Cambridge & Pearson Edexcel Past Paper Questions

Solve. 27ᵏ = 9

y is inversely proportional to (x+1)². When x = 1, y = 5. Find y when x = 9.

f(x) = 2x² +7x+4 g(x) = 2x+6

40 students can take part in three activities, Art (A), Dancing (D) and Gardening (G). • 5 do not take part in any of the activities • 12 do Art on...

1 (a) In October, Sara is charged $84.25 for water. A tax of 8% is added to this amount. Calculate the total amount Sara is charged for water in O...

2 (a) The table shows the number of exercise classes attended in one week by each of 80 members of a gym. | Number of classes | 0 | 1 | 2 | 3 ...

3 (a) [Figure geometry diagram with circle, tangent, and angles] Points A, B and C are on the circle, centre O. AOC and OBE are straight lines. DE...

4 (a) [Figure diagram of villages P, Q, R with bearings] The diagram shows the positions of three villages, P, Q and R. R is due west of P and Q i...

5 (a) [Figure showing 10 number cards: 2, 2, 2, 3, 4, 5, 5, 6, 8, 9] Khalid has these 10 number cards. He takes a card at random, notes the number...

6 (a) [Figure diagram of a right-angled triangle with sides 8, 2x, 3x+5] The diagram shows a right-angled triangle, with dimensions given in centi...

7 (a) On the grid below, draw the graph of y = 2ˣ for 0 ≤ x ≤ 4. [Figure grid for plotting graph] (b) [Figure graph of y = 1/(2x²) + 3x for -1 ≤ ...

8 A is the point (−2, 3) and B is the point (4, 5). (a) Find the coordinates of the midpoint of AB. (b) Show that the equation of line AB is 3y ...

9 (a) Solve 3x-8 = 7. x = (b) Solve the inequality 7x < 3(2-x). (c) Solve 3/(x-2) + x/(x+5) = 1. x = (d) Simplify (2x²+3x+4xy +6y) / (2x² +...

10 (a) A cuboid measures 6.2 cm by 4.8 cm by 2.5 cm. Each measurement is given correct to the nearest millimetre. Calculate the upper bound of the...

Jasmine buys a family holiday to India. Here is some information about the cost. Flights | $700 Hotel | $1550 Total cost | $2250 Jasmine change...

The pie chart summarises the ages of people at a science fair. [Figure showing a pie chart with sectors labeled 'Over 30', 'Under 16', '21 to 30', ...

Complete the table for y = x³/2 - 3x - 1. x | -3 | -2 | -1 | 0 | 1 | 2 | 3 y | | 1 | 1.5 | | -3.5 | -3 | 3.5 Line L passes through the poin...

Here are the first three patterns in a sequence made from counters. [Figure showing three patterns of counters: Pattern 1 (8 counters), Pattern 2 (...

The mass of 4 cards and 3 envelopes is 85 g. The mass of 2 cards and 5 envelopes is 67 g.

Asma has this fair 8-sided spinner. [Figure showing an 8-sided spinner with sectors labeled 1, 2, 1, 2, 6, 1, 2, 1] Leon has 7 red counters, 6 gre...

P is the point (-5, 2), Q is the point (3, 7) and QR = (-4 / 6). OACB is a quadrilateral and N is a point on AB. OA = a and OB = b. OA = 2BC and B...

[Volume of cone = (1/3)πr²h] [Curved surface area of a cone = πrl] The diagram shows a paper cup in the shape of a cone. The diameter of the top of...

The diagram shows an open box in the shape of a cuboid. The height of the box is x cm. The width of the box is 5 cm more than its height. The lengt...

ABCD is a field on horizontal ground. The bearing of B from A is 070°. The bearing of D from A is 125°. C is due south of B and due east of D. AD =...

1 (a) The temperature was -2°C. The temperature decreases by 8°C. Find the temperature after this change. (b) On another day, the temperature incre...

2 Find 45% of $1.20.

3 Write these fractions in order of size, starting with the smallest. 11/12, 4/5, 27/30, 13/15

4 [Figure shows positions of two ships A and B, with North lines indicated for both. Scale: 1 cm to 30 m] The diagram shows the position of two shi...

5 (a) Write 306.248 (i) correct to 2 decimal places, (ii) correct to 2 significant figures. (b) By writing each number correct to 1 significant fig...

6 (a) Write 4×4×4×4×4 as a power of 4. (b) Simplify (√5)² (c) Simplify (2x³)⁴.

7 (a) Work out 7/8 - 3/4. (b) Work out 1 3/5 ÷ 4/7. Give your answer as a mixed number in its lowest terms.

8 Factorise 3a² + 12a.

9 (a) In the Venn diagram, shade the region represented by A ∩ B. [Figure showing two intersecting circles A and B within a universal set E] (b) Th...

10 (a) Write the number 320000000 in standard form. (b) Evaluate (2×10⁻³)/(4×10⁹). Give your answer in standard form.

11 (a) Write 120 as a product of its prime factors. (b) 315 = 3² × 5 × 7. Use this information to find the smallest integer value of n, such that 3...

12 Expand and simplify. (a) 3(2x+1)-2(4x+3) (b) (x+5)(x-3)

13 (a) The nth term of a sequence is 3n²-1. Find the first three terms of the sequence. (b) These are the first five terms of a different sequence....

14 B, C and D are points on the circumference of a circle, centre O. AB is a tangent to the circle at B. BD is a diameter and OCA is a straight lin...

15 Triangle ABC is mathematically similar to triangle DEC. AB = 12 cm, BC = 27 cm, CD = 7 cm and DE = 3 cm. [Figure showing triangles ABC and DEC, ...

16 [Figure shows a coordinate grid with a line L passing through (0,1) and (2,5). A shaded region is also shown.] (a) Find the gradient of the line...

17 The diagram shows the speed-time graph of Sam's journey from home to work. [Figure shows a speed-time graph. Speed (m/s) on y-axis (max 20), Tim...

18 b is directly proportional to the square of a. When a = 3, b = 18. Find b when a = 5.

19 ABD is an equilateral triangle. C lies on DB and AC is perpendicular to DB. Show that triangle ADC is congruent to triangle ABC. Give a reason f...

20 A farmer records the mass of each of his sheep. Some of the results are summarised in the table and illustrated in the histogram. [Table with Ma...

21 A = (3 1; -4 2) A+2B = (1 5; 10 12) (a) Find B. (b) Find A⁻¹.

22 (a) x²-6x-7 = (x+a)²+b. Find the value of a and the value of b. (b) Hence solve the equation x²-6x-7 = 0. Show your working.

23 [Volume of a cone = 1/3 πr²h, curved surface area of a cone = πrl] [Surface area of a sphere = 4πr²] A solid cone has radius y cm. The slant hei...

Work out 80÷0.02.

Put one pair of brackets into this calculation to make it correct. 4 + 4 ÷ 4 – 4 = 4

Write 7.54×10⁻⁴ as an ordinary number.