June 2021 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions

hour 30 minutes

Time

reference

Mathematics B

PAPER 1

You must have: Ruler graduated in centimetres and millimetres,

Total Marks

protractor, pair of compasses, pen, HB pencil, eraser, calculator.

Tracing paper may be used.

Instructions

• Use black ink or ball-point pen.

• Fill in the boxes at the top of this page with your name,

centre number and candidate number.

• Answer all questions.

• Answer the questions in the spaces provided

– there may be more space than you need.

• Calculators may be used.

Information

• The total mark for this paper is 100.

• The marks for each question are shown in brackets

– use this as a guide as to how much time to spend on each question.

Advice

• Read each question carefully before you start to answer it.

• Check your answers if you have time at the end.

• Without sufficient working, correct answers may be awarded no marks.

• Good luck with your examination.

P65920A

Answer all TWENTY SEVEN questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1 Factorise fully 8 xy 2 − 18 xy

A pattern is made using a four by four grid with both grey squares and white squares.

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

A pattern is made using a four by four grid with both grey squares and white squares.

Shade two more squares to make a pattern that has rotational symmetry of order 2

Make x the subject of y = t x + 4 y 2

Each time Arhan plays a game of chess, the probability that he does not win is 0.64

Arhan plays 75 games of chess.

Calculate an estimate for the number of games he wins.

Solve the simultaneous equations 4 x + 4 y = 18

4 x + 6 y = 35

Show clear algebraic working.

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

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

B

accurately drawn

25 cm

C

50 cm

35 cm

A

D

The diagram shows a quadrilateral ABCD in which

BC = 25 cm AB = 50 cm CD = 35 cm angle BAD = angle CDA = 90°

Calculate the perimeter, in cm, of quadrilateral ABCD.

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

Michael’s age is n years.

Navtej’s age is three times Michael’s age.

Indre is 8 years younger than Navtej and 20 years older than Michael.

Find the value of n.

Show clear algebraic working.

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

B

C

A

D

The diagram shows the rectangle ABCD.

The region R consists of all the points inside the rectangle that are

greater than 4 cm from B,

closer to BA than to CD.

Using ruler and compasses only and showing all your construction lines, show, by

shading, the region R.

Label the region R.

A shopkeeper sells a radio for $27

For this selling price, the shopkeeper makes a profit of 8%

Calculate the selling price of the radio so that the shopkeeper would make a profit of 35%

$ .......................................................

The integer N is greater than 120

When N is divided by 28 the remainder is 3

When N is divided by 120 the remainder is 3

Find the least value of N.

You must show your working.

Greg is organising a day out for his students.

Each of his students has to choose to take part in at least one activity chosen from

rock climbing (R) and canoeing (C ).

The cost for rock climbing is $42

The cost for canoeing is $34

The total cost for all the activities chosen by the students is $3702

Given that n(R ∩ C ' ) = 32 and that n(R ∪ C ) = 68

find the number of Greg’s students who chose to take part in both rock climbing and canoeing.

Write as a single fraction in its simplest form

x

x

−

6

8

2

−

3

4

Show clear algebraic working.

A

accurately drawn

E

B

D

C

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

BED and AEC are straight lines.

Prove that triangle ABE is similar to triangle DCE.

E

Diagram NOT

accurately drawn

D

A

X

C

B

The diagram shows a square based right pyramid ABCDE. The point X is the centre of

the base so that the point E is vertically above X.

EX = 15 cm AB = 8 cm

Calculate the size, in degrees to 3 significant figures, of the acute angle between

AE and AX.

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

Without using a calculator and showing all your working, express

−

4

12

4

12

in the form a −

b where a and b are integers.

Simplify fully 5

a b

2

1

(

)

x y

Simplify fully 9

4

2

2

x y

3

−

2

4

Find the set of values of x for which −2x + 4 ≤ 3x − 6 < 2x + 2

On the number line below, represent the set of values of x for

which −2x + 4 ≤ 3x − 6 < 2x + 2

x

0

1

2

3

4

5

6

7

8

9

10

B

Diagram NOT

accurately drawn

25 m

D

A

C

20 m

In the diagram, AB represents a vertical cliff of height 25 m.

The points C and D are buoys on the surface of the sea so that CDA is a horizontal

straight line.

The angle of elevation of B from C is 33° and CD = 20 m.

Calculate the size, in degrees to 3 significant figures, of the angle of depression of D from B.

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

A

D

G

Diagram NOT

accurately drawn

E

F

B

C

ABCD is a rectangle in which AB = x 3 cm and BC = x cm.

EFG is an equilateral triangle with sides of length y cm.

The area of rectangle ABCD is equal to the area of triangle EFG.

Find the ratio

the perimeter of the rectangle ABCD : the perimeter of the triangle EFG.

(

) : b where a and b are integers.

Give your answer in the form a

b

A solid right circular cone is made of brass.

The mass of the cone is 5080 grams, to the nearest 10 grams.

The radius of the base of the cone is 8.5 cm, to 2 significant figures.

The density of the brass is 8.73 g / cm³, to 3 significant figures.

Given that

mass

=

density

volume

and taking the value of $\pi$ as 3.142

calculate the upper bound of the height of the cone.

Give your answer to one decimal place.

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

A and B are two mathematically similar containers.

Container A has surface area of 1550 mm² and container B has surface area of 10 478 mm²

Given that

volume of container B − volume of container A = 62 160 mm³

calculate the volume, in mm³, of container A.

....................................................... mm³

A

B

Diagram NOT

C

accurately drawn

D

E

P

F

G

H

In the diagram AB, BC, CD, DE, EF, FG and GH are seven sides of a regular n-sided polygon.

ABP and HGP are straight lines.

The size of each exterior angle of the polygon is x°

The size of each interior angle of the polygon is 7 x°

Calculate the size of ∠GPB

Show your working clearly.

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

In a region of a country, two types of eagle, type A and type B, can be found.

In 2003 the ratio of the number of type A eagles to the number of type B eagles was 2 : 5

In 2015 the ratio of the number of type A eagles to the number of type B eagles was 4 : 3

From 2003 to 2015, the number of type A eagles had increased by 16

From 2003 to 2015, the number of type B eagles had decreased by 107

Calculate the number of type B eagles in this region in 2015

One solution of the equation 6x3 + 17x2 − 5x − 6 = 0 is −1

2

Find the other 2 solutions of the equation.

Show clear algebraic working.

A particle P is moving along a straight line.

At time t seconds, t ≥ 0, the displacement, x metres, of P from a fixed point O on the line

is given by

x = k + 6t − 2kt2

where k is a constant.

When t = 0, P is at the point A on the line.

When P is at the point B on the line, P is instantaneously at rest.

Given that AB = 0.9 m, calculate the value of k.

Show your working clearly.

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

There are 30 students in a class.

All the students in the class take a test.

Here are the marks in the test for the 12 girls in the class.

35 42 67 83 21 24 56 32 69 98 x 49

where x > 70

Find the median of the girls’ marks.

The mean mark for the 12 girls is 54.5

There are 30 students in a class.

All the students in the class take a test.

Here are the marks in the test for the 12 girls in the class.

35 42 67 83 21 24 56 32 69 98 x 49

where x > 70

Find the value of x.

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

The mean mark for the boys is 56

There are 30 students in a class.

All the students in the class take a test.

Here are the marks in the test for the 12 girls in the class.

35 42 67 83 21 24 56 32 69 98 x 49

where x > 70

Calculate the mean mark for the 30 students in the class.

A =

−

2

2

−

Given that the inverse of matrix A is 1 2

1

−

a

2

3

find the value of a.

a = .......................................................

−

9

11

A =

−

2

2

−

Hence find the matrix B such that ABA−1 =

−

8

11