Total marks: 100 · Duration: 2 hours · Tier: Extended
Instructions to candidates
- Answer all questions.
- Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
- Write your answer to each question in the space provided. Show all necessary working clearly.
- You must not use a calculator.
- Give exact answers (fractions, surds or in terms of π) where the question asks for them.
- Diagrams are not drawn to scale. Where a question describes a shape in words, you may find it helpful to sketch it.
Information
- The total mark for this paper is 100.
- The number of marks for each question or part question is shown in brackets [ ].
- This mock follows the 2025–2027 Cambridge IGCSE Mathematics (0580) format: Paper 2 is the Extended non-calculator paper.
Paper
1 Write 0.0507 correct to 2 significant figures. [1]
2 Work out 3 1/3 − 1 3/4. Give your answer as a mixed number in its simplest form. [3]
3 By rounding each number to 1 significant figure, estimate the value of (61.2 × 0.495) ÷ 2.98. Show your working. [2]
4 84 = 2² × 3 × 7 and 120 = 2³ × 3 × 5.
(a) Find the highest common factor (HCF) of 84 and 120. [1]
(b) Find the lowest common multiple (LCM) of 84 and 120. [2]
5 (a) Write down the value of 5⁰. [1]
(b) Simplify (x⁴)³. [1]
(c) Find the value of 16^(−3/4). [2]
6 Calculate (4.8 × 10⁵) ÷ (1.6 × 10⁻²). Give your answer in standard form. [2]
7 The angles of a triangle are in the ratio 2 : 3 : 7. Find the size of the largest angle. [2]
8 (a) Increase 60 by 35%. [1]
(b) After a 20% increase, the price of a book is $96. Find the price before the increase. [2]
9 (a) Find the nth term of the sequence 2, 8, 18, 32, … [1]
(b) The first three terms of a geometric sequence are 3, −6, 12. Find the 5th term. [2]
10 Solve the simultaneous equations. Show your working.
4x + 3y = 5 6x − 5y = 17 [3]
11 (a) Solve the inequality 2(3 − x) < 5x + 20. [2]
(b) Write down the smallest integer that satisfies the inequality. [1]
12 Factorise completely.
(a) 12x²y − 18xy² [2]
(b) 2x² + 7x − 15 [2]
13 (a) Simplify (√12 + √27)². [2]
(b) Rationalise the denominator and simplify 6/(√5 − √2). [2]
14 Each interior angle of a regular polygon is 160°. Find the number of sides of the polygon. [2]
15 PQRS is a cyclic quadrilateral. Angle PQR = (2x + 10)° and angle PSR = (3x − 5)°.
Find the value of x. Give a reason for your answer. [3]
16 In a group of 40 students, 22 study Art (A), 17 study Music (M) and 7 study both.
(a) Find n((A ∪ M)′). [2]
(b) A student who studies Music is chosen at random. Find the probability that this student also studies Art. [1]
17 A sector of a circle has radius 6 cm and angle 60°.
(a) Find the area of the sector. Give your answer in terms of π. [2]
(b) Find the perimeter of the sector. Give your answer in terms of π. [2]
18 f(x) = 5 − 2x and g(x) = x/3 + 1
(a) Find fg(6). [2]
(b) Find f⁻¹(x). [2]
(c) Solve f(x) = g(x). [2]
19 (a) Write x² + 6x − 4 in the form (x + a)² + b. [2]
(b) Write down the coordinates of the turning point of y = x² + 6x − 4. [1]
20 y is inversely proportional to the square root of x. When x = 9, y = 6.
Find y when x = 36. [3]
21 A line has equation 3x + 2y = 12.
(a) Find the gradient of the line. [1]
(b) Find the coordinates of the point where the line crosses the x-axis. [1]
(c) Find the equation of the line that is perpendicular to 3x + 2y = 12 and passes through (2, 1). [2]
22 (a) A right-angled triangle has a hypotenuse of 10 cm and one angle of 30°. Find the exact lengths of the other two sides.
You may use sin 30° = 1/2 and cos 30° = √3/2. [2]
(b) Given that sin 60° = √3/2, write down the value of sin 120°. [1]
23 The table shows the scores of 20 players in a game.
| Score | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Frequency | 3 | 5 | 6 | 4 | 2 |
(a) Calculate the mean score. [3]
(b) Find the median score. [1]
24 a = (3, −2) and b = (−1, 4), written as column vectors.
(a) Find 2a − b. [2]
(b) Find |b|. Give your answer as a surd. [1]
25 A curve has equation y = 2x³ − 6x + 1.
(a) Find dy/dx. [2]
(b) Find the coordinates of the two turning points of the curve. [3]
26 (a) Simplify (x² − 4)/(x² + x − 6). [3]
(b) Write 2/(x + 1) − 1/(x − 2) as a single fraction in its simplest form. [3]
27 Describe fully the single transformation that maps every point (x, y) onto the point (−x, −y). [2]
28 A bag contains 4 black beads and 2 white beads. Two beads are taken at random, without replacement.
Find the probability that one bead of each colour is taken. [3]
29 The side of a square is 8.5 cm, correct to the nearest millimetre.
(a) Write down the lower bound of the side length. [1]
(b) Find the upper bound of the perimeter of the square. [1]
30 The number of bacteria in a dish doubles every 3 hours. At 9 am there are 500 bacteria.
Find the number of bacteria at 9 pm on the same day. [2]
31 A car starts from rest and accelerates uniformly to 20 m/s in 8 seconds. It then travels at 20 m/s for 12 seconds.
Find the total distance travelled. [3]
32 A = {x : 2 < x ≤ 7, x is an integer}
(a) List the elements of A. [1]
(b) Write down n(A). [1]
END OF QUESTIONS — TOTAL: 100 MARKS