Sample paper · GCSE Foundation · grades 1–5

GCSE Foundation 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 Foundation qualification — number 25%, algebra 20%, ratio, proportion and rates of change 25%, geometry and measures 15%, probability 7.5%, statistics 7.5% — with a calculator allowed. AO1 / AO2 / AO3 at this tier: 50% / 25% / 25%.

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GCSE Foundation sample Paper 2 (calculator)

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

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1.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?
(a)9/10
(b)3/5
(c)4/15
(d)2/5
2.Make x the subject of the formula y = 2x − 9.
y = 2x − 9
(a)x = (y + 9) / 2
(b)x = (y − 9) / 2
(c)x = 2(y + 9)
(d)x = y / 2 + 9
3.A sunflower is 140 cm tall. A tomato plant is 80 cm tall. Write the height of the tomato plant as a fraction of the height of the sunflower, giving your answer in its simplest form.
(a)7/4
(b)3/7
(c)4/11
(d)4/7
4.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.
(a)SSS – all three corresponding sides are equal
(b)RHS – a right angle, hypotenuse and one other side are equal
(c)SAS – two sides and the included angle are equal
(d)ASA – two angles and the included side are equal
5.A grower knows that the probability that one of their seeds germinates is 0.6. The grower wants to expect 300 of the seeds to germinate. Work out how many seeds the grower should plant.
(a)120
(b)180
(c)500
(d)750
6.Noah wrote down the numbers 9, 3, 7, 1, 5 and said, “The median is 7, because 7 is in the middle of my list.” Is Noah right? Give a reason for your answer.
(a)Yes — the mean of the five numbers is 7, so the median is 7 as well.
(b)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 5.
(c)No — in order the numbers are 1, 3, 5, 7, 9, so the median is 3.
(d)Yes — 7 is the third of the five numbers he wrote, so it is the median.
7.A train journey takes 45 minutes, correct to the nearest 5 minutes. Using t for the actual time of the journey in minutes, write down the error interval for t.
(a)42.5 ≤ t < 47.5
(b)40 ≤ t < 50
(c)42.5 ≤ t ≤ 47.5
(d)44.5 ≤ t < 45.5
8.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.
(a)3n − 2
(b)3n + 1
(c)3n + 4
(d)n + 3
9.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
10.A shopkeeper builds a display from two cuboid boxes, shown in the diagram. She wants to cover the front of the display with coloured paper. Work out the total area of the front elevation, in square centimetres.
(a)4700 cm²
(b)2000 cm²
(c)7200 cm²
(d)2700 cm²
11.Two ordinary fair dice are rolled and the two scores are added together. Work out the probability that the total is a prime number.
(a)13/36
(b)19/36
(c)7/18
(d)5/12
12.A carton of orange juice holds 1.35 litres. Ruby pours the juice equally into 4 identical glasses. Work out how much juice is in each glass, giving your answer as a fraction of a litre in its simplest form.
(a)27/20
(b)17/50
(c)27/5
(d)27/80
13.Two expressions are 6(x − 1) and 6x − 6. A student says these are equivalent for every value of x. Is the student correct?
(a)Yes, but only when x is a whole number.
(b)No, since 6(x − 1) means 6x − 1.
(c)No, brackets always change an expression's value.
(d)Yes, since expanding 6(x − 1) gives 6x − 6.
14.Write the ratio 8 : 15 in the form 1 : n.
(a)1.875 : 1
(b)1 : 1.875
(c)8 : 1.875
(d)1 : 0.53
15.Lines JK and LM are parallel. A straight line crosses JK at point P and crosses LM at point Q. Angle KPQ = 118°. Angle KPQ and angle MQP are co-interior (allied) angles. Work out angle MQP.
(a)62°
(b)59°
(c)90°
(d)118°
16.For any two whole numbers, the product of the numbers is equal to the product of their highest common factor and their lowest common multiple. The highest common factor of 6 and 8 is 2, and 6 × 8 = 48. Work out the lowest common multiple of 6 and 8.
(a)24
(b)12
(c)48
(d)96
17.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.
(a)k + 5
(b)k − 5
(c)5k
(d)5 − k
18.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.
(a)500 m
(b)50 m
(c)5 m
(d)0.05 m
19.A café offers sandwiches with one filling from 5 choices and one type of bread from 4 choices. Cheese and mustard, which is one of the 5 fillings, is not available on gluten-free bread, which is one of the 4 breads. Work out how many different sandwiches are possible.
(a)16
(b)15
(c)19
(d)20
20.Two cars leave the same point at the same time and travel in opposite directions. One travels at 80 km/h and the other at 60 km/h. Work out how long it takes until the cars are 350 km apart.
(a)5 hours
(b)2.5 hours
(c)17.5 hours
(d)4.375 hours

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.