Sample paper · GCSE Higher · grades 4–9

GCSE Higher sample Paper 1 (non-calculator)

The real Paper 1 is 1.5 hour 30 minutes and 80 marks, non-calculator, and all three papers carry equal weight. This sample is 20 original questions in the same content proportions as the Higher qualification — number 15%, algebra 30%, ratio, proportion and rates of change 20%, geometry and measures 20%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.

Non-calculatorGCSE Higher

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GCSE Higher sample Paper 1 (non-calculator)

Maths · GCSE Higher · Paper 1 · Non-calculator · 20 questions

MathsUKwww.geekhero.co.uk

1.Work out √144 − 2 × 3 + √25
(a)35
(b)11
(c)1
(d)7
2.The graph of y = f(x) has a maximum turning point at (5, 8). Which of these correctly gives the corresponding turning point on the graph of y = −f(x + 1), and its type?
(a)(4, −8), a minimum point
(b)(4, 8), a minimum point
(c)(6, −8), a minimum point
(d)(4, −8), a maximum point
3.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.
(a)4:3:1
(b)4:3:2
(c)2:150:50
(d)3:4:1
4.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.
(a)(3, 3)
(b)(4, 0)
(c)(4, 3)
(d)(3.5, 3)
5.Priya spins a fair spinner with P(red) = 0.3, and separately flips a fair coin with P(heads) = 0.5. Using a tree diagram, work out the probability that she gets red AND heads.
(a)0.5
(b)0.8
(c)0.15
(d)0.65
6.The seven members of Team A took 20, 21, 22, 23, 24, 25 and 40 seconds to finish a task. The seven members of Team B took 20, 30, 32, 34, 36, 38 and 40 seconds. Tomás says that because the two teams have the same range, their times are spread out in the same way. Is Tomás right? Give a reason for your answer.
(a)Yes, each team has seven times, so the spreads match
(b)Yes, sets with equal ranges are spread out alike
(c)No, Team B's times have a higher mean than Team A's
(d)No, the range uses only the fastest and slowest time
7.A number, y, is equal to 8.2 when rounded to 1 decimal place. Write down the error interval for y.
(a)8.15 ≤ y < 8.25
(b)8.15 < y < 8.25
(c)8.1 ≤ y < 8.2
(d)8.2 ≤ y < 8.3
8.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.
(a)16 cm
(b)24 cm
(c)84 cm
(d)28 cm
9.In a science lesson Priya has 10 litres of a solution that is 30% salt. She adds water to make a solution that is 20% salt. Work out how many litres of water she adds.
(a)15 litres
(b)5 litres
(c)3 litres
(d)2 litres
10.A shape is reflected in the line y = −x. Which of these points is invariant under this reflection?
y = −x
(a)(4, −4)
(b)(−4, −4)
(c)(5, 5)
(d)(4, 4)
11.Grace rolls two ordinary fair dice at the same time and works out the total of the two scores. Work out the probability that the total is greater than 10.
(a)33/36
(b)4/36
(c)2/36
(d)3/36
12.Priya has 24 red beads and 36 blue beads. She makes identical bracelets, using every bead and with none left over. Work out the greatest number of bracelets she can make.
(a)6
(b)72
(c)60
(d)12
13.The graph of y = f(x) has a minimum turning point at (3, 2). Write down the coordinates of the minimum turning point of the graph of y = f(x) + 5.
(a)(3, 7)
(b)(−2, 2)
(c)(8, 2)
(d)(3, −3)
14.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
(a)4
(b)0.8
(c)16
(d)3
15.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.
(a)£3
(b)£15.20
(c)£12
(d)£48
16.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.
(a)6x + 12
(b)6x + 2
(c)x + 12
(d)8x
17.A tangent to a curve at the point where x = 3 passes through the points (1, 2) and (5, 14). A candidate says: "The gradient of the tangent at x = 3 is 3, because 14 − 2 = 12 and 12 ÷ 4 = 3." Which statement is correct?
(a)The gradient is 3; the candidate's method is right.
(b)The gradient is −3; the subtraction was done the wrong way round.
(c)The gradient is 16; the two changes were added instead of divided.
(d)The gradient is 1/3; the division was done the wrong way round.
18.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.
(a)Horizontal, because both points have a y-coordinate
(b)Neither, because both coordinates differ
(c)Horizontal, because the x-coordinates increase from A to B
(d)Vertical, because both points have an x-coordinate
19.The graph of y = cos x is transformed onto the graph of y = cos(x − 90°). State the direction of the translation and which standard graph the image is.
y = cos(x)
(a)Positive x-direction, 90°; image is y = sin x.
(b)Negative x-direction, 90°; image is y = sin x.
(c)Positive x-direction, 90°; image is y = −sin x.
(d)Positive y-direction, 90°; image is y = sin x.
20.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.
(a)£7.20
(b)£22.20
(c)£9.70
(d)£10.20

How the 20 questions are shared out

Number — 3 questions (15% of the qualification)
Algebra — 6 questions (30% of the qualification)
Ratio, proportion and rates of change — 4 questions (20% of the qualification)
Geometry and measures — 4 questions (20% of the qualification)
Probability — 2 questions (7.5% of the qualification)
Statistics — 1 question (7.5% of the qualification)

Where an area has fewer printable questions than its share, the shortfall is filled from the other areas. These are original questions, not past papers.