June 2022 · Paper 1R (4MB1/01R) (Edexcel IGCSE Maths): Exam Questions

Calculate the value of

−

12 3

9 91

.

.

Give your answer as a decimal to 5 significant figures.

The nth term of a sequence is given by 7 - 4n

Determine whether –123 is a term of this sequence.

Show your working clearly.

N

Diagram NOT

accurately drawn

133°

A

N

x°

C

B

The diagram shows the position of two ports, A and B, and the position of a ship C

The bearing of port B from port A is 133°

Given that C is due west of B

calculate the value of x

x = .......................................................

Without using a calculator and showing all your working, calculate

35

2 7

×

9

10

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

………………………

Make h the subject of 2(h - 6) = 4g + 2

Solve the inequality 3 - 2x < 5 + 6x

Here is a list of six numbers.

$\pi$

20

4

2

5

18

4

−

3

$\pi$

9

4

2

2

5

3

Write down the two numbers in the list that are natural numbers.

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

8 cm

Diagram NOT

accurately drawn

10 cm

The diagram shows a right circular solid cylinder of diameter 8 cm and height 10 cm.

3, the volume of the cylinder.

Calculate, to the nearest cm

3

....................................................... cm

1 second = 10

14 microseconds into hours.

Change 4.5 × 10

Give your answer in standard form.

....................................................... hours

Patrick sells a painting for 557.75 euros.

He makes a profit of 15% on the price he paid for the painting.

Calculate the price Patrick paid for the painting.

....................................................... euros

Here are the marks that Srinjoy scored in each of 7 tests.

21 24 25 18 28 25 20

Write down the mode of these 7 marks.

After taking an 8th test, Srinjoy’s mean mark for all 8 tests is 22.5

Here are the marks that Srinjoy scored in each of 7 tests.

21 24 25 18 28 25 20

Calculate his mark for the 8th test.

Find the value of 12xy - 15y when x = 2 and y = –3

Factorise completely 12xy - 15y

The diagram shows a trapezium.

Diagram NOT

(2x - 1) cm

accurately drawn

4 cm

(3x + 2) cm

The lengths of the parallel sides of the trapezium are (3x + 2) cm and (2x - 1) cm.

The height of the trapezium is 4 cm.

2

Given that the area of the trapezium is 28 cm

find the value of x

x = .......................................................

B

A

C

The diagram shows a farmer’s field that is in the shape of a ΔABC

The farmer is going to grow carrots in the region of the field which is

•

nearer to A than to B

and

•

nearer to AB than to AC

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

region T inside the field in which the farmer is going to grow his carrots.

Shade the region and label it T

y

y - x = 2

Diagram NOT

accurately drawn

R

x

O

3x + y = 15

The diagram shows part of the shaded infinite region R which has three straight

boundary lines.

Write down the three inequalities that define the shaded region R

B

Diagram NOT

accurately drawn

C

A

D

F

E

The diagram shows the square ACEF and the equilateral triangles ABC and CDE

Prove that ΔECB is congruent to ΔACD

Without using a calculator and showing all your working, express

−

4

2 3

3

1

in the form a 3 + b where a and b are integers.

Diagram NOT

accurately drawn

O

S

R

118°

P

Q

In the diagram, P, Q and R are points on a circle with centre O

PRS is a straight line and ∠QRS = 118°

Calculate, in degrees, the size of ∠OQP

Give reasons for each stage of your working.

∠OQP = .......................................................°

C

Diagram NOT

accurately drawn

6 m

24°

B

O

D

A

In the diagram A, B and C are points on a circle with centre O and radius 6 m.

AD and CD are tangents to the circle.

OBD is a straight line such that ∠ODC = 24°

Calculate the perimeter, in m to 3 significant figures, of the shaded region.

....................................................... m

The incomplete table and incomplete histogram give information about the length of time,

in minutes, that each of 105 runners took to complete a half marathon.

None of the 105 runners took longer than 190 minutes to complete the half marathon.

Use this information and the information in the histogram to complete the table.

The incomplete table and incomplete histogram give information about the length of time,

in minutes, that each of 105 runners took to complete a half marathon.

None of the 105 runners took longer than 190 minutes to complete the half marathon.

Use the information in the table to complete the histogram.

Frequency

density

0

0

20

40

60

80

100

120

140

160

180

200

Time (minutes)

The points A and B are such that the coordinates of A are (3, –2) and BA

4

Find the coordinates of point B

(.......................... , ..........................)

The point C has coordinates (m, n) where m > 3

→½ = 5

Given that ½AC

The points A and B are such that the coordinates of A are (3, –2) and BA

4

find an expression for m in terms of n

m = .......................................................

G

H

Diagram NOT

accurately drawn

F

E

6

x cm

−

3

8

B

C

x

18

cm

x

−

1

2

3 cm

D

A

The diagram shows cuboid ABCDEFGH in which

6

x

18

AD = 3 cm DC =

cm AH =

x cm

−

3

8

x

−

1

2

where 0 < x < 3

8

k

Given that the length of CH is L cm, where L =

and k is a positive integer,

x

x

−

−

(

3

8

)(

1

2

)

find the value of k

Show your working clearly.

k = .......................................................

Given that x = 0.3

3, of the cuboid.

G

H

Diagram NOT

accurately drawn

F

E

6

x cm

−

3

8

B

C

x

18

cm

x

−

1

2

3 cm

D

A

The diagram shows cuboid ABCDEFGH in which

6

x

18

AD = 3 cm DC =

cm AH =

x cm

−

3

8

x

−

1

2

where 0 < x < 3

8

k

Given that the length of CH is L cm, where L =

and k is a positive integer,

x

x

−

−

(

3

8

)(

1

2

)

calculate the volume, in cm

3

....................................................... cm

A dice has eight faces numbered 1, 2, 3, 4, 5, 6, 7 and 8

The table shows information about the probability that, when the dice is rolled once, it

will land on each of the possible numbers.

When the dice is rolled once, the probability that the dice will land on the number 5 is 0.2

The dice is rolled 250 times.

Calculate an estimate for the number of times the dice will land on an odd number.

A

B

=

−

2

2

3

4

Find

A - B

A

B

=

−

2

2

3

4

Find

3A + 2B

The matrix C is such that A = BC

A

B

=

−

2

2

3

4

Find

Find C

C =

A

Diagram NOT

accurately drawn

B

5 cm

x cm

E

15 cm

y cm

120°

D

7x cm

C

A, B, C and D are four points on a circle.

The chord AC intersects the chord BD at E

AE = 5 cm EC = y cm DE = 15 cm EB = x cm DC = 7x cm ∠DEC = 120°

Find the value of x and the value of y

Show your working clearly.

x = .......................................................

y = .......................................................

Given that

area of ΔABE : area of ΔCDE = 1 : n

A

Diagram NOT

accurately drawn

B

5 cm

x cm

E

15 cm

y cm

120°

D

7x cm

C

A, B, C and D are four points on a circle.

The chord AC intersects the chord BD at E

AE = 5 cm EC = y cm DE = 15 cm EB = x cm DC = 7x cm ∠DEC = 120°

find the value of n

n = .......................................................

The equation of a curve C is y = (kx

The point A on C has x coordinate equal to –1

The tangent to C at A has gradient equal to –8

Show that the x coordinates of the stationary points on C satisfy the equation

2 + 6x - 1 = 0

3x

2 + 6x - 1 in the form a(x + b)

2 + c where a, b and c are integers.

The equation of a curve C is y = (kx

The point A on C has x coordinate equal to –1

The tangent to C at A has gradient equal to –8

Write 3x

The equation of a curve C is y = (kx

The point A on C has x coordinate equal to –1

The tangent to C at A has gradient equal to –8

Hence find the exact x coordinate of each of the stationary points on C

Show your working clearly.

x is directly proportional to w

y is inversely proportional to

w

y = 2 when x = 1

4

p = q

Find the value of p and the value of q such that xy

p = .......................................................

q = .......................................................