The New GCSE #4 : Calculator Papers side-by-side

I thought I’d approach my analysis of the second calculator paper for each exam board in a different way. This time I shall reserve all judgement and simply (without comment) put the questions side by side, in 10% chunks. ie: “to earn the first ten percent of marks on each paper, you must answer these” etc. I’ll let you judge difficulty etc. I shall use no words, but simply… President Barack Obama facial expressions.


Edexcel and AQA are out of 80, whereas OCR is out of 100, so there needs to be a bit of adjustment. Also there’s no guarantee each 10% will line up exactly with the end of a question, so this quasi-science is already flawed, but you knew that. Questions are also summarised and abbreviated, not exactly as written.

The First 10% ish (0%-10%)


Q1: Person A & B have £300 each to change to Euros.
“Get 1.04 euros for £1 on amounts < £500.
Get 1.12 euros for £1 when you change >= £500.”
They put their money together before changing to Euros. How much extra money do they get by putting it together before exchanging? [3 marks]

Person throws dice until she gets a six. Work out the probability they throw the dice
i) twice
ii) once
iii) > twice [4 marks] ~ 9 % of paper


Q1: Person is in a class of 28. 3 are left handed. There are 1250 in school.
i) estimate number of left handed in the school [3 marks]
ii) is this likely to be over/under estimation? EXPLAIN [1 mark]
iii) Person B is in a different school in a class of 26, 6 are left handed. Person B says “in our 2 classes there are 54 students, 9 of them are left handed. This bigger sample will improve our estimate”.
What assumption has Person B made? Explain if argument is correct. [2 marks]

Q2: 18kg of copper is mixed with 10.5 kg of zinc to make an alloy.
Density of copper = 9g/cm3, density of zinc = 7 g/cm3
i) work out the volume of copper use in the allow [2 marks]
ii) what is the density of the alloy? [4 marks] ~12% of paper.


Q1: Which of these calculates density?
mass x volume
mass^2 x volume
mass / volume
volume / mass  [1 mark]

Q2: Circle equivalent fraction to 2.375
23/75     9/4     19/8     75/23   [1 mark]

Q3: Circle the equation of the x axis
x + y = 0        x – y = 0        x = 0        y = 0  [1 mark]

Q4: Angles of a quadrilateral are 140, 80, 60 and 80
What type could it be?
kite      parallelogram      rhombus      trapezium   [1 mark]

Q5: Solid cuboid is made from cm cubes. Plan, front and side elevations are shown (diagram*)
How many cm cubes made the cuboid?   [2 marks]

Q6: Times that 80 customers waited at a supermarket checkout shown below (freq table with ranges shown*)
i) In which class interval is the median? [1 mark]
ii) “90% of our customers wait less than 6 minutes” – does the data support the statement *show your working [2 marks] ~11% of paper


The Next 10% ish (10%-20%):


Q3: Take a square and equilateral triangle. Side of square = x cm, side of triangle is 2cm more than side of square. Both have equal perimeters.
i) work out the perimeter of the square  [3 marks]
ii) the length of the diagonal of the square is y cm, and height of triangle is z cm. Which has a greater value? [4 marks] ~9% of paper


Q3 i) Solve 5x + 1 > x – 18  [3 marks]
ii) Write largest integer that satisfies 5x – 1 < 10  [1 mark]
iii) Solve 3x2 = 75   [2 marks]
iv) Solve
4x + 3y = 5
2x + y   = 3   [3 marks] ~9 % of paper


Q7: 50 people took a test. 30 predicted they’d fail. 36 actually passed. Of these 36, 3x as many predicted pass as predicted fail. Complete the frequency tree (*diagram, col 2 = ‘prediction, col 3 = actual’)   [3 marks]

Q8: Person ran Lucky Dip. Tickets 50p, Tickets ending ’00’ win £12, tickets ending ‘5’ win £1.50.
750 tickets numbered 1 – 750.
Person sold all winning tickets, and some losing tickets. Profit = £163.
How many losing tickets did he sell? [6 marks] ~ 11% of paper


The Next 10% ish (20%-30%) *To avoid “bias” I’m swapping the order this time!! :
* not a scientific way of removing bias.


Q4: Interest in Account A : 3.5% compound per year, no withdrawals until end of 3 years.
Interest in Account B: 4% for first year, 3.5% second year, 3% third year. Withdrawals at any time.
i) Which gives most money after 3 years. Give difference to nearest penny. [5 marks]
ii) Why might you not use Account A ? [1 mark]

Q5: n2 – n + 11 generates a sequence including some primes.
i) Find the 1st three terms  [2 marks]
ii) Show that the sequence does not only generate primes. [2 marks]
iii) “Odd square numbers have 3 factors” Give an example and counter example [2 marks] ~12% of paper


Q9: Write 280 as a product of prime factors [2 marks]

Q10: Expand and simplify (y + 5)(y – 4)  [2 marks]

Q11 i) Find angle of a right-angled triangle with 2 sides given (11cm hy 8cm adj) [2 marks]
ii) Find opp length of right angled triangle with angle 30 and adj 37cm [2 marks] ~10%


Q4: Person has 140 chickens. Each lays 6 eggs per week. Person gives each chicken 100g of food per day. Food costs £6.75 for 25kg. What is the cost per 12 eggs?
[5 marks]

Q5: Person invests £5000 for 2 years at 3% compound interest per annum. Pays 20% tax on interest each year. Tax taken from account at year end. How much is in the account at the end of 2 years? [4 marks] ~11%


The Next 10% ish (30%-40%)


Q5 Cont R is common factor of 288 and 360. It is a common multiple of 4 and 6. It is larger than 25. Find 2 possible values for R [4 marks]

Q6: 3 diagrams: 2 x freq density/Time (Male & Female) 1 x scatter graph (Time / Age)

i) What information from the diagrams can be used to support the following:

The older John’s colleagues are, the lower their estimate is [1 mark]

Males in the sample tend to underestimate the interval and females in the sample tend to over estimate the interval [2 marks]

Comment on whether any conclusions can be drawn for the UK population from the results of this sample.[2 marks]

Q7: Show that 64 2/3 is equal to 16.[2 marks] ~11%


Q12 Cylinder has radius 40cm and depth 150cm. It is filled at a rate of 0.2 litres per second.

1 litre = 1000cm2

Does it take longer than 1 hour to fill the tank? [4 marks]

Q13: x(x+4)  x2 + 4x
For how many values of x is x(x+4) equal to x2 + 4x? (circle your answer)

0     1     2     all

[1 mark]

Q14 Person A sells cards.
She adds 30% profit to the cost.
She sells the cards for £2.34 each.
She wants to increase her profit to 40% of the cost price.
How much should she sell each card for? [3 marks] ~10%


Q6: Use a ruler and compass to construct a right-angled triangle equal in area to the rectangle shown (*diagram) The base has been drawn for you. [3 marks]

Q7: ABCD is a rhombus. M is the midpoint of BD (diagonal). E is the point on BD such that DE = CE. Calculate angle MCE [3 marks]

Q8: In a school competition each athlete has to throw a javelin 200m.
The points scored are worked out using P1=16(D – 3.8)
where P is the number of points scored when the javelin is thrown D metres.
i) If you throw 42m, what is your score?
ii) If you score 584 points, what was your distance? [4 marks] ~12.5%


The Next 10% ish (40%-50%) *To avoid “bias” I’m swapping the order AGAIN!! :
* not a scientific way of removing bias.


Q15 (6 x 10a) + (6 x 10b) + (6 x 10c) = 6006.6
Write a possible set of values for a, b ,c [3 marks]

Q16 Find the equation of the line that is parallel to y = 5x – 3 and passes through (-2,4)

[3 marks]

Q17 Make 2 criticisms of this histogram (*diagram) [2 marks] ~10%


Q8 (cont) Points scored for running 200m are worked out using P2 = 5(42.5 – T)2g
where P is the number of points scored when time to run 200m is T.
Person A scores 1280 points in the 200m
i) Work out the time in seconds that it took Person A to run 200m.
ii) The formula for number of points scored in 200m should not be used for T > n. State the value of n and explain [4 marks]

Q9: Triangle ABC has a right angle at C. BAC = 48o, AB= 9.3cm. Calculate BC. [3 marks]


Q8: The rule of nines states that a whole number is a multiple of 9 if the sum of its digits is divisible by 9.
i) Show that 292158 is divisible by 9 [1 mark]
ii) Any 2-digit number with tens digit a and units digit b can be written as (10a + b)

By writing this as 9a + a + b show that the rule of nines works for two-digit whole numbers [2 marks]

iii) Extend your argument to show that the rule of nines works for three digit whole numbers [2 marks]

Q9: A, R and W each watch a different film. A’s is +30 minutes than W’s.
R’s is twice as long as W’s
Altogether the films last 390 minutes.
How long is each film? [4 marks] ~9%


The Next 10% ish (50%-60%)


Q18 Draw a cumulative frequency graph on the grid provided to represent this data : (*table of times as ranges, and number of films). [3 marks]

ii) Estimate the number of these films with running time < 2 1/2 hours [1 mark]

Q19 w is directly proportional to y
w is inversely proportional to x2

i) When y = 4, w = 14. Work out the value of w when y = 9  [2 marks]

ii) When x = 2, w = 5. Work out the value of w when x = 10  [3 marks]

iii) Which graph shows the relationship between y and x? (*4 graphs given) [1 mark] ~12.5%


Q10: Diagrams show a sequence made from grey and white tiles.


i) Find an expression in terms of n for the number of grey tiles [2 marks]
ii) Find an expression in therms of n for the total number of grey and white tiles in Pattern. Give your answer in its simplest form.[3 marks]iii) Is there a pattern for which the total number of grey and white tiles is 231? Give a reason [2 marks]
iv) The total number of grey tiles and white tiles is always an odd number. Why? [2 marks] ~11%


Q10 i) Work out the average speed between 2 and 8 seconds from this distance/time graph (*diagram) [ 2 marks]

ii) Estimate the speed of the animal at 6 seconds [4 marks]

iii) “I think this animal can move at over 20 m/s” Do you agree? Explain [2 marks]

Q11 i) 88% of people passed Literacy exam. 76% passed numeracy exam. Show this in a Venn diagram. [3 marks] ~11%


The next 10% ish  (60%-70%)


Q20 This iterative process can be used to find approximate solutions to x3 + 5x -8 = 0


i) Use this to find a solution of x3 +5x – 8 =0
Start with x = 1 [3 marks]

ii) By substituting answer to part a) into x3 + 5x – 8 comment on the accuracy of your solution to x3 + 5x – 8 = 0 [2 marks]

Q21 ABCD is a parallelogram. Triangle is Isosceles.
Prove y = x


[5 marks] ~12.5%


Q11 (from Venn) cont. ii) One person is picked at random. What is the probability they passed numeracy given that they passed literacy?

iii) passed literacy given they passed only one section? [4 marks]

Q12 Person A cuts the corners from square paper to create a regular octagon. A and B are vertices, O is the centre. AOB = 45o. Find the area of the octagon [3 marks]

ii) Find the area of the original square [5 marks] ~12%


Q11: Size of animal population in 2014 was 2500. Size increases exponentially. Person A assumes rate of increase is 20% per year.
i) Using this assumption, work out size of population in 2009. [3 marks]
ii) Assumption is too high. Explain how part i) is affected [1 mark]

Q12: A rectangular sheet of paper can be cut into 2 identical rectangular pieces in 2 different ways (cut across middle width, or cut across middle height)
i) When original is cut, the perimeter of each new piece is 50cm. When it is cut in the other way, perimeter of the two pieces is 64cm. What is the perimeter of the original?[5 marks] ~11%


Penultimate 10%ish (70%-80%)


Q22 P = 120 coins. T = Coins from 20th Century B = British coins


A coin is chosen at random. It is British. Work out the probability that it is from the 20th Century [5 marks]

Q23 Estimate the acceleration at 6 seconds from the graph (*speed time graph shown)

[3 marks] ~10%


Q13: i) Using the scatter graph (*diagram) comparing rainfall in 2013 and in 2012, add the boxplot of rainfall in 2013 underneath the boxplot of rainfall in 2012 (*diagram2) [3 marks]
ii) Compare the distributions [2 marks]

Q14:  The quantity of heat, H calories, delivered by a current I amps, acting for t seconds to heat an amount of water is given by the formula:

H = atl2 – b

where a and b are constants.
i) Rearrange the formula to make I the subject [2 marks]
ii) Using the graph (*diagram) work out the average rate of decrease of the temperature of the water between t = 0 and t = 800.
iii) The rate of decrease of the temperature of water at time T seconds is equal to the average rate of decrease of the temperature of the water between t = 0 and t = 800.
Find an estimate for the value of T. Show your working [4 marks] ~14%


Q12 cont iii) Person B has a square of card and makes a regular octagon. The sides of the square are half as long as Person A’s. Find the ratio of areas between their octagons. [2 marks]

Q13: Two similar pyramids have surface areas 180 and 80cm^2. The volume of pyramid A is 810cm^3. Show that the volume of pyramid B is 240cm^3 [5 marks]

Q14 Calculate x:


[5 marks] ~12%

obama sweats

FINAL 10% (90%-100% – we seem to have lost 10% somewhere. Do the maths.)


Q23 (cont) Find the average speed of the car for the journey (from speed time graph)

[4 marks]

iii) Is your answer (please circle)

underestimate     exact     overestimate [1 mark]

Q24 Show that:


[5 marks] ~12.5%


Q15 Straight line goes through (p,q) and (r,s) where

p+ 2 = r

q + 4 = s

Find the gradient. [3 marks]

Q16 A unit fraction is the reciprocal of a positive integer. Unit fractions can be written as the sum of two different unit fractions e.g. 1/2 = 1/3 + 1/6

Write the following unit fractions as the sum of two different unit fractions:

1/ 4 = 1 / ? + 1 / ?

1/5 = 1 / ? + 1 / ?

1/6 = 1 / ? + 1 / ?

[3 marks]

Q17 y = 6x^4 + 7x^2 and x = sqrt (w + 1)

Find teh value of w when y = 10. [6 marks] ~12 %]


Q15: i) Prove that the recurring decimal o.151515 has the value 5 / 33 [2 marks]
ii) x = 1 / (2 183 x 5 180)
Show that when x is written as a terminating decimal, there are 180 zeros after the decimal point. [2 marks]
iii) The reciprocal of a prime number p (where p is neither 2 nor 5) when written as a decimal is always recurring. A theorem states
“The period of a recurring decimal is the least value of n for which p is a factor of 10n – 1″
Person A uses his calculator to show that 37 is a factor of 103 – 1.
Person A states “The period of the recurring dedcimal equal to the reciprocal of 37 is 3 because 37 is a factor of 103 – 1. This shows the theorem is true in this case”

Explain why Person A’s statement is incomplete. [2 marks]



Person A spins the spinner above twice. Her score is the sum of the two spins. The probability she gets a total of 4 is 16 / 81. Find the value of x [5 marks] ~14%


10 thoughts on “The New GCSE #4 : Calculator Papers side-by-side

  1. Do you have, or can you point me to, the marking scheme for the Edexcel paper?
    I am particularly interested in how they want the examinee to approach Q16, the spinner question.
    It is mentioned elsewhere, namely :
    that it is ‘a question that Ofqual’s panel of mathematicians thought was among the hardest’ at this level

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