4MB1/02 — June 2024 (Edexcel IGCSE Maths): Past Paper

Write 0.000 015 96 in standard form. The star, Sirius, is approximately 81 460 000 000 000 km from Earth. Light from Sirius takes approximately 3142.7 days to reach Earth.

Calculate the speed, in km/s to one significant figure, that light travels from Sirius to Earth. Give your answer in standard form. Show your working clearly.

A B C The diagram shows triangle ABC Using ruler and compasses only and showing all your construction lines, construct

the locus of the points that are 3 cm from B

the perpendicular bisector of AC

the bisector of ∠ACB The region R consists of all the points inside the triangle that are closer to A than to C, closer to BC than to AC and more than 3 cm from B

Show, by shading, the region R Label the region R

A college offers courses in Astronomy (A), Biology (B), Chemistry (C) and Physics (D) A group of 220 students are asked which of these courses they study. Here is some information about the numbers of students who study these subjects. n A 58 n B C D x n B D n B C D' 35 n B C D 20 The incomplete Venn diagram on the opposite page shows some other information about the numbers of students who study these subjects.

Using all the information given, complete the Venn diagram giving the number of elements in each appropriate subset, in terms of x where necessary. Given that n C' 105

find the value of x One of the 220 students is chosen at random.

Write down the probability that this student studies Biology only.

Write down the probability that this student studies Chemistry but not Biology. E B C 16 15 A D

Triangle A and triangle D are drawn on the grid opposite. Triangle A is reflected in the x-axis to give triangle B

On the grid, draw and label triangle B Triangle A is transformed to triangle C by a rotation of 90° clockwise about the point (0, 0)

On the grid, draw and label triangle C Triangle D is the image of triangle A under a single transformation.

Describe fully this transformation. Triangle A is transformed to triangle E under the transformation with matrix M where M

On the grid, draw and label triangle E Triangle E is transformed to triangle B under the transformation with matrix N

Using a combination of transformation matrices or otherwise, find the matrix N.

[The inverse of matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is $\frac{1}{ad-bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$]

5A particle P is moving along a straight line. At time t seconds, the displacement, x metres, of P from a fixed point O on the line is given by x kt 2 t 3 When t = 2 the velocity of particle P is 24 m/s Particle P comes to instantaneous rest at the point A Find the distance, in metres, between O and A

The probability of a spinner landing on red is 0.6 This spinner is spun once.

Write down the probability that the spinner does not land on red. This spinner is spun twice.

Calculate the probability that the spinner does not land on red either time. This spinner is spun 140 times.

Calculate the expected number of times the spinner will land on red. A bag contains n counters. The counters are red or blue or green such that number of red counters : number of blue counters : number of green counters = 2 : 1 : 1 A sample of 3 counters is taken at random from the bag without replacement. The probability of getting 2 red counters followed by a blue counter is

Calculate the probability of getting 3 green counters. Give your answer as a fraction. b b 2 4ac bx c 0 are x 2a

E 100 cm Diagram NOT F accurately drawn H 40 cm D C A 30° B Figure 1 Figure 1 shows a right triangular prism ABCDEF The base ABCD is on a horizontal plane. CF = DE = 40cm EF = DC = AB = 100cm FBC The point H lies on the line BF such that BH = 57.5 cm

Show that EH = 102.5 cm

Calculate, in degrees to 3 significant figures, ∠EHD [ Cosine rule: $a^2$ = $b^2$ + $c^2$ – 2bc cos A ]

A Swiss company makes three different types of watches, diver, calendar and automatic. The numbers of each type of watch made in January is such that diver : calendar : automatic = 4 : 6 : 5 The number of calendar watches the company makes in January is 54

Calculate the number of diver watches the company makes in January. Mel works for the company. She earns 32 Swiss francs for each hour worked plus 6% of the value of the watches she sells. In January Mel works 120 hours and sells watches to the value of 13 000 Swiss francs.

Calculate the total amount Mel earns in January. In February Mel works 150 hours and earns a total amount of 8040 Swiss francs.

Calculate the value of the watches Mel sells in February. In March the company makes 250 automatic watches. The cost to make each automatic watch is 80 Swiss francs. 64% of these automatic watches are sold for 140 Swiss francs each. The remaining automatic watches are sold in America for $216 each. Using an exchange rate of 1 Swiss franc = $1.08

calculate the total profit, in Swiss francs, the company makes on these 250 automatic watches.

A graph has equation $y = \frac{x^2}{4} - 3 - \frac{1}{x} \quad x \ne 0$

Complete the table of values for the graph.

On the grid opposite, plot the points from your completed table and draw the graph $y = \frac{x^2}{4} - 3 - \frac{1}{x}$

Using your graph, find estimates, to one decimal place, of the solutions of the equation $\frac{x^2}{4} - 3 = \frac{1}{x}$

By drawing a suitable line on the grid, find the range of values, to one decimal place, of $x$ in $-4 \le x \le 4$ for which $\frac{x^2}{4} - 3 - \frac{1}{x} \le 0$

f(x) 6 x³ (6 p 1) x 2 (5 p q ) x 2 where p and q are integers. Given that 2 x 1 is a factor of f(x)

show that 2 p q Given that x p is also a factor of f(x)

find the value of p and the value of q Show clear algebraic working.

Factorise fully f(x) b b 2 4ac bx c 0 are x 2a

f is the function such that f : x ↦ 2 x − 5 x > 1

Find the value of m for which f(m) = 0 g is the function such that 7 8x g:xα 2x

Find g(–1)

State the value of x which must be excluded from any domain for g

Find the value for x, to 3 significant figures, for which f(x) = g(x) Show your working clearly. h is the function such that h : x ↦ 2 x 2 4 x 5 x

Express h(x) in the form a x b c where a, b and c are integers.

Hence find the inverse function h–1 in the form h −1 : x ↦ ...