Edexcel IGCSE Maths B Paper 2 June 2022 question paper 4MB1/02R

The Venn diagram shows information about the numbers of students in a school who study History (H), Music (M) and Geography (G).

Find the number of students who study Geography.

Find the number of students who study exactly two of the subjects History, Music and Geography.

On the Venn diagram above, shade the region that represents the set H G

E is the universal set and A and B are two sets such that

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A B = {multiples of 3}

A B = {2, 4, 8, 10}

(A B) = {1, 7}

Use the information about the sets E, A and B to complete the Venn diagram below.

Find n(B)

Figure 1 shows part of a regular 16‑sided polygon in which PA and AB are two sides. Figure 1 also shows the isosceles triangle ABC in which AB = CB = 5 cm.

PAC is a straight line.

Calculate the length, in cm to 3 significant figures, of AC.

Arup collects information about the time delay, in minutes, of some trains. He is going to draw a pie chart for his results.

The incomplete table below gives some information about his results together with the size, in degrees, of the angle of each of three sectors in his pie chart.

Time delay (t minutes)	Frequency	Angle (in degrees)
1 t 5	42	168
5 t 10		92
10 t 20	15
20 t 25
25 t 40	2	8

Complete the table.

Calculate an estimate, in minutes to 3 significant figures, for the mean time delay of these trains.

Triangles A, B, C and D are drawn on the grid above.

Describe fully the single transformation that maps

triangle A onto triangle B

triangle A onto triangle C

triangle A onto triangle D

Triangle E is the image of triangle A under an enlargement with scale factor –2 and centre of enlargement (4, 0)

On the grid, draw and label triangle E

Dan is going to play one game of squash and one game of chess against his friend. The probability that Dan will win the game of squash is

The probability that Dan will win the game of chess is

Complete the probability tree diagram.

Find the probability that Dan will win exactly one game.

Given that Dan won exactly one game,

calculate the probability that he won his game of squash.

In 2018, a badminton club had 460 members.

Of these members,

A were younger than 30

B were aged between 30 and 60 inclusive

C were older than 60

Given that A:B:C = 2: 5: 3

find the total number of members who were aged 30 or older in 2018

In 2018, the annual membership fee for each member who was older than 60 was $65 The annual membership fee for each other member was $135

Calculate the total amount, in $, that the 460 members paid in annual membership fees in 2018

The annual membership fee for each member who was older than 60 in 2019 was 4% greater than the annual membership fee for each member who was older than 60 in 2018

Calculate the annual membership fee for each member who was older than 60 in 2019

The badminton club buys 12 shuttlecocks for a total cost of $5.10

The club then sells the shuttlecocks to members for $0.50 each.

Calculate the percentage profit, to 3 significant figures, made by the club on each shuttlecock that was sold.

Figure 2 shows a badminton net ABCD and two supports for the net.

The badminton net is shaded in the diagram.

Figure 2 gives information about the dimensions of the badminton net. Each measurement is given to the nearest cm.

Calculate the upper bound, in cm², of the area of the net ABCD

A particle P is moving along a straight line through the fixed point O

The speed, v m/s, of P at time t seconds is given by

Complete the table of values for v 2

Give your values of v to 2 decimal places.

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

Using your curve, find an estimate, to one decimal place, for the speed of P when t = 1.75

The acceleration of P at time t seconds where 1 t 5 is a m/s²

Find an expression for a in terms of t

Using your answer to part (d), find the value of t when P has its minimum speed in

Turn over for a spare grid if you need to redraw your curve.

Only use this grid if you need to redraw your curve.

The equation of the straight line L is y = 2 – 3x

Find the exact coordinates of the points where L crosses the coordinate axes.

The functions f and g are defined as

Find g(–2)

Find the values of x for which ff(x) + g(x) = 0

Show your working clearly and give your answer in the form

where a, b and c are integers.

Express the inverse of the composite function fg in the form (fg)^–1:x ...

Figure 3 shows three points A, B and C on a circle with centre O where AOB is a diameter of the circle.

D is the point on AC such that AD:DC = 3: 2

Given that OA → = a and AD → = b

find, in terms of a or b or a and b where appropriate, a simplified expression for (i) AC → (ii) CO
→ (iii) DB →

E is the point such that CEO and DEB are straight lines. → → → →

By considering both AD + DE and AC + CE

find a simplified expression for → AE in terms of a and b

Given that a = 7 cm and b = 6 cm,

calculate the exact area, in cm², of ΔABC

The determinant of matrix A is equal to the determinant of matrix B

Show that k is a root of the equation

Given that f(k) = 2k³ + 5k² – 28k – 15

use the factor theorem to show that (k + 5) is a factor of f(k)

Hence, factorise completely f(k)

The transformation with matrix C, where C is a 22 matrix, is equivalent to the transformation with matrix A followed by the transformation with matrix B

Given that k is positive,

find matrix C

Figure 4 shows a rectangle ABCD and an isosceles triangle EFG with EG = FG

AB = (2x + 3) cm BC = (4x – 8) cm EF = (4x + 2) cm

The perimeter of the rectangle is Pcm and the area of the triangle is Tcm²

Given that P T

find the range of possible values of x

Show your working clearly.