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

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1.Meera says that 0.7 ÷ 0.1 = 0.07. Work out the correct value of 0.7 ÷ 0.1.
(a)7
(b)0.07
(c)70
(d)0.7
2.Line P has equation y = −2x + 5 and line Q has equation 2y = x + 6. Are lines P and Q perpendicular to each other?
y = -2x + 5y = x + 6
(a)Yes — the gradients multiply to −2 × 1/2 = −1.
(b)No — the product is −1, but perpendicular needs 1.
(c)No — Q's gradient is 2, and −2 × 2 = −4, not −1.
(d)Yes — both equations have a negative x-term.
3.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.
(a)1.3
(b)−1.3
(c)7.7
(d)14.4
4.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.
(a)75°
(b)105°
(c)37°
(d)146°
5.A call centre finds that 40% of its calls are about billing. 35% of the calls about billing are dealt with in under five minutes. The centre takes 500 calls on Monday. Work out how many of Monday's calls you would expect to be about billing and dealt with in under five minutes.
(a)70
(b)200
(c)375
(d)175
6.Harry counted the coins he found on each of six days: 5, 7, 8, 9, 11, 30. Write down the outlier.
(a)30
(b)8.5
(c)11
(d)5
7.A cinema has 250 seats. 12% of the seats are reserved. Work out how many of the seats are reserved.
(a)3
(b)30
(c)25
(d)24
8.The nth term of a sequence is n² − 2n + 5. Work out the 10th term.
(a)68
(b)85
(c)80
(d)125
9.£1 is worth 1.25 US dollars. Write the ratio of pounds to dollars in its simplest form, using whole numbers.
(a)1:1
(b)5:4
(c)1:5
(d)4:5
10.A rotation of 200° clockwise about the origin is applied, and the image is then rotated 250° anticlockwise about the origin. Work out the single angle of rotation, measured clockwise and between 0° and 360°, that has the same overall effect as the two rotations combined.
(a)310°
(b)130°
(c)50°
(d)90°
11.A garden centre recorded 240 plant sales using a frequency tree. The first stage splits the sales into three types: shrubs, bedding plants and trees. 96 sales were shrubs, 114 were bedding plants and the rest were trees. Work out the probability that a sale chosen at random from these 240 was a tree.
(a)2/5
(b)1/8
(c)19/40
(d)3/40
12.Write these fractions in order, starting with the smallest: 2/3, 3/5, 5/6, 1/2
(a)1/2, 3/5, 2/3, 5/6
(b)5/6, 2/3, 3/5, 1/2
(c)1/2, 3/5, 5/6, 2/3
(d)1/2, 2/3, 3/5, 5/6
13.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.
(a)−4.5
(b)50
(c)29.5
(d)8
14.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.
(a)22p
(b)79200p
(c)2.2p
(d)1320p
15.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.
(a)180°
(b)60°
(c)90°
(d)45°
16.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?
(a)x = 4
(b)x = −4
(c)x = 0
(d)x = 8
17.After a 20% discount, a jacket costs £48. Work out the original price of the jacket.
(a)£40
(b)£60
(c)£57.60
(d)£38.40
18.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.
(a)A tangent always passes through the centre of the circle
(b)A tangent is always parallel to the radius it touches
(c)The angle in a semicircle is 90°
(d)The angle between a tangent and a radius is 90°
19.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15
20.Solve x² − 6x = 0.
(a)x = 0
(b)x = 3
(c)x = 6
(d)x = 0 or x = 6

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.