Unit 3 H Mock Paper

7/18/2019 Unit 3 H Mock Paper

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Edexcel GCSE

Centre Number Candidate Number

Write your name here

Surname Other names

Total Marks

Paper Reference

Turn over

*W41054A0120*W41054A©2011 Edexcel Limited.

6/6/3/3

Mathematics BUnit 3: Number, Algebra, Geometry 2 (Calculator)

Higher Tier

Mock paper

Time: 1 hour 45 minutes

You must have: Ruler graduated in centimetres and millimetres,

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

paper may be used.

5MB3H/01

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.

• If your calculator does not have a π button, take the value of π to be

3.142 unless the question instructs otherwise.

Information

• The total mark for this paper is 80.

• The marks for each question are shown in brackets

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

• Questions labelled with an asterisk (*) are ones where the quality of your

written communication will be assessed.

Advice

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

• Keep an eye on the time.

• Try to answer every question.

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



2

*W41054A0220*

GCSE Mathematics 2MB01

Formulae – Higher Tier

You must not write on this formulae page.

Anything you write on this formulae page will gain NO credit.

Volume of prism = area of cross section × length

r

Volume of cone

Curved surface area of cone =

=Volume of sphere

Surface area of sphere = 4 r 2

r 3=

r

In any triangle ABC

A B

C

b a

c

Sine Rule

Cosine Rule a2= b2+ c2 – 2bc cos A

= =a b c

sin A sin B sin C

4

3

Area of triangle ab sin C =1

2

1

3

The Quadratic Equation

The solutions of ax2 + bx + c = 0

where a ≠ 0, are given by

24

2

− ± ( − )=

b b ac x

a

Area of trapezium = (a + b)h1

2

sectioncross

l e n g t h

a

h

b

hl

r 2h

rl



3

*W41054A0320* Turn over

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1 5 identical calculators cost a total of £31.75

Work out the cost of 7 of these calculators.

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

(Total for Question 1 is 2 marks)

2 Use your calculator to work out67 92 13 9

3 4 9 8

. .

. .

−

×

Write down all the figures from your calculator display.

You must give your answer as a decimal.

… … … … .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .… … … … … … .




4

*W41054A0420*

3 Wheat biscuits of the same size can be bought in large boxes, medium boxes and

small boxes.

A large box costs £3.69 and contains 48 biscuits.

A medium box costs £1.78 and contains 24 biscuits.

A small box costs £1.14 and contains 12 biscuits.

Which size of box is the best value for money?

Explain your answer.

You must show all your working.


*



5


4 (a) Solve 7( x – 4) = 35

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

(2)

–3 n < 4

n is an integer.

(b) Write down the possible values of n.

… … … … .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .… … … … … … .

(2)

(c) Solve the inequality 5 x + 3 > 3 x – 11

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


5 Edgar had a maths test and a science test.

He got 68% in the maths test.

He got 36 out of 55 in the science test.

Which test did Edgar get the better mark in, maths or science?


*



6

*W41054A0620*

6 The diagram shows an accurate scale drawing of two towns, Middleton and Newtown.

A new shopping centre is going to be built.

The shopping centre will be

less than 12 km from Middleton and

less than 15 km from Newtown.

On the diagram, shade the region where the shopping centre can be built.


7 Make t the subject of the formula 3t + b = a2

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


Middleton Newtown

Scale: 1 cm to 2 km



7


8 The diagram shows a prism.

Work out the volume of the prism.

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


Diagram NOT

accurately drawn

8 cm

12 cm

15 cm

7 cm

5 cm



8

*W41054A0820*

9 The diagram shows the region inside a running track.

This region is in the shape of a rectangle with a semi-circle at both ends.

The rectangle has a length of 105 m.

It has a width of 64 m.

The semi-circles each have a diameter of 64 m.

The groundsman is going to cover this region with grass seed.

One sack of grass seed will cover 250 m2.

How many sacks of grass seed does the groundsman need?



105 m

64 m

105 m

Diagram NOT

accurately drawn



9


10 The equation x3 + 6 x2 = 500 has a solution between 6 and 7

Use a trial and improvement method to find this solution.

Give your answer correct to one decimal place.


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




10

*W41054A01020*

11

(a) Rotate triangle T 90° clockwise about the point (0, 0).

(2)

–6

–6

–4

–2

O x

y

2

4

6

–4 –2 2 4 6

T



11


(b) Describe fully the single transformation which maps shape P onto shape Q.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(3)


–2

–2

2

4

6

8

10

12

14

O 2 4 6 8 10 12 x

y

P

Q



12

*W41054A01220*

12 On the grid, draw the graph of y = x2 – 2 x – 5 for –1 x 5


–8

–6

–4

–2

–1 1 2 3 4 5O

2

4

6

8

10

12

y

x



13


13 The diagram shows a right-angled triangle.

Angle ACB = 90°.

AB = 12.4 cm.

CB = 9.7 cm.

Work out the value of x.

Give your answer correct to 1 decimal place.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


14 Work out 5.6 × 108 × 3 × 10 –5

Give your answer in standard form.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Diagram NOT

accurately drawn

12.4 cm

x°

A

BC 9.7 cm



14

*W41054A01420*

15 Solve the simultaneous equations.

3 x + 2 y = 8

6 x – 5 y = 34

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

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


16 (a) A holiday costs £840 plus 20% VAT.

Calculate the total cost of the holiday.

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

(3)

In a sale, normal prices are reduced by 45%. The sale price of another holiday is £462

(b) Work out the normal price of this holiday.

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

(3)




15


17 LMN is an equilateral triangle.

Work out the height of triangle LMN .

Give your answer correct to 3 significant figures.

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


Diagram NOT

accurately drawn

9 cm

9 cm9 cm

L

N



16

*W41054A01620*

18 Kalinda has two solid cylinders made of the same material.

The cylinders are mathematically similar.

Cylinder A has a diameter of 6 cm.

Cylinder B has a diameter of 18 cm.

Cylinder A has a mass of 80 g.

Work out the mass of cylinder B.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . g


19 Solve 5 x2 – 3 x – 7 = 0

Give your solutions correct to 3 significant figures.

… …… …. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . … …… …… ….


Diagram NOT

accurately drawn

A

B

18 cm6 cm



17


20

A, B, C and D are points on the circumference of a circle.

EDF is a tangent to the circle.

AB = AD.

Angle ADE = 54°.

Work out the size of angle BCD.

You must give a reason for each stage in your working.


*Diagram NOT

accurately drawn

F

D

E

54° C

B

A



18

*W41054A01820*

21 The diagram shows a field.

RT = 134 m.

Angle TRS = 55°.

Angle RST = 92°.

Work out the area of the field. Give your answer correct to 3 significant figures.

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


Diagram NOT

accurately drawn

S

55°

92°

134 m

R

T



19

*W41054A01920*

22 Solve the equation

6

2 2 31

x

x

x+

+

−

=

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


TOTAL FOR PAPER IS 80 MARKS



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