diameters and median of masses.
▶️Answer/Explanation

Answers:

  1. Mode diameter = 70 cm (appears most frequently – 3 times)
  2. Median mass = 181 g (ordered list: 102,135,152,180,181,200,231,412,500 → middle value)

Question 16: Graphs and Equations

a
Find the equation of line L in form y = mx + c.
▶️Answer/Explanation

Correct answer: y = ½x – 1

Explanation: 1. Identify two points on line L, e.g., (0,-1) and (2,0)
2. Calculate gradient (m) = (0 – (-1))/(2 – 0) = 1/2
3. y-intercept (c) = -1 (where line crosses y-axis)
4. Equation: y = ½x – 1

b
Complete table for y = x² – 2x – 3 and draw graph.
▶️Answer/Explanation

Answers:

  1. Table values:
    • x = -2 → y = (-2)² – 2(-2) – 3 = 4 + 4 – 3 = 5
    • x = 0 → y = -3 (given)
    • x = 1 → y = 1 – 2 – 3 = -4
    • x = 4 → y = 16 – 8 – 3 = 5
  2. Smooth U-shaped parabola through all points (-2,5), (-1,0), (0,-3), (1,-4), (2,-3), (3,0), (4,5)
c
Write down the equation of the line of symmetry.
▶️Answer/Explanation

Correct answer: x = 1

Explanation: For quadratic y = ax² + bx + c, line of symmetry is x = -b/2a
Here a=1, b=-2 → x = -(-2)/2 = 1

d
Find negative x-value where line L and parabola intersect.
▶️Answer/Explanation

Correct answer: x ≈ -0.6 (accept -0.5 to -0.7)

Explanation: 1. Set equations equal: ½x – 1 = x² – 2x – 3
2. Rearrange: x² – 2.5x – 2 = 0
3. Solve graphically or using quadratic formula
4. Negative solution is x ≈ -0.6

Question 17: Probability

a
Complete the probability tree diagram (Bag A: P(blue)=0.8, Bag B: P(blue)=0.3).
▶️Answer/Explanation

Correct answer:

  • Bag A white: 0.2 (1 – 0.8)
  • Bag B white: 0.7 (1 – 0.3)
  • Complete tree with all probabilities
b
Find probability both beads are white.
▶️Answer/Explanation

Correct answer: 0.14

Explanation: P(white from A AND white from B) = P(white A) × P(white B) = 0.2 × 0.7 = 0.14

Question 18: Transformations

a
Describe the transformation mapping shape A to shape B.
▶️Answer/Explanation

Correct answer: Rotation 90° anticlockwise about origin (0,0)

Explanation: – Shape B is shape A rotated quarter-turn anticlockwise – All points rotate 90° about the origin

b
Draw transformed shapes (translation and enlargement).
▶️Answer/Explanation

Answers:

  1. Translation by vector (-5,-6): move all points 5 left, 6 down
  2. Enlargement scale factor 3, center (1,4): triple distance from center point

Question 19: Rearranging Formulas

Rearrange w = 7t – 5 to make t the subject.
▶️Answer/Explanation

Correct answer: t = (w + 5)/7

Explanation: 1. Add 5 to both sides: w + 5 = 7t
2. Divide both sides by 7: (w + 5)/7 = t

Question 20: Inequalities

a
Write down the smallest even integer satisfying y > 2.5
▶️Answer/Explanation

Correct answer: 4

Explanation: Even integers > 2.5: 4, 6, 8,…
Smallest is 4

b
Write inequality for the number line (-5 to 6 with open circle at -2 and closed at 4).
▶️Answer/Explanation

Correct answer: -2 < x ≤ 4

Explanation: – Open circle at -2 → x > -2
– Closed circle at 4 → x ≤ 4
– Combined: -2 < x ≤ 4

Question 21: Venn Diagrams and Sets

a
Given:
Universal set ξ = {a, b, d, e, f, h, i, m, p, t, u}
X = {a, e, i, u}
Y = {d, e, m, p, t, u}
Complete the Venn diagram.
 
▶️Answer/Explanation

Correct answer:

X
a, i
e, u
Y
d, m, p, t
e, u
Outside: b, f, h

Explanation: – Intersection (X ∩ Y): e, u
– X only: a, i
– Y only: d, m, p, t
– Outside both: b, f, h

b
List the elements of X ∩ Y
▶️Answer/Explanation

Correct answer: e, u

Explanation: The intersection contains elements that are in both X and Y

c
Find n(X’) [number of elements not in X]
▶️Answer/Explanation

Correct answer: 7

Explanation: Total elements = 11
Elements in X = 4
Elements not in X = 11 – 4 = 7
These are: b, d, f, h, m, p, t

Question 22: Rounding and Bounds

The length, L, of a road is 39,700 m, correct to the nearest 50 m. Complete the inequality statement about L.
▶️Answer/Explanation

Correct answer: 39,675 ≤ L < 39,725

Explanation: When rounding to nearest 50 m:
– Lower bound = 39,700 – 25 = 39,675
– Upper bound = 39,700 + 25 = 39,725
– The value can equal the lower bound but must be less than the upper bound

Question 23: Simultaneous Equations

Solve:
1) 3x – 5y = 22
2) 7x + 10y = 8
▶️Answer/Explanation

Correct answer: x = 4, y = -2

Explanation: Method 1: Elimination
1. Multiply equation 1 by 2: 6x – 10y = 44
2. Add to equation 2: (6x + 7x) + (-10y + 10y) = 44 + 8 → 13x = 52 → x = 4
3. Substitute x=4 into equation 1: 3(4) – 5y = 22 → 12 – 5y = 22 → -5y = 10 → y = -2

Method 2: Substitution
1. From equation 1: 3x = 22 + 5y → x = (22 + 5y)/3
2. Substitute into equation 2: 7[(22 + 5y)/3] + 10y = 8
3. Multiply through by 3: 7(22 + 5y) + 30y = 24 → 154 + 35y + 30y = 24 → 65y = -130 → y = -2
4. Then x = (22 + 5(-2))/3 = (22 – 10)/3 = 12/3 = 4

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