Sample paper · GCSE Higher · grades 4–9

GCSE Higher sample Paper 2 (calculator)

The real Paper 2 is 1.5 hour 30 minutes and 80 marks, 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 a calculator allowed. AO1 / AO2 / AO3 at this tier: 40% / 30% / 30%.

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GCSE Higher sample Paper 2 (calculator)

Maths · GCSE Higher · Paper 2 · Calculator · 20 questions

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1.A necklace is made from red beads and gold beads in the ratio 7 : 3. What fraction of the beads are gold?
(a)3/7
(b)7/3
(c)7/10
(d)3/10
2.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.
(a)9
(b)25
(c)18.75
(d)15
3.A cyclist rides 17.5 km on Saturday and 12.25 km on Sunday. Write the distance ridden on Saturday as a fraction of the distance ridden on Sunday, giving your answer in its simplest form.
(a)10/7
(b)7/10
(c)10/17
(d)3/7
4.A solid pyramid has a square base of side 6 cm. Its apex is directly above the centre of the base, at a vertical height of 8 cm. Work out the volume of the pyramid.
(a)16 cm³
(b)96 cm³
(c)144 cm³
(d)288 cm³
5.An ordinary fair dice is rolled twice. Work out the probability of getting at least one 5.
(a)30/36
(b)11/36
(c)25/36
(d)12/36
6.The masses, m kg, of 60 parcels are grouped like this: 0 ≤ m < 5, 22 parcels; 5 ≤ m < 10, 20 parcels; 10 ≤ m < 20, 9 parcels; 20 ≤ m < 30, 5 parcels; 30 ≤ m < 50, 4 parcels. Write down the class interval that contains the median mass.
(a)0 ≤ m < 5
(b)5 ≤ m < 10
(c)10 ≤ m < 20
(d)20 ≤ m < 30
7.Work out ∛64.
(a)21.3
(b)4
(c)192
(d)8
8.Which expression is equivalent to 6x − (2x − 5)?
(a)8x + 5
(b)8x − 5
(c)4x − 5
(d)4x + 5
9.A car uses fuel at a constant rate. It uses 24 litres of fuel to travel 300 km. Assuming the same rate, work out how many litres of fuel are needed for a journey of 175 km.
(a)21 litres
(b)1.4 litres
(c)14 litres
(d)24 litres
10.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?
(a)SAS
(b)RHS
(c)ASA
(d)SSS
11.At a sports club, the numbers of members who play tennis and badminton are: 50 members play tennis, 40 members play badminton, and 18 members play both tennis and badminton. A member who plays tennis is chosen at random. Work out the probability that this member also plays badminton.
(a)9/25
(b)9/20
(c)1/4
(d)1/5
12.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾
(a)x
(b)x⁽³⁄¹⁶⁾
(c)x³
(d)x⁽¹⁄²⁾
13.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.
(a)y = x + 2
(b)y = 2x − 1
(c)y = 2x + 1
(d)y = 2x + 3
14.Two numbers A and B are in the ratio 3:5. When 6 is added to B, the ratio of A to the new value of B is 1:2. Work out the value of A.
(a)18
(b)30
(c)9
(d)6
15.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
(a)17
(b)24
(c)15
(d)7.5
16.The graph of y = f(x) has a root (an x-intercept) at x = 5. Work out the x-coordinate of the corresponding root on the graph of y = f(x + 2).
(a)3
(b)2
(c)5
(d)7
17.Two numbers are in the ratio 3 : 7. Their sum is 60. Work out the positive difference between the two numbers.
(a)80
(b)60
(c)4
(d)24
18.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.
(a)110°
(b)70°
(c)140°
(d)20°
19.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?
(a)The total cost for a job lasting 1 hour.
(b)The hourly rate the plumber charges.
(c)The number of hours worked before charging starts.
(d)The fixed call-out fee, charged before the hourly rate.
20.Show that the equation x³ − x − 3 = 0 has a solution between x = 1 and x = 2, by working out f(1) and f(2), where f(x) = x³ − x − 3.
y = x
(a)f(1) = −3 and f(2) = −1
(b)f(1) = −3 and f(2) = 3
(c)f(1) = 3 and f(2) = −3
(d)f(1) = −2 and f(2) = 5

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.