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Candidate
No. / / / 0 / 3 / Signature
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Paper Reference(s)
/03
Edexcel GCSE
Mathematics A
Paper 3 – (Non Calculator)
Higher Tier
Practice Exam
Time: 1 hour 45 minutes
Team Leader’s use only
Materials required for examination / Items included with question papers
Ruler graduated in centimetres and millimetres, protractor, compasses,
pen, HB pencil, eraser.
Tracing paper may be used. / Formulae sheet.
Instructions to Candidates
In the boxes above, write your Centre Number and Candidate Number, your surname, initial(s) and signature.
Check that you have the correct question paper.
Answer ALLthe questions in the spaces provided in this question paper.
Supplementary answer sheets may be used.
Information for Candidates
The total mark for this paper is 100.
The marks for the various parts of questions are shown in round brackets, e.g.: (2).
Calculators may NOT be used.
This question paperhas 25 questions. There are no blank pages.
Advice to Candidates
Work steadily through the paper.
Do not spend too long on one question.
Show all stages in any calculations.
If you cannot answer a question, leave it and attempt the next one.
Return at the end to those questions you have left out.
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UG012657 – Edexcel GCSE Mathematics 2540: Practice Papers with Mark Schemes Higher Tier Paper 3H
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EDEXCEL
Formula – Higher Tier
You must not write on this formula page.
Anything you write on this formulae page will gain NO credit.
Volume of prism = area of cross-section length
Volume of sphere = r3
Surface area of sphere = 4 r2
Volume of cone = r2h
Curved surface area of cone = rl
In any triangleABC
Sine Rule: = =
Cosine Rule:a2 = b2 + c2 –2bc cos A
Area of a triangle = ab sin C
The Quadratic Equation
The solutions of ax2 + bx + c = 0, where a 0, are given by
x =
Answer ALL TWENTY FIVE questions.
Write your answers in the spaces provided.
You must write down all stages in your working.
You must NOT use a calculator.
1.Work outan estimate for the value of
…………………..
(Total 2 marks)
2. 20 students took a short test.
The table gives information about their marks in the test.
Mark / Frequency7 / 1
8 / 4
9 / 10
10 / 5
Work out the mean mark.
……………………..
(Total 3 marks)
3.Jane drove 320 km from her home to the airport.
The travel graph shows Jane’s journey.
During the journey, Jane stopped for a break.
(a)(i)For how long did Jane stop for her break?
…………………………minutes
(ii)How far had Jane travelled in the first 90 minutes?
…………………….. km
(2)
(b)Work out the steady speed at which Jane travelled after her break.
……………………. km/h
(2)
Ben leaves Jane’s home at 13 30
He drives towards the airport at a speed of 100 kilometres per hour.
(c)Use the travel graph to find an estimate for the time at which Ben catches up with Jane.
………………..
(3)
(Total 7 marks)
4.Here is the plan and front elevation of a prism.
The front elevation shows the cross section of the prism.
On the grid below, draw the side elevation of the prism.
(Total 3 marks)
5.The diagram shows a regular hexagon and a regular octagon.
Work out the size of the angle marked x.
………………… o
(Total 3 marks)
6.(a) Write 300 as a product of its prime factors.
…………………….
(2)
x and y are both whole numbers
(b) (i) Find a possible value of x
…………………….
(ii) Find a possible value of y
…………………….
(2)
(Total 4 marks)
7. Siobhan bought a box of 40 oranges for £2.
of the 40 oranges were damaged so she threw them away.
She sold the remaining oranges at x pence each.
She made a profit of 40%.
Calculate the value of x.
x = …………………….
(Total 5 marks)
8. Here are the first 4 terms of an arithmetic sequence
3 7 11 15
Find an expression, in terms of n, for the nth term of the sequence.
…………………………
(Total 2 marks)
9. The cost, in pounds, of buying time on a satellite link can be worked out using this rule.
The cost of buying n hours of satellite time is C pounds.
Write down a formula for C in terms of n.
…………………………
(Total 3 marks)
10.
Work out the volume of the triangular prism
State the units with your answer.
…………………………
(Total 3 marks)
11.(a)Solve 6x + 2 = 4x − 7
x = ……………………..
(2)
(b)Solve
x = ……………………..
(3)
(Total 5 marks)
12. This coloured wheel is spun.
The coloured sectors are not all the same size.
When the wheel stops the colour indicated by the pointer is written down.
The probability that the pointer will point to each of the colours yellow and blue is given in the table.
The probability that the pointer will point toRedis equal to the probability that it will point toGreen.
Number / Red / Yellow / Blue / GreenProbability / x / 0.45 / 0.11 / x
(a) Work out the value of x.
…………………….
(2)
Rosie spins the spinner 200 times.
(b) Work out an estimate for the number of times the pointer will point to Yellow.
…………………….
(2)
(Total 4 marks)
13.In the space below, use ruler and compasses to construct an angle of size 90° at P.
You must show all construction lines.
(Total 3 marks)
14.
Describe fully the single transformation that will map shape P onto shape Q.
......
......
(Total 3 marks)
15. This table shows some expressions
The letters w, x, y, and z represent lengths.
and 3 are numbers that have no dimensions.
Three of the expressions could represent areas.
Tick the boxes underneath the three expressions which could represent areas.
(Total 3 marks)
16. (i)Factorise
..………………………..
(ii)Hence, solve
…………………………
(Total 3 marks)
17. ,
(a) Work out the value of pq
Give your answer in standard form.
…………………………
(2)
(b) Work out the value of
Give your answer in standard form.
…………………………
(2)
(Total 4 marks)
18. Alan regularly travels from Manchester to Oxford.
He travels on two different trains.
His 1st train is from Manchester to Birmingham and his 2nd train is from Birmingham to Oxford.
On the 1st train, the probability that he gets a window seat is .
On the 2nd train, the probability that he gets a window seat is .
Alan is travelling from Manchester to Oxford tomorrow.
(a)Complete the probability tree diagram to show the outcomes of Alan’s seating
on the two trains.
Label clearly the branches of the probability tree diagram.
(2)
(b) Work out the probability that Alan will get a window seat on the 1st train and the 2nd train.
…………………………
(2)
(c) Work out the probability that Alan will get a window seat on at least one of the trains.
…………………………
(3)
(Total 7 marks)
19.
P, Q and R are points on a circle, centre O.
POQ is a straight line.
TQ and TR are tangents to the circle.
Angle TQR = 56°.
(a)Explain why angle PQR = 34°.
………………………………………………………………………………………………..
………………………………………………………………………………………………..
(1)
(b)Calculate the size of angle PRT.
Give reasons for your answer.
…………………..°
(3)
(Total 4 marks)
20. (a)Work out
(i)70
……………………..
(ii)4‾ 2
………………………
(iii)
……………………….
(3)
(b) Find the value of x
x =……………………….
(2)
(Total 6 marks)
21. (i)Expand and simplify (a – b)2
……………………………..
(ii)Show that = a2 + b2
(iii)Hence, or otherwise, find the value of 102.52 + 97.52
…………………………..
(Total 5 marks)
22.
The diagram shows a solid wooden cone.
The height of the cone is 6 cm.
The base radius of the cone is 8 cm.
(a)Find the volume of the cone.
Give your answer as a multiple of .
………………… cm3
(2)
(b) Find the area of the curved surface of the cone.
Give your answer as a multiple of .
………………… cm2
(3)
( Total 5 marks)
23. The table and histogram give information about how long, in minutes, some students
took to complete a homework.
Time (t) in minutes / Frequency0 < t ≤ 10 / 20
10 < t ≤ 15
15 < t ≤ 30
30 < t ≤ 50 / 62
50 < t ≤ 60 / 23
(a)Use the information in the histogram to complete the table.
(2)
(b)Use the table to complete the histogram.
(2)
(Total 4 marks)
24. Solve the equation
…………………………
(Total 7 marks)
25.
The diagram shows a sketch of part of the curve with equation y = p + q cosx°,
wherep and q are integers.
The curve cuts the y-axis at (0, 3)
(a)Find the value of pand the value of q.
p = …...….………….
q = …..…..………….
(2)
A is a minimum point on the curve.
(b) Write down the x coordinate of A.
…..…..………….
(1)
(Total 3 marks)
TOTAL FOR PAPER: 100 MARKS
END
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UG012657 – Edexcel GCSE Mathematics 2540: Practice Papers with Mark Schemes Higher Tier Paper 3H