June 2023 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions

Write down two of the following six numbers that are irrational numbers.

ϖ

3

36 0 2.

3 −1

18

2

............................... , ...............................



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

when k = − 4

k

−

5

2



Using ruler and compasses only and showing all your construction lines, construct the

perpendicular bisector of AB

A

B

Diagram NOT

A

accurately drawn

D

B

C

E

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



Solve the inequality 4

3

6

5



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







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

2 3

3 5

5

7

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



Make x the subject of y

4



Calculate

2

10

4

10

180

182

Give your answer in standard form.



Factorise fully 8

ab

b

28 2



y

y

Factorise 5

9

18

2



A

E

B

Diagram NOT

accurately drawn

D

C

The diagram shows the trapezium ABCD

E is the midpoint of AB and DEC is an equilateral triangle.

Prove that ΔAED is congruent to ΔBEC

Without using a calculator and showing all your working express

−

3 180

2 245

a where a is an integer.

in the form



The position vector of A is

3





8

The point B has coordinates ( 2, − 4)

→½

Find ½AB

→½ = ..............................................................

½AB



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

0

90

100

110

120

130

80

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.

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 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

y is directly proportional to

w

Given that y = 10 when w = 25

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



The curve C has equation y

5 where b is a constant.

x

2

x

C has a stationary point when x = 1.5

Find the value of b

b = ..............................................................



E

F

H

C

A

B

A 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



Express

 as a single fraction in its simplest form.

 





y

y

y

y

3

3

4

6

7

20

2

Show clear algebraic working.



9.8 m

A

B

D

C

20.4 m

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

..............................................................°



A

1

4

Find

A − B













A

1

4

Find

5A + 2B













A

1

4

Find

B−1













Solve the simultaneous equations

x

y

3

4

25

x

y

26

2

2

Show clear algebraic working.



Diagram NOT

A

B

accurately drawn

3.8 cm

C

H

O

4.5 cm

D

5 cm

E

G

F

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



C

Diagram NOT

accurately drawn

E

F

A

B

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