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

Write down two of the following six numbers that are irrational numbers. 36 0.2 3 −1 18 …………… , ……………

The nth term of a sequence is given by 12 − 5n Find the sum of the 2nd term and the 6th term of the sequence.

Find the value of k 2 − 5k when k = − 4

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

The diagram shows the triangle ABC D is a point on the line AC E is a point on the line BC BA is parallel to ED BC = 10.8 cm EC = 8.1 cm DE = 3.6 cm Work out the length, in cm to one decimal place, of BA cm

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

Solve the inequality 4 x 3 6 x

The price of a cup of coffee is decreased by 8% The price of a cup of coffee after the price decrease is $2.53 Calculate, in $, the price of this cup of coffee before the decrease. $

y 3x + 2y = −2 O R x The diagram shows the shaded finite region R which has three straight boundary lines. Write down the three inequalities that define the shaded region R

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

Given that, for all values of x, x² − 6x + 5 = (x − a)² + b find the value of a and the value of b a = b =

Without using a calculator and showing all your working, work out 3 5 2 +3 5 7 Give your answer as a mixed number in its simplest form.

Make x the subject of y

Calculate 2 10 180 4 10 182 Give your answer in standard form.

Factorise fully 8ab + 28b 2

Factorise 5 y 2 9 y

The diagram shows the trapezium ABCD E is the midpoint of AB and DEC is an equilateral triangle. Prove that Δ AED is congruent to ΔBEC

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

Without using a calculator and showing all your working express 3 180 − 2 245 in the form a where a is an integer.

The position vector of A is The point B has coordinates ( 2, − 4) → Find ½ AB ½ → ½ AB ½=

The table gives information about the weights, in grams, of 100 birds.

Use the information in the table to draw a histogram on the grid below. Frequency density 80 90 100 110 120 130 Weight in grams

Here are eight numbers written in ascending order. −20 −15 3 5 x 77 85 90 The mean of the eight numbers is 2 more than the median of the eight numbers. Find the value of x x =

A biased dice has six faces numbered 2, 4, 6, 8, 10 and 12 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 once.

Calculate the probability that the number the dice lands on is less than 7 The dice is thrown 80 times.

Calculate the expected number of times the dice will land on 12

y is directly proportional to w Given that y = 10 when w = 25

find a formula for y in terms of w x is inversely proportional to t3

Write down an expression for x in terms of t and c where c is a constant.

The curve C has equation y x 2 5 where b is a constant. x C has a stationary point when x = 1.5 Find the value of b b =

solid cylinder with diameter x cm and height x cm is placed inside a hollow cube ABCDEFGH of side x cm. Given that AF = 27 cm, find the volume, in cm³ to 3 significant figures, of the space inside the cube that is not taken up by the cylinder cm³

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

Express 2 as a single fraction in its simplest form. y 3 3 y 6 y 7 y 20 Show clear algebraic working.

The diagram shows a horizontal garden ABCD in the shape of a trapezium with AB parallel to DC AB = 9.8 m DC = 20.4 m AD = BC Point B is due east of point A The area of the garden is 392.6 m² Calculate the bearing, in degrees to the nearest degree, of D from A °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, D, C · Figure values: 9.8, 20.4.

A 1 4 Find

A − B

5A + 2B

B−1

Solve the simultaneous equations 3 x 4 y x 2 y 2 Show clear algebraic working.

In the diagram B, C, E and F are points on a circle centre O ABOFGH is a regular hexagon such that OB and OF are radii of the circle. BCD and FED are straight lines. BC = 3.8 cm CD = 4.5 cm ED = 5 cm Calculate the area, in cm² to 3 significant figures, of triangle CDF cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, C, H, O, D, E, G, F · Figure values: 3.8, 4.5, 5.

for Question 28 C Diagram NOT accurately drawn E F B A D The diagram shows a triangle ABC and a circle DEF BEC is the tangent to the circle at the point E with BC = 16 cm. CFA is the tangent to the circle at the point F with CA = 10 cm. ADB is the tangent to the circle at the point D with BA = 20 cm. Calculate the radius, in cm to one decimal place, of the circle cm

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