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

Find the Lowest Common Multiple (LCM) of 60 and 135

Show your working clearly.

The nth term of a sequence is given by 9ní

Determine whether 214 is a term of this sequence.

Show your working clearly.

Here are four numbers written in order of size.

w            x 24

The range of the four numbers is 18

The median of the four numbers is 10

Find the value of w and the value of x.

w = ......................................................

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

Diagram NOT

8 cm

accurately drawn

12 cm

The diagram shows a right circular cylinder of radius 8 cm and height 12 cm.

Calculate the volume, in cm³ to the nearest cm³, of the cylinder.

...................................................... cm³

Solve 2

3

= 9

5

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

Q = cðíc

Work out the value of Q when c í

Q = ......................................................

Without using a calculator and showing all your working, work out

2 3

4$\div$11

12

Give your answer in its simplest form.

B

Diagram NOT

accurately drawn

O

A

x

132°

D

C

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

Angle ADC = 132°

Calculate, in degrees, the size of angle x.

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

y = 4x3í 7

2x

Find d

y

d

x

d

y

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

d

Given that a is a positive integer, expand and simplify fully

(

)

a

a

a

a

5

20

5

A

Diagram NOT

accurately drawn

FP

C

P

4 cm

D

5 cm

B

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

The chord AB intersects the chord CD at P.

AP FP      PB = 5 cm PD = 4 cm

Calculate, in cm, the length of CP.

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

y

x = 1



6

5

4

y = 1

2 x

3

2

1

O

x

1

2

3

4

5

6



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

A motorbike was bought for £8600

The motorbike depreciated in value by 20% in the first year after it was bought

and by 15% in each of the following years.

Find the value of the motorbike exactly 3 years after it was bought.

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

$A = \begin{pmatrix} 4 & 3 \\ 2 & -1 \end{pmatrix} \quad B = \begin{pmatrix} 4 & x \\ 2y & 7 \end{pmatrix}$

Given that $5A + nB = \begin{pmatrix} 8 & 27 \\ 1 & -26 \end{pmatrix}$ where $n$ is an integer,

find the value of $n$, the value of $x$ and the value of $y$.

$n = ......................................................$

$x = ......................................................$

$y = ......................................................$

x u 105 + y u 103 = k u 105

Express k in terms of x and y.

Give your answer in its simplest form.

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

Calculate (8.5 u 1064) u (4 u 1068)

Give your answer in standard form.

C

B

D

A

E

The diagram shows triangle ACE.

The point B on CA and the point D on CE are such that BD is parallel to AE.

BD FPWRVLJQLILFDQWILJXUHV

AE = 9.3 cm to 2 significant figures.

Area of BCD = 15.4 cm² to 3 significant figures.

Calculate the upper bound, to 3 significant figures, for the area of ACE.

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

D

A

ƒ

Diagram NOT

B

accurately drawn

x

123°

F

G

E

C

The diagram shows three straight lines ABC, DBE and FECG.

∠ABD ƒDQG∠BEF = 123°

Calculate the size, in degrees, of angle x.

Give a reason for each stage of your working.

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

Martin, Jonas and Suzy are three art students.

Martin has x crayons.

Jonas has three times as many crayons as Martin.



6X]\KDVIHZHUFUD\RQVWKDQ-RQDV

These three students have a total of 56 crayons.

Use all this information to write down an equation in x.

Martin, Jonas and Suzy are three art students.

Martin has x crayons.

Jonas has three times as many crayons as Martin.



6X]\KDVIHZHUFUD\RQVWKDQ-RQDV

These three students have a total of 56 crayons.

Find the number of crayons Suzy has.

The sum of the interior angles of a regular polygon is 2700°.

Calculate the size, in degrees to one decimal place, of each interior angle of the regular polygon.

A

B

(í

2 ) cm

D

C

The diagram shows rectangle ABCD.

AD = BC = (í

2 ) cm

Area of ABCD = 3(5

2 í) cm²

2 ) cm

Show that the length of AB can be written in the form (a + b

where a and b are integers to be found.

Show your working clearly.

Solve the simultaneous equations

3x + 4y = 4.5

2x - 3y = 11.5

Show clear algebraic working.

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

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

A

Diagram NOT

accurately drawn

D

E

B

C

ABC is an isosceles triangle with AB = AC.

D and E are the midpoints of the sides AB and AC respectively.

Prove that triangles EBC and DCB are congruent.

Given that 27

y = 32x$\times$3x + 1

9

find an expression for y in terms of x.

Give your answer in its simplest form.

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

The scale drawing shows the positions of two posts, A and B.

A third post, C, is equidistant from A and B.

Using ruler and compasses only, construct the locus of points that are equidistant

from A and B.

Given that C is also on a bearing of 250° from B,

The scale drawing shows the positions of two posts, A and B.

A third post, C, is equidistant from A and B.

find and mark the position of C on the scale drawing with a cross (×).

Label the cross C.

The scale drawing shows the positions of two posts, A and B.

A third post, C, is equidistant from A and B.

Find by measurement from the scale drawing, the distance, in metres to the nearest

metre, of C from A.

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

The line L1 has equation 5x + 4y = 16

The line L2 is parallel to L1 and passes through the point with coordinates (8, 15)

L2 crosses the x-axis at the point A and the y-axis at the point B.

Calculate the length, to the nearest whole number, of AB.

Use the factor theorem to show that (2xíLVDIDFWRURIx3 + 23x2íxí

x

x

x

Hence, solve 6

23

−

5

−

4

3

2

0

=

x

2

−

1

Show clear algebraic working.

The diagram shows quadrilateral ABCD.

A

Diagram NOT

FP

accurately drawn

B

128°

85°

D

9 cm

6.4 cm

C

AB FP      BC = 9 cm CD = 6.4 cm

‘
ABC = 128° ‘
ADC = 85°

Calculate the area, in cm² to 3 significant figures, of quadrilateral ABCD.

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

The table below gives information about the lengths of time, in minutes, that 75 cars were parked in a car park on Sunday.

Calculate an estimate for the mean length of time, in minutes to one decimal place, that the cars were parked in the car park on Sunday.

The incomplete table and incomplete histogram give information about the lengths of time, in minutes, that 132 cars were parked in the car park on Monday.

Complete the histogram and the table.

Given that P is inversely proportional to the square of w and that P = 16 when w = 5

find the value of P when w = 12.5

P = ......................................................

Given also that P is inversely proportional to y and that P ZKHQy = 4

Given that P is inversely proportional to the square of w and that P = 16 when w = 5

find the value of y when w = 2

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