IGCSE Mathematics - International (0607) — May–June 2025, Paper 63

8 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

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Question 1 · 6 marks · Number - sequences and patterns

In this investigation you will look at the numbers in a pyramid of numbers. The numbers are placed in order in rows. Each row has one more number than the row above. (Row 1…

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Question 2 · 6 marks · Number - sequences and patterns

To find a number in the pyramid add its position in the row to the last number in the row above. Example: N(6, 4) is in row 6. The last number in row 5 is 15. N(6, 4) is in…

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Question 3 · 13 marks · Number - sequences and patterns

Numbers in the pyramid can be joined to make a diamond. The four numbers are always written in order from smallest to largest. A diamond D(a, b, c, d) has a width equal to the…

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Question 4 · 5 marks · Statistics - scatter diagrams

Matteo finds some data about the average length of kingfish at different ages (Age x years, Length L cm): (1, 28), (2, 39), (3, 48), (4, 57), (5, 64), (6, 71), (7, 78), (8, 84),…

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Question 5 · 1 mark · Statistics - validity of models

Irene finds this data about older kingfish (Age x years, Length L cm): (11, 98), (12, 102), (13, 105), (14, 109), (15, 112), (16, 114), (17, 117), (18, 119), (19, 121), (20, 122).…

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Question 6 · 7 marks · Algebra - simultaneous equations

Irene uses this model for the length of a kingfish: L = ax^2 + bx + 2. Use the lengths at age 10 years (L = 94) and at age 20 years (L = 122) to write two equations in terms of a…

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Question 7 · 7 marks · Algebra - evaluating functions

Mayuko uses a different model for the length of a kingfish: L = 123 / (1 + 3.2 × 10^(-kx)), where k is a positive constant. Use this model to find the length of the kingfish when…

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Question 8 · 5 marks · Graphs - sketching quadratic functions

Sketch Irene's model from Question 6(b) (L = -0.32x^2 + 12.4x + 2) for values of x between 0 and 30.

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