Sample paper · GCSE Foundation · grades 1–5

GCSE Foundation 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 Foundation qualification — number 25%, algebra 20%, ratio, proportion and rates of change 25%, geometry and measures 15%, probability 7.5%, statistics 7.5% — with no calculator-only items. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.

Non-calculatorGCSE Foundation

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GCSE Foundation sample Paper 1 (non-calculator)

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

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1.Write 12 as a product of its prime factors.
(a)2² × 3
(b)2 × 3²
(c)2 × 3
(d)2 × 6
2.Write down the y-intercept of the line with equation y = 3x + 8.
y = 3x + 8
(a)−8
(b)11
(c)3
(d)8
3.£2000 is invested in a savings account that pays 5% compound interest each year. Work out the value of the investment at the end of 2 years.
(a)£2200.00
(b)£2205.00
(c)£205.00
(d)£2100.00
4.A cylindrical candle and a cone-shaped candle have the same base radius and the same height. State the cone's volume as a fraction of the cylinder's volume.
(a)The same as the cylinder's volume
(b)Two thirds of the cylinder's volume
(c)One third of the cylinder's volume
(d)Half the cylinder's volume
5.The probability that a spinner lands on blue is 2/5. Write this probability as a percentage.
(a)20%
(b)40%
(c)2%
(d)4%
6.A straight line is drawn on a scatter graph to show the trend of the points. Write down the name given to this line.
(a)A line joining the first and last points
(b)A horizontal line through the mean
(c)A line of best fit
(d)A line of symmetry
7.A laptop costs £720. A carrying case for it costs 1/9 of the price of the laptop. Work out the cost of the carrying case.
(a)£72
(b)£640
(c)£80
(d)£6480
8.Write down the expression that means 5 more than half of n.
(a)(n + 5)/2
(b)5n/2
(c)2n + 5
(d)n/2 + 5
9.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.
(a)4
(b)15
(c)25
(d)19
10.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?
(a)Wrong: multiply by angle ÷ 360, not divide by it.
(b)Wrong: multiply by the angle only, no division.
(c)Wrong: use radius × angle, not circumference.
(d)Correct: dividing by the angle in degrees works.
11.On a probability scale from 0 to 1, the points impossible (0), unlikely (0.25), evens (0.5) and certain (1) are marked. An event has a probability of 0.3. Between which two neighbouring marked points does 0.3 lie?
(a)evens and certain
(b)impossible and evens
(c)impossible and unlikely
(d)unlikely and evens
12.Work out 5/6 × 2/9, giving your answer in its simplest form.
(a)7/15
(b)5/27
(c)15/4
(d)5/3
13.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
14.Write 0.25 as a percentage.
(a)2.5%
(b)0.25%
(c)250%
(d)25%
15.Work out the distance between the points (−3, 4) and (5, −2).
(a)14
(b)100
(c)50
(d)10
16.Work out √144
(a)72
(b)36
(c)12
(d)14
17.Simplify (5x² + 3x − 2) − (2x² − x + 5)
(a)3x² + 4x + 3
(b)3x² + 2x + 3
(c)7x² + 2x + 3
(d)3x² + 4x − 7
18.A salt solution has a concentration of 10%. The solution contains 50 g of salt. Work out the total mass of the solution.
(a)450 g
(b)5 g
(c)500 g
(d)5000 g
19.Work out the highest common factor of 20 and 32.
(a)8
(b)4
(c)2
(d)160
20.A metal has a density of 7.8 g/cm³. Work out the density of the metal in kg/m³.
(a)7.8 kg/m³
(b)78000 kg/m³
(c)7800 kg/m³
(d)780 kg/m³

How the 20 questions are shared out

Number — 5 questions (25% of the qualification)
Algebra — 4 questions (20% of the qualification)
Ratio, proportion and rates of change — 5 questions (25% of the qualification)
Geometry and measures — 3 questions (15% 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.