Edexcel IGCSE Maths B Paper 1 June 2022 question paper 4MB1/01

The nth term of a sequence is given by 4n – 12

Write down the first 2 terms of the sequence.

Bronze is made from copper and tin in the ratio of 22: 3 by weight.

Calculate the weight of copper, in kg, needed to make 12.5 kg of bronze.

A pattern on a white grid is made from 6 shaded squares.

Shade exactly 2 more squares so that the 8 shaded squares will make a pattern with rotational symmetry of order 4

Make u the subject of

Without using a calculator and showing all your working, evaluate

Give your answer as a mixed number in its simplest form.

Factorise completely

Inzamam cycles 6.4 km from his home to school.

He leaves home at 07 40 and arrives at school at 08 20

Calculate his average speed, in km/h, for the journey.

Rohan asked each of the students in his school what colour paper they would prefer him to use for their worksheets.

There are 150 students in Rohan’s school.

Using his results, Rohan drew the following accurate pie chart.

Find how many of the 150 students preferred blue paper.

Solve

2(x + 7) = 5 x – 6

Above is a Venn diagram showing the sets , , and E

is the set of natural numbers,

Place each of the following four numbers in the correct place in the above diagram.

4 22

The diagram shows a biased spinner with four colours blue, red, green and yellow.

When the spinner is spun once

• the probability it lands on blue is twice the probability it lands on red

• the probability it lands on yellow is three times the probability it lands on blue

• the probability it lands on green is 0.25

Find the probability the spinner lands on yellow.

Here is a list of four numbers.

Find the median of these four numbers.

Give your answer in standard form.

Using the diagram above, prove that the sum of the angles of triangle ABC is the same as the sum of the angles on the straight line DCE

Give a reason for each stage of your proof.

The numbers A, B, and C are given as products of their prime factors.

= 3⁵7⁴ 1039

Find the Highest Common Factor (HCF) of A, B and C

Exactly one of the three numbers is the square of an integer N

Calculate the value of N

OABC is a sector of a circle, centre O, with AOC = 100

The area of the sector is 27 cm²

Calculate the perimeter, in cm to 3 significant figures, of the sector.

Show your working clearly.

find the exact value of x

The diagram shows triangle ABC

The region R consists of all the points inside the triangle that are closer to C than to B and also closer to AB than to AC

Using ruler and compasses only and showing all your construction lines, construct and show by shading the region R

Label the region R

The diagram above shows the line L, the line with equation y = 2 and the line with equation y = x drawn on a grid.

Find an equation of the line L

Write down the three inequalities that define the region shaded in the diagram.

ABCD is a kite so that the points A, B, C and D lie on a circle with radius 7.5 cm. The diagonals, AC and BD, of the kite intersect at point E, so that AE = 3 cm. The line AEC is a diameter of the circle.

Find the area of the kite ABCD

In a triangle ABC

Calculate, in cm² to 3 significant figures, the smaller of the areas of the two possible triangles ABC

There are 25 sweets in a bag.

n of the sweets are orange.

The rest of the sweets are yellow.

Chana takes a sweet at random from the bag.

She eats the sweet.

Chana takes at random another sweet from the bag.

She eats the sweet.

The probability that Chana eats one orange sweet and one yellow sweet is

Write down the probability that both sweets taken by Chana are the same colour.

Find the possible values of n

Show clear algebraic working.

f(x) = 2x³ + 9x² – 14x – 9

Using the factor theorem, show that (2x – 1) is not a factor of f(x)

where a and b are integers to be found.

Hence find the exact solutions of f(x) = 0

A particle P is moving along a straight line. At time t seconds, the displacement, s metres, of P from a fixed point O on the line is given by

At time T seconds, where T 9, P is at the point A on the line.

At A, particle P instantaneously reverses its direction of motion and moves back towards O

Find the value of T

As P moves from A back towards O, the greatest speed of P is Vm/s

Find the value of V