CIE iGCSE Mathematics Paper 3 Prediction - 2025

CIE iGCSE Mathematics Paper 3 Full Access

CIE iGCSE Mathematics Paper 3 Prediction – 2025

Preparing for your IGCSE exam can be daunting, but with the right approach, you can achieve your goals with CIE iGCSE Mathematics Paper 3 Prediction

Ace your iGCSE exam! Find exam-style questions, detailed notes, and helpful resources to boost your understanding

iGCSE Practice Questions, Past Papers , Flashcards and notes available for iGCSE Students at IITian Academy.

Question 1: Pictogram

The pictogram shows the number of text messages sent by five students in one day.

Name of student	Number of text messages
Kira	○ ○ ○ ○
Matt	○ ○ ○ ○
Dani	○ ○ ○ ○ ○
Hana	○ ○ 4
Ramos	○

Key: ○ represents …… text messages

Kira sent 15 text messages. Complete the key.

▶️Answer/Explanation

Correct answer: 4

Explanation: Kira has 4 circles representing 15 messages, so each circle represents 15 ÷ 4 = 3.75 messages. However, since we can’t have a fraction of a message in the key, we round to the nearest whole number, which is 4 messages per circle.

Find the number of text messages sent by Hana.

▶️Answer/Explanation

Correct answer: 9

Explanation: Hana has 2 circles and 4 messages. Using the key from part (a), each circle represents 4 messages, so 2 circles = 8 messages plus the additional 4 gives 12 messages. However, the mark scheme indicates the answer is 9, suggesting the key is actually 3 messages per circle (2 circles = 6 messages + 3 = 9). There seems to be a discrepancy here – follow the mark scheme answer of 9.

Question 2: Factors

Write down all the factors of 68.

▶️Answer/Explanation

Correct answer: 1, 2, 4, 17, 34, 68

Explanation: To find all factors of 68, we look for all numbers that divide 68 exactly:

1 × 68 = 68
2 × 34 = 68
4 × 17 = 68

These are all the factor pairs, giving us the complete list of factors.

Question 3: Brackets

Insert one pair of brackets to make this statement correct: 4 × 6 – 2 + 1 = 17

▶️Answer/Explanation

Correct answer: 4 × (6 – 2) + 1 = 17

Explanation:

Without brackets: 4 × 6 – 2 + 1 = 24 – 2 + 1 = 23 ≠ 17
With brackets: 4 × (6 – 2) + 1 = 4 × 4 + 1 = 16 + 1 = 17

The brackets change the order of operations, making the subtraction happen before the multiplication.

Question 4: Reciprocal

Write down the reciprocal of 4.

▶️Answer/Explanation

Correct answer: 1/4 or 0.25

Explanation: The reciprocal of a number is 1 divided by that number. Therefore, the reciprocal of 4 is 1 ÷ 4 = 1/4 or 0.25.

Question 5: Calculations

Find the value of 24².

▶️Answer/Explanation

Correct answer: 576

Explanation: 24 squared means 24 multiplied by itself: 24 × 24 = 576.

Find the value of ³√2197.

▶️Answer/Explanation

Correct answer: 13

Explanation: The cube root of 2197 is the number that when multiplied by itself three times equals 2197. 13 × 13 × 13 = 2197, so ³√2197 = 13.

Question 6: Temperature

The lowest temperature recorded at Scott Base in Antarctica is -57.0°C. The highest temperature recorded at Scott Base is 63.8°C more than this. Calculate the highest temperature recorded at Scott Base.

▶️Answer/Explanation

Correct answer: 6.8°C

Explanation: To find the highest temperature, we add the difference to the lowest temperature: -57.0°C + 63.8°C = 6.8°C.

Question 7: Currency Exchange

Lee changes $450 into euros. The exchange rate is $1 = 0.8476 euros. Calculate the amount in euros that Lee receives.

▶️Answer/Explanation

Correct answer: 381.42 euros

Explanation: To convert dollars to euros, multiply the dollar amount by the exchange rate: $450 × 0.8476 = 381.42 euros.

Question 8: Substitution

Given W = t/2 (7t – 4), find the value of W when t = 18.

▶️Answer/Explanation

Correct answer: 1098

Explanation: Substitute t = 18 into the equation: W = 18/2 (7×18 – 4) = 9 (126 – 4) = 9 × 122 = 1098

Question 9: Construction

A triangle has sides 6 cm, 7 cm and 8 cm. Using a ruler and compasses only, construct the triangle. The 6 cm line has been drawn for you. Show all your construction arcs.

▶️Answer/Explanation

Correct answer: A correctly constructed triangle with all construction arcs visible.

Explanation:

Start with the given 6 cm side (let’s call it AB).
Using a compass set to 7 cm, draw an arc from point A.
Using a compass set to 8 cm, draw an arc from point B.
The point where these two arcs intersect is point C of the triangle.
Join A to C and B to C to complete the triangle.
All construction arcs must be clearly visible.

Question 10: Calculation

Calculate (13.7 + 14.02) ÷ (-0.31 + ³√15.625). Give your answer correct to 2 decimal places.

▶️Answer/Explanation

Correct answer: 12.66

Explanation:

Numerator: 13.7 + 14.02 = 27.72
Denominator: -0.31 + ³√15.625 = -0.31 + 2.5 = 2.19
Division: 27.72 ÷ 2.19 = 12.657 (to 3 decimal places)
Rounded to 2 decimal places: 12.66

Question 11: Circle Geometry

The line XY touches the circle at the point R. Write down the mathematical name for the line XY.

▶️Answer/Explanation

Correct answer: Tangent

Explanation: A tangent is a straight line that touches a circle at exactly one point (the point of tangency).

Points P and Q lie on the circle. Write down the mathematical name for the line PQ.

▶️Answer/Explanation

Correct answer: Chord

Explanation: A chord is a straight line joining two points on the circumference of a circle.

The area of the circle is 43.5 cm². Calculate the radius of the circle.

▶️Answer/Explanation

Correct answer: 3.72 cm

Explanation: Using the area formula A = πr²: r² = A/π = 43.5/π ≈ 43.5/3.142 ≈ 13.84 r = √13.84 ≈ 3.72 cm

The diameter of a different circle is 6.4 cm. Calculate the circumference of this circle. Give your answer in millimetres.

▶️Answer/Explanation

Correct answer: 201 mm

Explanation:

First calculate circumference in cm: C = πd = π × 6.4 ≈ 20.106 cm
Convert to mm: 20.106 cm × 10 = 201.06 mm
Rounded to nearest mm: 201 mm

Question 12: Stem-and-Leaf Diagram

The stem-and-leaf diagram shows the scores of each of 27 students in a test. Find the range of the scores.

2 | 8 8 9
3 | 2 5 6 6 7 8 8
4 | 0 1 1 2 3 4 6 7 9
5 | 1 3 4 5 5 7 8
6 | 2
Key: 2 | 8 represents a score of 28

▶️Answer/Explanation

Correct answer: 34

Explanation:

Lowest score: 28
Highest score: 62
Range = highest – lowest = 62 – 28 = 34

When the score for another student is included in the diagram the new range is 38. Find the two possible scores for this student.

▶️Answer/Explanation

Correct answer: 24, 66

Explanation:

Current range is 34 (62-28)
New range needs to be 38, which is 4 more than current range
Either:
- New lowest score: 28 – 4 = 24
- Or new highest score: 62 + 4 = 66

Question 13: Travel Graph

Abjit cycles from his home to the swimming pool. The travel graph for his journey is drawn on the grid. On his journey he passes the cinema and the shop.

Write down where Abjit stops on his journey to the swimming pool.

▶️Answer/Explanation

Correct answer: shop

Explanation: The graph shows a flat line (no distance change) at the shop location, indicating a stop.

Abjit is cycling fastest between the shop and the swimming pool. Explain how you know this from looking at the graph.

▶️Answer/Explanation

Correct answer: The steepest gradient [or equivalent explanation]

Explanation: Speed is represented by the slope of the graph. The steepest section (between shop and pool) indicates the highest speed.

c(i)

Show that the distance from Abjit’s home to the cinema is 4km.

▶️Answer/Explanation

Working: $ \text{Distance} = \text{Speed} \times \text{Time} = 20\,\text{km/h} \times 0.2\,\text{hours} = 4\,\text{km} $

Explanation: 12 minutes = 0.2 hours. Using the formula distance = speed × time.

c(ii)

Complete the scale on the vertical axis of the grid by showing at least two other values.

▶️Answer/Explanation

Correct answer: Example: 2, 4, 6, 8 marked on distance axis

Explanation: Since home-to-cinema = 4km (from part c(i)), the scale should show consistent intervals (e.g., 0, 2, 4, 6, 8 km).

Calculate the speed, in km/h, that Abjit cycles from the cinema to the shop.

▶️Answer/Explanation

Correct answer: 12 km/h

Explanation: From graph: distance = 8km – 4km = 4km, time = 20 minutes = 1/3 hour. Speed = 4km ÷ (1/3)h = 12 km/h.

Complete the travel graph for his journey home (takes 24 minutes at constant speed).

▶️Answer/Explanation

Correct answer: Straight line from (1034, 8) to (1058, 0)

Explanation: Returns home in 24 minutes (x-axis) from 8km to 0km (y-axis) at constant speed → straight declining line.

Calculate the average speed, in km/h, for the whole journey.

▶️Answer/Explanation

Correct answer: 16.6 or 16.55… km/h

Explanation: Total distance = 8km × 2 = 16km. Total time = 58 minutes = 0.966… hours. Average speed = 16 ÷ 0.966… ≈ 16.55 km/h.

g(i)

Calculate the circumference of the wheel (radius = 29cm). Give your answer correct to 1 decimal place.

▶️Answer/Explanation

Correct answer: 182.2 cm

Explanation: $ C = 2\pi r = 2 \times \pi \times 29 \approx 182.2\,\text{cm} $ (to 1 d.p.).

g(ii)

Calculate the number of complete turns the wheel makes when travelling 500m.

▶️Answer/Explanation

Correct answer: 274

Explanation: 500m = 50,000cm. Number of turns = $ \frac{50,000}{182.2} \approx 274.4 $ → 274 complete turns.

Question 14: Solid Shapes

Irina has some solid building blocks.

Write down the mathematical name of this solid.

▶️Answer/Explanation

Correct answer: Cylinder

Explanation: The shape has two circular bases and a curved surface, characteristic of a cylinder.

Irina describes a shape with 12 edges, 8 vertices, and all faces the same shape. Write down the mathematical name.

▶️Answer/Explanation

Correct answer: Cube or cuboid

Explanation: Both cubes and cuboids have 12 edges and 8 vertices. The mention of “all faces the same shape” suggests a cube (though a square-faced cuboid would also fit).

c(i)

Show that BC = 5.2 cm, correct to 1 decimal place.

▶️Answer/Explanation

Working: $ BC = \sqrt{6^{2}-3^{2}} = \sqrt{36-9} = \sqrt{27} ≈ 5.196 $ cm → 5.2 cm (1 d.p.)

Explanation: Using Pythagoras’ theorem for right-angled triangle ABC.

c(ii)

Find the area of triangle ABC.

▶️Answer/Explanation

Correct answer: 7.8 cm²

Explanation: $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \times 5.196 ≈ 7.794 $ cm²

c(iii)

Calculate the volume of the triangular prism (length = 8cm).

▶️Answer/Explanation

Correct answer: 62.4 cm³

Explanation: $ \text{Volume} = \text{Area of triangle} \times \text{length} = 7.8 \times 8 = 62.4 $ cm³

d(i)

Calculate the area of the end face of this block.

▶️Answer/Explanation

Correct answer: 28 cm²

Explanation: $ \text{Area} = \frac{1}{2} \times (5 + 9) \times 4 = 28 $ cm² (Trapezium area formula)

d(ii)

Find the value of x when volume = 336 cm³.

▶️Answer/Explanation

Correct answer: 12

Explanation: $ \text{Volume} = \text{Area} \times x \Rightarrow 336 = 28 \times x \Rightarrow x = 12 $ cm

Question 15: Sphere Calculations

A sphere has a surface area of 177 cm². Calculate the radius of the sphere.

▶️Answer/Explanation

Correct answer: 3.75 cm

Explanation:

Surface area = 4πr² = 177
r² = 177 ÷ (4π) ≈ 177 ÷ 12.566 ≈ 14.085
r = √14.085 ≈ 3.75 cm

Calculate the volume of the sphere.

▶️Answer/Explanation

Correct answer: 221 cm³

Explanation:

Volume = (4/3)πr³
Using r = 3.75 cm: (4/3)π(3.75)³ ≈ 4.18879 × 52.734 ≈ 221 cm³

Question 16: Ratio and Profit

Jo and Mira buy a shop in the ratio 7:15. Mira pays $84,000 more than Jo. Work out how much they each pay.

▶️Answer/Explanation

Correct answer: Jo: $73,500; Mira: $157,500

Explanation:

Difference in ratio parts: 15 – 7 = 8 parts
8 parts = $84,000 → 1 part = $10,500
Jo’s share: 7 × $10,500 = $73,500
Mira’s share: 15 × $10,500 = $157,500

b(i)

The shop makes $56,000 profit. Jo receives 12% of the profit. Calculate how much Jo receives.

▶️Answer/Explanation

Correct answer: $6,720

Explanation: 12% of $56,000 = 0.12 × 56,000 = $6,720

b(ii)

Mira receives $14,000 of the profit. The rest is put in a bank account. Calculate the bank amount as a percentage of the profit.

▶️Answer/Explanation

Correct answer: 63%

Explanation:

Total distributed: $6,720 (Jo) + $14,000 (Mira) = $20,720
Bank amount: $56,000 – $20,720 = $35,280
Percentage: (35,280 ÷ 56,000) × 100 = 63%

b(iii)

Mira invests $14,000 at 2.4% per year compound interest. Calculate the value after 4 years.

▶️Answer/Explanation

Correct answer: $15,400

Explanation:

Using compound interest formula: A = P(1 + r/100)ⁿ
A = 14,000(1 + 0.024)⁴ ≈ 14,000 × 1.0995 ≈ 15,393
Rounded to nearest $100: $15,400

Question 17: Prime Factors and Multiples

The number N is written as a product of its prime factors: N = 2⁴ × 3²

Work out the value of N.

▶️Answer/Explanation

Correct answer: 144

Explanation:

N = 2⁴ × 3² = 16 × 9 = 144

Find the highest common factor (HCF) of 120 and N.

▶️Answer/Explanation

Correct answer: 24

Explanation:

Prime factors of 120: 2³ × 3 × 5
Prime factors of N (144): 2⁴ × 3²
HCF = product of lowest powers of common primes: 2³ × 3 = 8 × 3 = 24

Find the lowest common multiple (LCM) of 120 and N.

▶️Answer/Explanation

Correct answer: 720

Explanation:

LCM = product of highest powers of all primes present
2⁴ × 3² × 5 = 16 × 9 × 5 = 720

Question 18: Sequences

(a) These are the first five terms of a sequence: 7, a, b, c, 31

(b) These are the first five terms of another sequence: 4, 11, 18, 25, 32

In the sequence where the same number is added each time, find the values of a, b, and c.

▶️Answer/Explanation

Correct answer: a = 13, b = 19, c = 25

Explanation:

First term = 7, fifth term = 31
Common difference = (31 – 7) ÷ 4 = 6
Sequence: 7, 13, 19, 25, 31

b(i)

Find the nth term of the sequence 4, 11, 18, 25, 32.

▶️Answer/Explanation

Correct answer: 7n – 3

Explanation:

Common difference = 7
First term (n=1): 4 = 7×1 – 3
Second term (n=2): 11 = 7×2 – 3
Therefore nth term = 7n – 3

b(ii)

Show that 361 is a term in the sequence.

▶️Answer/Explanation

Correct answer: 7n – 3 = 361 → n = 52 (integer)

Explanation:

Set 7n – 3 = 361
7n = 364 → n = 52
Since n is an integer, 361 is the 52nd term

Question 19: Mean Scores

In a quiz, the mean score of 12 adults is 43.25. The mean score of 16 children is 39.75. Calculate the mean score of all 28 people.

▶️Answer/Explanation

Correct answer: 41.25

Explanation:

Total adults score: 12 × 43.25 = 519
Total children score: 16 × 39.75 = 636
Combined total: 519 + 636 = 1155
Mean score: 1155 ÷ 28 = 41.25

Question 20: Unit Conversion

Luca walks at 5.4 km/h. Write this speed in m/s.

▶️Answer/Explanation

Correct answer: 1.5 m/s

Explanation:

Convert km to m: 5.4 km = 5400 m
Convert hours to seconds: 1 h = 3600 s
Speed = 5400 ÷ 3600 = 1.5 m/s

Question 21: Geometry Problems

a(i)

Measure angle $k$

▶️Answer/Explanation

Angle measurement diagram

Correct answer: 326°

Explanation: Using a protractor, angle $k$ measures 326° (reflex angle).

a(ii)

Write down the mathematical name for this type of angle

▶️Answer/Explanation

Correct answer: reflex

Explanation: An angle between 180° and 360° is called a reflex angle.

Complete the statements about parallel lines

▶️Answer/Explanation

Correct answers:

Angle c is alternate to angle x

Angle d is corresponding to angle x

Explanation:

– Alternate angles (Z-angles) are equal and form a “Z” shape

– Corresponding angles (F-angles) are in matching positions at each intersection

Find the value of y in the parallelogram

▶️Answer/Explanation

Correct answer: 138°

Working:

In a parallelogram, adjacent angles are supplementary:

$ y + 42° = 180° $

$ y = 180° – 42° = 138° $

Find angle $ACB$ in the circle diagram

▶️Answer/Explanation

Correct answer: 73°

Working:

1. Central angle theorem: $ \angle BOC = 2 \times 17° = 34° $

2. Triangle BOC is isosceles: $ \angle OBC = \angle OCB $

3. $ 34° + 2\angle OCB = 180° $

4. $ \angle OCB = \frac{146°}{2} = 73° $

Find the number of sides of a regular polygon with interior angle 171°

▶️Answer/Explanation

Correct answer: 40

Working:

$ 171 = \frac{(n-2) \times 180}{n} $

$ 171n = 180n – 360 $

$ 9n = 360 $

$ n = 40 $

Calculate the value of $x$ in the right-angled triangle

▶️Answer/Explanation

Correct answer: 23.6° (or 23.57° to 23.58°)

Working:

$ \sin(x) = \frac{7.4}{18.5} = 0.4 $

$ x = \sin^{-1}(0.4) ≈ 23.58° $

Question 22: Floor Plan and Calculations

The diagram shows a plan, $ABCDE$, of the floor of a room in Jo’s house. $F$ is a point inside the room.

a(i)

Show that $EF=1.9$m

▶️Answer/Explanation

Working: $ EF = DC – AB = 5.5\,\text{m} – 3.6\,\text{m} = 1.9\,\text{m} $

Explanation: Horizontal distance calculated by subtracting AB length from DC length.

a(ii)

Work out $AF$

▶️Answer/Explanation

Correct answer: 3 m

Explanation: $ AF = BC – ED = 4.7\,\text{m} – 1.7\,\text{m} = 3\,\text{m} $ (vertical distance calculation)

Calculate the area of the floor

▶️Answer/Explanation

Area calculation diagram

Correct answer: 23 m²

Working:

1. Rectangle ABMC: $ 3.6 \times 4.7 = 16.92\,\text{m}^2 $

2. Rectangle DEFM: $ 1.9 \times 1.7 = 3.23\,\text{m}^2 $

3. Triangle AFE: $ \frac{1}{2} \times 1.9 \times 3 = 2.85\,\text{m}^2 $

Total area: $ 16.92 + 3.23 + 2.85 = 23\,\text{m}^2 $

Calculate the volume of the cupboard (base area = 1.2 m², height = 2.3 m)

▶️Answer/Explanation

Correct answer: 2.76 m³

Working: $ \text{Volume} = 1.2\,\text{m}^2 \times 2.3\,\text{m} = 2.76\,\text{m}^3 $

Units: cubic meters (m³)

Calculate the total cost of 275 floor tiles at \$1.64 each

▶️Answer/Explanation

Correct answer: \$451

Working: $ 275 \times 1.64 = 451\,\text{dollars} $

Calculate the area of a semicircular patio with radius 2.3 m

▶️Answer/Explanation

Correct answer: 8.31 m²

Working: $ \frac{1}{2} \times \pi \times (2.3)^2 = \frac{1}{2} \times \pi \times 5.29 ≈ 8.31\,\text{m}^2 $

Note: Accept answers between 8.309 to 8.311

CIE iGCSE Mathematics Paper 3 Prediction

CIE iGCSE Mathematics Paper 3 Prediction - 2025