4MB1/01 — January 2023 (Edexcel IGCSE Maths): Past Paper

The nth term of a sequence is given by 6n 2 − 5 Find the difference between the 2nd term and the 4th term of the sequence.

Find the Highest Common Factor (HCF) of 60 and 165 Show your working clearly.

Factorise fully 6af + 30 f 2

4Without using a calculator and showing all your working, calculate 1 1 4 ÷ 2 3 2 Give your answer as a mixed number in its simplest form.

Solve the inequality 5 x ≤ 3 x + 15

Calculate 4.2 1072 5.5 1075 Give your answer in standard form.

The price of a holiday is reduced by 4% in a sale. Haniya pays $600 of the sale price when she books the holiday. She pays the remainder of the sale price in 4 equal monthly payments of $180 Calculate the price of the holiday before the sale. $

The straight line L1 has equation y + 4x = 5 The straight line L2 is parallel to L1 and passes through the point (2, ‒6) Find the equation for L2 in the form y = mx + c

y B A 4 −7 −6 −5 −4 −3 −2 −1 O 1 2 3 4 5 6 x Quadrilateral A and quadrilateral B are drawn on a grid. Quadrilateral B is the image of quadrilateral A under a single transformation. Describe fully this single transformation.

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

Without using a calculator and showing your working clearly, find the value of the integer a so that 2 300 108 a a =

Write down the value of a0 where a > 0

Simplify fully 2 w2 × 11w5

Simplify fully 4 y 8

A, B, C and D are points on a circle. EDF is the tangent to the circle at the point D Angle BDF = 75° Calculate, giving your reasons, the size, in degrees, of ∠BCD °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, C, E, D, F · Figure values: 75°.

a t v = 8.91 to 3 significant figures. u = 5.82 to 3 significant figures. t = 9 to 1 significant figure. Calculate the lower bound, to 3 significant figures, of a Show your working clearly.

The diagram shows a regular pentagon ABCDE and three sides, FE, EG and GH, of a regular n-sided polygon. AB is horizontal. EG is vertical. DEF 69 Calculate the value of n n =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: F, D, E, C, G, A, B, H · Figure values: 69°.

The diagram shows a sphere of radius r cm and a right circular cone with base radius r cm and vertical height 20 cm. Diagram NOT accurately drawn r cm 20 cm r cm The volume of the sphere is 1.5 times the volume of the cone. Find the value of r r =

P is inversely proportional to the square root of W P = 1600 when W = 1.96 Find the value of W when P = 800 W =

Quadrilateral A is transformed to quadrilateral B under a reflection in the line y = − x 4 2 Quadrilateral B is transformed to quadrilateral C under the matrix 1 3 Quadrilateral C is the image of quadrilateral A under the matrix N Find the matrix N N

Diagram NOT accurately drawn A B The diagram shows two mathematically similar solids A and B The volume of solid A is 1125 cm³ The volume of solid B is 576 cm³ Given that surface area of solid A + surface area of solid B = 3198 cm² calculate the surface area of solid B cm²

A X B Y D Scale: 1 cm represents 2 metres C The quadrilateral ABCD is a scale drawing of Simon’s garden. There is a tree at the point X and a tree at the point Y

Construct the locus of all points inside the quadrilateral that are 10 metres from C

Using ruler and compasses only and showing all your construction lines, construct the locus of all points inside the quadrilateral that are equidistant from X and Y

Construct the locus of all points inside the quadrilateral that are 6 metres from AB Simon is going to place a light in the garden so that it is closer to X than to Y, more than 6 metres from AB and more than 10 metres from C

Show, by shading, the region where Simon can place the light. Label the region R

Sarah records the number of visits to the cinema that each of the 19 students in her class made in June. The table below shows her results.

Write down the mode of the number of visits to the cinema.

Find the median number of visits to the cinema. Bhaskor joins Sarah’s class. The mean number of visits to the cinema, after Bhaskor joins the class, for the 20 students in June is 1.7

Calculate the number of visits to the cinema Bhaskor makes in June.

Diagram NOT accurately drawn Speed (m/s) u 0 4 6 8 Time (t seconds) The diagram shows a sketch of the speed-time graph of part of a cyclist’s journey along a straight horizontal road.

Calculate the deceleration, in m/s2, for the last 2 seconds of this part of the cyclist’s journey m/s2 At time t = 0 seconds, the speed of the cyclist is u m/s The cyclist travelled a total distance of 65 m in the 8 seconds.

Calculate the value of u u =

The bar chart gives information about the number of pieces of music downloaded last month for each of 30 students in a class. Number of students 4 0-2 3-5 6-8 9-11 12-14 15-17 Number of pieces of music downloaded

Calculate the percentage of students who downloaded more than 8 pieces of music last month

…………… %

Calculate an estimate for the mean number of pieces of music each student downloaded last month.

Simplify x 3 x² 4 Show your working clearly.

Use the factor theorem to show that x 1 is a factor of 18 x³ 9 x 2 17 x

Factorise fully 18 x³ 9 x 2 17 x Show clear algebraic working.

A particle P is moving along a straight line that passes through the point O The displacement, x metres, of P from O at time t seconds (t ≥ 0) is given by x t 3 4t 2 3t At time t seconds, the velocity of P is v m/s

Find an expression for v in terms of t v = The particle P comes to instantaneous rest at the point A

Find, in metres, the distance OA m

D Diagram NOT accurately drawn 60° 5 3 cm 5 15 cm A C 10 3 cm B The diagram shows a pyramid ABCD with a horizontal triangular base ABC DC = 5 3 cm DB = 10 3 cm AC = 5 15 cm ADB DCA DCB

Calculate the length, in cm to one decimal place, of AB cm

Calculate the area, in cm² to 3 significant figures, of triangle ABC

…………… cm²