June 2019 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions

Write 8693 to 2 significant figures.

Write 0.0374 to 2 significant figures.

Find the Lowest Common Multiple (LCM) of 18, 30 and 48

Show your working clearly.

A pattern is made with white squares and shaded squares.

Shade one more square to make a pattern with exactly 1 line of symmetry.

A pattern is made with white squares and shaded squares.

Shade one more square to make a pattern with rotational symmetry of order 2

Work out 2 1

÷

6

4

Show your working clearly and give your answer as a fraction in its simplest form.

Given that y

=

2

x

−

2

x

find d

y

d

x

d

y

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

d

A straight line passes through the points with coordinates (2, –10) and (–3, 5)

Calculate the gradient of the line.

Expand and simplify (4x - 5)(2x + 3)

The nth term of a sequence is given by 24 - 5n

Find the sum of the 3rd term and the 10th term of the sequence.

Each exterior angle of a regular polygon is 9°

Calculate the number of sides of the polygon.

In a sale, the price of a book is reduced by 15%

The price of the book before the sale was £7.60

Calculate the sale price of the book.

£ .......................................................

Simplify 2x2 q 3x5

Simplify (4a2b3)3

The function f is defined for all values of x by f : x 6 x2 - 2

Write down the range of f.

12

The function g is given by g : x 6

x

3

4

where

≠

−

3

x

4

The function f is defined for all values of x by f : x 6 x2 - 2

Calculate fg

Find the value of 3c2 when c = –8

Factorise completely 3c2 + 6c

Simplify fully 3

−

8

−

3

2

x

4

−

36

A

Diagram NOT

accurately drawn

R

C

P

Q

B

The diagram shows ABC.

APQR is a parallelogram where P is the midpoint of AB, Q is the midpoint of BC and

R is the midpoint of AC.

Prove that PBQ and RQC are congruent.

Here is a biased spinner labelled 1, 2, 3, 4, 5, 6

1

6

2

5

3

4

The table below shows information about the probability that when the spinner is spun

once it will land on each of the numbers 1, 2, 3, 4, 5, 6

Abdul is going to spin the spinner 300 times.

Calculate an estimate for the number of times the spinner will land on number 1

Here is a biased spinner labelled 1, 2, 3, 4, 5, 6

1

6

2

5

3

4

The table below shows information about the probability that when the spinner is spun

once it will land on each of the numbers 1, 2, 3, 4, 5, 6

Abdul is going to spin the spinner 300 times.

Calculate the probability that when the spinner is spun once it lands on number 6

Here is ABC.

C

6 cm

30°

2 cm

A

B

Calculate the area, in cm², of ABC.

....................................................cm²

Here is PQR.

Q

12 cm

x°

P

R

4 cm

Here is ABC.

C

Diagram NOT

accurately drawn

6 cm

30°

2 cm

A

B

Calculate the value, to 3 significant figures, of x.

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

There are 9 marbles in bag A and 11 marbles in bag B.

In bag A, there are 3 red marbles, 2 yellow marbles and 4 green marbles.

In bag B, there are 2 red marbles, 4 yellow marbles and 5 purple marbles.

Ted takes at random one marble from bag A and one marble from bag B.

Calculate the probability that the two marbles are not the same colour.

The period, T seconds, of a simple pendulum of length L metres is given by the formula

L

= 6 28

.

T

g

L = 1.32 to 3 significant figures.

g = 9.8 to 2 significant figures.

Calculate the upper bound, to 3 significant figures, of T.

The incomplete histogram and the incomplete table give information about the time taken, in

minutes, for some students to each complete a piece of homework. No student took less than

10 minutes to complete the homework and no student took longer than 60 minutes to complete

the homework.

Complete the histogram and the table.

Make x the subject of

2

x

x

y

−

5

=

−

3

3

w

2

y

Give your answer as a single fraction.

E

C

D

F

2.3 m

0.5 m

A

B

1.2 m

ABCDEF is a right triangular prism in which

AB = 1.2 m BC = 2.3 m AF = 0.5 m ∠FAB = 90°

Calculate the total surface area, in m², of the prism.

....................................................m²

In a survey, 60 students were asked whether they study any of History (H),

Geography (G) or Latin (L).

Of these students

27 study History

25 study Geography

18 study Latin

13 study both History and Latin

2 study both Geography and Latin

8 study History only

No students study History and Geography and Latin.

Use the information to complete the Venn diagram.

E

H

G

L

In a survey, 60 students were asked whether they study any of History (H),

Geography (G) or Latin (L).

Of these students

27 study History

25 study Geography

18 study Latin

13 study both History and Latin

2 study both Geography and Latin

8 study History only

No students study History and Geography and Latin.

Find the number of students who study History but not Latin.

In a survey, 60 students were asked whether they study any of History (H),

Geography (G) or Latin (L).

Of these students

27 study History

25 study Geography

18 study Latin

13 study both History and Latin

2 study both Geography and Latin

8 study History only

No students study History and Geography and Latin.

Find n(Hމ ˆ
[L ‰ G])

Y

Z

–3a + 5b

X

2a + 3b

O

→ = 2a + 3b and OY

→ = –3a + 5b

The diagram shows OXY where OX

→.

Find and simplify an expression, in terms of a and b, for YX

→ = −

2

35

The point Z on YX is such that OZ

a

b

9

9

Y

Z

–3a + 5b

X

2a + 3b

O

→ = 2a + 3b and OY

→ = –3a + 5b

The diagram shows OXY where OX

→.

Calculate, in its simplest form, the ratio of YZ : ZX

A

B

Diagram NOT

accurately drawn

62°

C

126°

O

D

In the diagram, A, B, C and D are points on a circle, centre O.

∠CBO = 62° and ∠BCD = 126°

Find the size, in degrees, of ∠BAD.

Give a reason for your answer.

∠BAD = .......................................................°

A

B

Diagram NOT

accurately drawn

62°

C

126°

O

D

In the diagram, A, B, C and D are points on a circle, centre O.

∠CBO = 62° and ∠BCD = 126°

Find the size, in degrees, of ∠ODC.

Give reasons for your working.

∠ODC = .......................................................°

$A = \begin{pmatrix} 2 & 3 \\ -5 & 1 \end{pmatrix} \quad B = \begin{pmatrix} 4 & k \\ 1 & -1 \end{pmatrix}$

The determinant of the matrix $A^2 - AB$ is equal to $3k + 28$

Find the value of $k$.

$k = .......................................................$

2x cm

A

B

The diagram shows a semicircle, with diameter AB, where AB = 2x cm.

The diagram also shows a circle, which is the circle with the greatest possible radius that

can be drawn inside the semicircle.

The perimeter of the shaded region is P cm and the area of the shaded region is A cm².

Given that P = A, find an expression for x in terms of ʌ

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

A 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 = –3t3 + 6t2 + kt + 4 t . 0

At time t seconds, the velocity of P is v m/s such that v = 9 when t = 2

Show that k = 21

Particle P comes to instantaneous rest at the point A.

A 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 = –3t3 + 6t2 + kt + 4 t . 0

At time t seconds, the velocity of P is v m/s such that v = 9 when t = 2

Using k = 21, find the value of t when P is at A.

t = .......................................................

A 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 = –3t3 + 6t2 + kt + 4 t . 0

At time t seconds, the velocity of P is v m/s such that v = 9 when t = 2

Find, to the nearest metre, the distance OA.

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