June 2018 · Paper 1R (4MB1/01R) (Edexcel IGCSE Maths): Exam Questions

Without using a calculator and showing all your working, calculate

13

2 7

×

5

8

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

Each interior angle of a regular polygon is 168°

Calculate the number of sides of the polygon.

The number of people living in Delhi is $1.7 \times 10^7$

The land area of Delhi is $1.5 \times 10^3$ square kilometres.

Calculate the average number of people per square kilometre living in Delhi.

Give your answer in standard form to 2 significant figures.

Given that y

=

−

x

3

x

find d

y

d

x

d

y

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

d

Without using your calculator, and showing all your working,

12

where a and b are integers.

express

in the form a

b

5

3

−

5

B

A

C

D

F

E

63°

G

In the diagram, ABC is parallel to DEF.

BEGLVDVWUDLJKWOLQHDQGǻEFG is isosceles with EF = EG and ∠EGF = 63°

Find the size, in degrees, of ∠ABE.

∠ABE = ....................................................................°

Solve the simultaneous equations

4

x

−

y

=

4

7

10

2

x

y

= −

2

Show clear algebraic working.

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

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

When a biased coin is thrown once, the probability that it lands Heads is 0.6

The coin is thrown 4 times.

Find the probability that the coin lands Heads exactly 3 times.

Solve 3

−

2

x

=

2

−

3

5

Show clear algebraic working.

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

X = 2a + b

X = 19.4 to 1 decimal place.

a = 2.4 to 1 decimal place.

Calculate the upper bound for the value of b.

Show your working clearly.

Make x the subject of x

a

4

=

3

c

−

x

3

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

Given that 6 q 53k + 4 = 750

find the exact value of k.

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

A

B

E

C

D

9.6 cm

The diagram shows triangle ACD and triangle ABE.

The point B is on AC and the point E is on AD such that BE is parallel to CD.

CD = 9.6 cm

Area of triangle ABE = 27 cm²

Area of trapezium BCDE = 21 cm²

Calculate the length, in cm, of BE.

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

y

x

On the grid, draw and label the straight line with equation

y = 2

y

x

x + y = 5

y

x

y = 2x + 1

y

x

On the grid, show by shading, the region defined by the inequalities

y . 2 and x + y - 5 and y - 2x + 1

Label the region R.

Barry and Carlos share $120 in the ratio 3 : 2

Barry gives 1

5 of his share to Mary.

Carlos gives 35% of his share to Mary.

Express the total amount that Barry and Carlos give to Mary as a fraction of the $120

Give your answer in its simplest form.

Simplify 2w4y3 q 3wy5

1

(

)

6

3

Simplify 27

a c

3

A and B are points on the circumference of a circle, centre O.

CBD is the tangent to the circle at B.

CAO is a straight line.

∠ABC = 38°

Giving your reasons, find the size, in degrees, of ∠ACB.

∠ACB = ...................................................................°

$\overrightarrow{OA} = \binom{4}{-2}$ and $\overrightarrow{OB} = \binom{-2}{6}$

Find $\overrightarrow{AB}$ as a column vector.

$\overrightarrow{OA} = \binom{4}{-2}$ and $\overrightarrow{OB} = \binom{-2}{6}$

Calculate the modulus of $\overrightarrow{AB}$.

Write $(3x+2) \div \left(\dfrac{3x^2-7x-6}{5}\right) - \dfrac{5}{x+3}$ as a single fraction in its simplest form.

Show clear algebraic working.

A

C

Diagram NOT

accurately drawn

O

B

The diagram shows a trapezium OACB in which

→ = a, AC

→

→ = 5b

= 3b, OB

OA

The point P lies on OC such that OP : PC = 5 : 1

D is the point such that OBD is a straight line and APD is a straight line.

Prove that OB : OD = 1 : 3

10 cm

18 cm

9 cm

15 cm

The diagram shows a right prism of length 9 cm.

A cross section of the prism is a trapezium in which the parallel sides are of

length 18 cm and 10 cm and the distance between these parallel sides is 15 cm.

Calculate the total surface area, in cm², of the prism.

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

T varies inversely as the square of y.

T = 0.32 when y = 5

Find a formula for T in terms of y.

T varies inversely as the square of y.

T = 0.32 when y = 5

Find the positive value of y when T = 200

Write x2 + 10x - 7 in the form (x + p)2 + q

Hence solve the equation x2 + 10x - 7 = 0

Give your answer in the form a

where a and b are integers.

±

b

Show your working clearly.

(x + 2) is a factor of x3 - 3x2 + ax + 12 where a is a constant.

Show that a = –4

(x + 2) is a factor of x3 - 3x2 + ax + 12 where a is a constant.

Factorise completely x3 - 3x2 - 4x + 12

A box of toy bricks contains only red bricks, blue bricks, green bricks, yellow bricks and

orange bricks.

A brick is taken at random from the box.

The table gives information about the probabilities that the brick is red or is blue or is

green or is yellow or is orange.

Calculate the value of x.

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

There are 39 blue bricks in the box.

A box of toy bricks contains only red bricks, blue bricks, green bricks, yellow bricks and

orange bricks.

A brick is taken at random from the box.

The table gives information about the probabilities that the brick is red or is blue or is

green or is yellow or is orange.

Find the number of yellow bricks in the box.

Alvaro draws a pie chart to show information about the number of bricks of each colour.

A box of toy bricks contains only red bricks, blue bricks, green bricks, yellow bricks and

orange bricks.

A brick is taken at random from the box.

The table gives information about the probabilities that the brick is red or is blue or is

green or is yellow or is orange.

Calculate the size of the angle, in degrees, of the sector for red bricks.

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

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

Find $3\mathbf{A} + 2\mathbf{B}$

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

Find $\mathbf{AB}$

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

Find $\mathbf{CB}$

Diagram NOT

A

accurately drawn

7 cm

B

9 cm

O

C

6 cm

D

E

F

In the diagram, ABDFE is a circle, centre O and radius 6 cm.

ABC and EDC are straight lines.

The arc EFD is of length 7

2 $\pi$ cm.

Calculate the length, in cm to 3 significant figures, of DC.

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