4MB1/01 — November 2024 (Edexcel IGCSE Maths): Past Paper

Factorise fully 28ab + 21b

A pattern is made with white squares and shaded squares.

Shade one more square to make a pattern with rotational symmetry of order 2 Here is a different pattern made from white squares and shaded squares.

Shade one more square to make a pattern with exactly one line of symmetry.

Using ruler and compasses only and showing all your construction lines, construct the perpendicular bisector of AB B A

The bearing of Port A from Port B is 276° Find the bearing of Port B from Port A

…………… °

Solve x x 7 7 x = ……………Solve x x 7 7 x =

A 2 x 7 4 B 2 2 7 y Given that x > 2 and y > 4 find the highest common factor (HCF) of A and B

A biased dice has six faces numbered 1, 2, 3, 4, 5 and 6 The table below shows information about the probability that, when the dice is thrown once, it will land on each of the numbers.

The dice is thrown 300 times. Calculate the expected number of times the dice will land on a number greater than 3

8 3 kg of onions cost £1.71 2 kg of onions and 5 kg of potatoes cost £5.34 Calculate the total cost, in £, of 3 kg of onions and 4 kg of potatoes. £

The diagram shows a solid cuboid ABCDEFGH EH = 12 cm GH = 5.5 cm BG = 6 cm Calculate the total surface area, in cm², of the cuboid cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, D, C, G, F, E, H · Figure values: 6, 5.5, 12.

y −5 −4 −3 −2 −1 O 1 2 3 4 5 x −1 −2 −3 L1 −4 −5 The straight line L1 is drawn on the grid. The straight line L2 is parallel to L1 and passes through the point with coordinates 9, 12 Find an equation for L2 Give your answer in the form y mx c

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Use the text description to work through it.

Calculate 2.3 10114 4.6 10117 Give your answer in standard form.

A, B, C and D are numbers such that A: B = 2:5 A: D = 3:8 B : C = 9 : 11 Find C : D Give your answer in its simplest form.

The diagram shows quadrilateral ABCD where B and C are on horizontal ground and BA and CD are vertical. BC = 12.2 metres AB = 1.7 metres ABC BCD The angle of elevation of D from A is 32° Calculate the length, in metres to 3 significant figures, of CD metres

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: D, A, B, C · Figure values: 1.7, 12.2.

Write as a single fraction in its simplest form x 1 2 x 5 7 4

A team takes part in a sports league. After 12 games its mean score per game is 96 After 14 games its mean score per game is 98 The ratio of its score in game 13 to its score in game 14 is 2 : 3 Calculate its score in game 14

In the diagram, BGE is an isosceles triangle with EG = BG ABC, DEF and EGH are straight lines. ABC is parallel to DEF DEB 113 BGH Find the size, in degrees, of ∠CBG Give a reason for each stage of your working. CBG °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, C, H, G, F, D, E · Figure values: 94°, 113°.

At the start of 2012, Fatima bought a car for $15 500 From the start of 2012 to the start of 2014, the value of the car decreased by 8% From the start of 2014 to the start of 2016, the value of the car decreased by 2.2% From the start of 2016 to the start of 2018, the value of the car decreased by x% At the start of 2018, the value of the car was $13 137.40 Calculate, to 2 significant figures, the value of x x =

Make t the subject of r 3t

A B 4 3 0 2

Find AB 3 2 C 5 6

Find C −1

In the diagram A, B, C and E are points on a circle with centre O DEF is the tangent to the circle at the point E BA = BC OAE CED Find the size, in degrees, of ∠BCE BCE °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, D, B, O, E, A, F · Figure values: 61°, 27°.

v 2 u 2 2as v = 25.4 to 1 decimal place u = 9.512 to 4 significant figures s = 15 to the nearest 5 Calculate the upper bound, to 3 significant figures, of a Show your working clearly.

On the number line, represent the inequality 5 y ≤ 3 y −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6

Solve the inequality 4 x + 2 ≥ 3 7 2 x

Use the factor theorem to show that x 5 is a factor of 2 x 3 9 x 2 11x

Hence, factorise completely 2 x 3 9 x 2 11x Show clear algebraic working.

The probability that Lethna takes the bus to work on Monday is 0.32 If Lethna takes the bus on Monday, the probability that she takes the bus on Tuesday is 0.47 If Lethna does not take the bus on Monday, the probability she will not take the bus on Tuesday is 0.71

Complete the tree diagram for this information. Monday Tuesday bus bus 0.32 not bus bus not bus not bus E is the event that Lethna takes the bus on exactly one of either Monday or Tuesday. F is the event that Lethna does not take the bus on Monday and does not take the bus on Tuesday.

Find which of the events, E or F, has the greater probability. Show your working clearly.

y Diagram NOT C P accurately drawn Q O R x L The diagram shows part of the curve C with equation y 3 x 2 16 x and part of the line L with equation 2 y 11x 110 P and Q are the points of intersection of C and L R is the point on the x-axis such that PR is parallel to the y-axis. Show that the area of triangle PQR is 442.75 cm² You must show clear algebraic working.

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Use the text description to work through it.

B Diagram NOT C accurately drawn E D A The diagram shows a solid pyramid P with vertices A, B, C and D ACD is the horizontal triangular base of P E is the point on AC such that AE = AC AC = 15.5 cm CD = 8.2 cm AED

Calculate, in cm to 3 significant figures, the length of ED cm The solid pyramid T is mathematically similar to P The area of the triangular base of T is 64.9 cm² Given that vertex B is vertically above point E and EBD

calculate, in cm³ to 3 significant figures, the volume of T

…………… cm³

A curve with equation y 9 x 2 16 x 5 is drawn on a grid where 1 unit = 1 cm on each axis. P and Q are two points on the curve. P is the point with coordinates 1, 2 The gradient of the tangent to the curve at Q is 6.5 Find the length, in cm to 3 significant figures, of PQ You must show clear algebraic working cm