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Mathematics A Paper 1 (Non - Calculator) Higher Tier PiXL Live Mock Paper Time: 1hour 45 minutes

2

*P40647A0224*

GCSE Mathematics 1MA0

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 Area of trapezium = 12

(a + b)h

Volume of sphere = 43!" 3 Volume of cone = 1

3!" 2h

Surface area of sphere = 4!" 2 Curved surface area of cone = !"#

In any triangle ABC The Quadratic Equation The solutions of ax2 + bx + c = 0

where $%&%0, are given by

x b b aca

= ! ± !( )2 42

Sine Rule aA

bB

cCsin sin sin

= =

Cosine Rule a2 = b2 + c2 – 2bc cos A

Area of triangle = 12

ab sin C

length

sectioncross

b

a

h

rl

r

h

C

ab

c BA

Answer ALL questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

You must NOT use a calculator.

Q1. Ouzma wants to find out the method of transport people use to travel to a shopping centre.

Design a suitable data collection sheet she could use to collect this information.

(Total 3 marks)

Q2.

This conversion graph can be used to change between metres and feet.

(a) Use the conversion graph to change 6 metres to feet.

..................................... feet (1)

(b) Use the conversion graph to change 8 feet to metres.

..................................... metres (1)

Robert jumps 4 metres. James jumps 12 feet.

(c) (i) Who jumps furthest, Robert or James?

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

(ii) How did you get your answer?

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

................................................................................................................ (2)

(Total 4 marks)

Q3*. Mrs White wants to buy a new washing machine.

Three shops sell the washing machine she wants.

Clean Machines Electrics Wash ‘n’ Go

Washing machine Washing machine Washing machine

Buy now pay later! off the usual price £280 £50 deposit plus of plus

10 equal payments of £27 £420 VAT at

Mrs White wants to buy the cheapest one. She decides to buy her washing machine from one of these 3 shops.

From which of these shops should she buy her washing machine? You must show how you decided on your answer.

..................................... (Total 6 marks)

Q4. (a) Expand (x + 2)(x + 3)

..................................... (2)

. (b) Factorise 5x – 10y

..................................... (1)

(b) Factorise fully 3pq – 12p2

..................................... (2)

(Total 5 marks)

Q5. Here are the heights, in cm, of 20 sunflower plants. 73 84 78 96 98 84 101 93 71 104 81 92 95 103 100 96 87 91 88 96 (a) Draw an ordered stem and leaf diagram for these heights.

(3)

(b) Work out the range.

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

(1)

(c) Find the median height.

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

(1) (Total 5 marks)

Q6*. Jennie’s council has a target of for households to recycle their waste.

In January, Jennie recycled of her household waste.

In February, she recycled 15 kg of her 120 kg of household waste.

Her result for March was 13% recycled out of 112 kg of household waste.

Has Jennie met the council’s target? Which was her best month for recycling? Show clearly how you got your answers.

(Total 4 marks)

Q7*

ABC is an isosceles triangle. Work out the size of the angle marked x. Give reasons for your answer

(Total 5 marks)

Q8. Here is a list of ingredients needed to make 12 scones. 220g self – raising flour

40g butter 150ml milk 2 tablespoons sugar

Viv is making scones for 15 people. She is marking 2 scones for each person.

Work out the amount of each ingredient she needs.

Self – raising flour……………………g

Butter……………………g

Milk……………………ml

Tablespoons of sugar……………..………..

(Total 3 marks)

Q9. (a) Express 120 as a product of its prime factors.

(2) (b) Find the highest common factor (HCF) of 90 and 120.

(1)

(Total 3 marks)

Q10. You can use this rule to work out the total charge for hiring a cement mixer.

Total charge = £30 plus £7 for each hour of hire

On Monday, Sally hired a cement mixer for 4 hours.

(a) Work out Sally’s total charge.

£ .................................. (2)

On Tuesday, Tom hired a cement mixer. Tom’s total charge was £51

(b) Work out for how many hours Tom hired the cement mixer.

.......................... hours (3)

(Total 5 marks)

Q11*. In the diagram all of the angles are in degrees. Find the size of angle CDE.

Diagram NOT accurately drawn

..................................... (Total 4 marks)

Q12.

The shape T is rotated by 180° about the point (3, 0) to give the shape U.

The shape U is rotated by 180° about the point (6, 0) to give the shape V.

Describe fully the single transformation that will map shape T to shape V.

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

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

(Total 3 marks)

Q13. The interior angle of a regular polygon is 160°.


(i) Write down the size of an exterior angle of the polygon.

.................................°

(ii) Work out the number of sides of the polygon.

................................. (Total 3 marks)

Q14. The cumulative frequency diagram gives information about the time, in minutes, 80 people were kept waiting at a hospital casualty department.

(a) Write down the number of people who waited for 20 minutes or less.

..................................... (1)

(b) Work out an estimate of the number of people who waited for between 26 minutes and 40 minutes.

..................................... (2)

The hospital has a target that no more than 15% of people are kept waiting for 40 minutes or more in the casualty department each day.

(c) Has the hospital achieved its target for the day? You must explain your answer.

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

......................................................................................................................... (2)

(Total 5 marks)

Q15. (a) Simplify 4m2 x 3m5

.

........................ (2)

(b) Simplify m0

......................... (1)

(c) Simplify (2x6y–1)3

......................... (2)

(Total 5 marks)

Q16. The population of Algeria is 34 million.

(a) Write 34 million in standard form.

..................................... (1)

The total land area of Algeria is 2.4 × 1012 m2. 5% of the total land area is used to grow crops.

(b) Work out the area of land in Algeria which is used to grow crops. Write your answer in standard form, in km2.

..................................... km2

(2) (Total 3 marks)

Q17. Simplify fully

.................................... (Total 3 marks)

Q18.

Edexcel GCSE in Mathematics Mock Papers © Edexcel Limited 2010 53

!""

Diagram NOTaccurately drawn B

C

O

A

168o

D

!!"#! $"#$%"%"#&'"()*$+,")$"+-'".*&./01'&'$.'")1"#".*&.2'!".'$+&'"&3

" 4$52'"!&$"6"789)

" :)&;")/+"+-'",*<'")1"#$52'"!%$3

" =)/"0/,+"5*>'"&'#,)$,"1)&"?)/&"@)&;*$53

33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3)

#$%&'()*%+),-./&0%1)"")2)3)4'+5/6

A, B, C and D are points on the circumference of a circle, centre 0.

Angle AOC = 168°

Work out the size of angle ADC.

You must give reasons for your working.

(Total 4 marks)

Q19. Martin and Luke are students in the same maths class.

The probability that Martin will bring a calculator to a lesson is 0.8. The probability that Luke will bring a calculator to a lesson is 0.6.

(a) Complete the probability tree diagram.

(2)

(b) Work out the probability that both Martin and Luke will not bring a calculator to a lesson.

................................. (2)

(Total 4 marks)

Q20. Solve the simultaneous equations

3x + 2y = 11

2x – 5y = 20

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

y = ..................................... (Total 4 marks)

Q21. Simplify

..................................... (Total 3 marks)

Q22. Mr Walton is responsible for maintaining fish stocks in a river. The table gives some information about the lengths, in centimetres, of a type of fish caught from the river.

Length (L) cm Frequency

0 < L ≤ 10 40

10 < L ≤ 20 60

20 < L ≤ 40 90

40 < L ≤ 80 60

L > 80 0

He wants to study the effect of returning to the river fish less than 50 cm in length that are caught.

Mr Walton suggests that fish which are less than 50 cm in length are returned to the river.

Draw a suitable statistical diagram for the information in the table.

Use it to find an estimate of the percentage of fish returned to the river.

..................................... % (Total 6 marks)

Q23. Express the recurring decimal as a fraction.

.................... (Total 3 marks)

Q24.


A cylinder has base radius x cm and height 2x cm.

A cone has base radius x cm and height h cm.

The volume of the cylinder and the volume of the cone are equal.

Find h in terms of x. Give your answer in its simplest form.

h = ............................. (Total 3 marks)

Q25. The graph of y = f(x) is shown on the grids.

(a) On this grid, sketch the graph of y = f(x) – 4.

(2)

(b) On this grid, sketch the graph of y = f( x).

(2)

(Total 4 marks)

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