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
GCSE Foundation sample Paper 1 (non-calculator)
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- 1.A van has a mass of 2,000 kg, correct to 1 significant figure. Using m for the mass of the van in kilograms, write down the error interval for m.
- 2.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.
- 3.Write 400 g : 1.5 kg as a ratio in its simplest form.
- 4.Triangle ABC is similar to triangle PQR. Side AB is 8 cm and corresponds to side PQ, which is 12 cm. Side AC is 6 cm and corresponds to side PR. Work out the length of PR.
- 5.A factory finds that the probability a randomly chosen light bulb is defective is 0.035. In a batch of 4,000 bulbs, work out how many bulbs you would expect to work correctly.
- 6.A vet records the weights, in kilograms, of 7 dogs, in the order she weighs them: 18, 12, 50, 10, 20, 14, 16. Work out the median weight.
- 7.Work out −7 − (−3).
- 8.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?
- 9.In a recipe the mass of chocolate to the mass of milk is in the ratio 1:4. Amelia uses 200 g of milk. Work out the mass of chocolate she needs.
- 10.Two straight paths cross at a junction in a park. One of the angles between them, measured with a protractor, is 76°. What is the size of the angle immediately next to it on a straight line?
- 11.A spinner is divided into sectors of 144°, 90° and 126°, coloured purple, orange and grey in that order. The spinner is spun 300 times. Work out how many times you would expect it to land on purple.
- 12.A country has an area of 25,000,000 hectares. Write this area in standard form.
- 13.Expand and simplify 2(a + 6) − 2(a − 7)
- 14.A company's turnover this year is £180,000. Last year's turnover was £120,000. Write down this year's turnover as a percentage of last year's turnover.
- 15.Write down the term for the distance all the way around the edge of a circle.
- 16.Work out 2⁵.
- 17.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?
- 18.In a mix of mortar the ratio of the mass of sand to the mass of cement is 5 : 2. Write the mass of cement as a fraction of the total mass of the mix.
- 19.Simplify x⁵ × x³ ÷ x², giving your answer as a single power of x.
- 20.A recipe for pancakes uses 240 g of flour to make pancakes for 6 people. Work out how many grams of flour are needed to make pancakes for 15 people, using the same recipe.
Answer key
- (a) 1,500 ≤ m < 2,500 — Method: a four-digit figure written to 1 significant figure has been rounded to the nearest 1,000, so the mass lies within half of 1,000, that is 500, of the figure given. Working: 2,000 − 500 = 1,500 and 2,000 + 500 = 2,500. The lower limit is included, because 1,500 kg rounds up to 2,000 kg to 1 significant figure, while 2,500 kg rounds up to 3,000 kg, so the upper limit is not. Answer: 1,500 ≤ m < 2,500. The distractors: 1,950 ≤ m < 2,050 comes from rounding to the nearest 100 instead of to 1 significant figure; 1,000 ≤ m < 3,000 goes a whole 1,000 either side instead of half of it; 1,500 < m ≤ 2,500 has the two limits the wrong way round.
- (d) £20 — Let f be the joining fee and m the monthly fee: f + 3m = 100 and f + 6m = 160. Subtracting the first equation from the second eliminates f: 3m = 60, so m = 20. A candidate who finds the joining fee instead of the monthly fee would get f = 100 − 3(20) = £40. A candidate who divides Ben's total by his number of months, ignoring that part of the cost is a fixed joining fee, would get 160 ÷ 6 ≈ £26.67. A candidate who divides the difference in cost by the total number of months instead of the difference in months would get (160 − 100) ÷ 9 ≈ £6.67.
- (a) 4 : 15 — Convert to the same unit first: 1.5 kg = 1500 g, since 1 kg = 1000 g. This gives the ratio 400 : 1500. Divide both parts by their highest common factor, 100, to get 4 : 15. Giving 40 : 150 divides by 10 only, which is not the highest common factor, so it is not fully simplified. Giving 15 : 4 swaps the order. Giving 4 : 1.5 has not converted 1.5 kg into grams, so the two parts are not measured in the same unit.
- (c) 9 cm — The scale factor from triangle ABC to triangle PQR is PQ ÷ AB = 12 ÷ 8 = 1.5. So PR = AC × 1.5 = 6 × 1.5 = 9 cm. (4 cm comes from using the scale factor upside down, AB ÷ PQ; 10 cm comes from adding the difference between AB and PQ, 4 cm, to AC instead of scaling; 16 cm comes from multiplying PQ by the ratio AB : AC instead of scaling AC by the correct scale factor.)
- (a) 3,860 — The probability a bulb works correctly is the complement of being defective: 1 − 0.035 = 0.965. Expected number working correctly = 0.965 × 4,000 = 3,860. Using the probability of being defective instead of its complement gives 4,000 × 0.035 = 140, the expected number of DEFECTIVE bulbs, not working ones. Shifting the decimal point in the complement, using 0.0965 instead of 0.965, gives 4,000 × 0.0965 = 386. Assuming every bulb works, ignoring the 0.035 probability altogether, gives the full batch of 4,000.
- (c) 16 kg — Method: sort the seven weights before finding the middle value. Working: in order, the weights are 10, 12, 14, 16, 18, 20 and 50 kg. There are 7 values, so the median is the 4th one: 16 kg. Reading off the 4th weight in the order the vet recorded them, 10 kg, skips the sorting step and is not the median. Working out the mean, 140 ÷ 7 = 20 kg, finds a different average altogether. Working out the range, 50 − 10 = 40 kg, finds the spread, not the middle value. Always sort your data first — the median lives in the ordered list, not the collection order.
- (b) −4 — To subtract a negative number, add its positive equivalent: −7 − (−3) becomes −7 + 3. Work out −7 + 3 to get −4. Treating "− (−3)" as simply "−3" without flipping the sign gives the wrong working −7 − 3, which is −10. Ignoring the negative sign on −7 and just subtracting the values, 7 − 3, gives 4, which loses the sign of the starting number. Flipping the sign of both numbers, 7 + 3, gives 10, which changes more than the double negative allows. So −7 − (−3) = −4.
- (d) w ≤ 630 — 'No more than 630 kg' means the weight can be exactly 630 kg or anything less, so the correct inequality is w ≤ 630, using 'less than or equal to' to include the limit itself. Writing w < 630 excludes 630 kg itself, as though the limit could not be reached exactly. Writing w ≥ 630 reverses the direction, describing a minimum weight rather than a maximum. Writing w > 630 both reverses the direction and excludes the boundary value. The inequality describing the lift's weight limit is w ≤ 630.
- (d) 50 g — Method: the milk is 4 parts of the ratio, so use the milk to find the value of one part, then read off the chocolate, which is 1 part. Working: one part = 200 ÷ 4 = 50, and the chocolate is one part. Answer: 50 g. The distractors: 40 g comes from treating the 200 g as the total mass of the mixture and splitting it into 1 + 4 = 5 parts; 250 g is the total mass of the finished mixture, the 200 g of milk plus the chocolate, rather than the chocolate on its own; 800 g comes from multiplying 200 by 4 instead of dividing, which scales the milk up rather than down to the chocolate.
- (b) 104 — Method: angles on a straight line add up to 180°. Working: 180° − 76° = 104°. A student who answers 76 has mistaken this for the vertically opposite angle, which is equal, rather than the adjacent angle on a straight line. A student who answers 90 has wrongly assumed the two paths must be perpendicular. A student who answers 14 has subtracted 76° from 90° instead of from 180°. Answer: 104°.
- (b) 120 — Purple's probability is its angle out of the full circle: 144° ÷ 360° = 2/5. Expected number on purple = 2/5 × 300 = 120. Assuming the three colours are equally likely, ignoring their different angles, gives 300 ÷ 3 = 100. Using orange's angle, 90°, instead of purple's 144° gives a probability of 1/4, so 300 × 1/4 = 75. Treating 144 as a percentage instead of finding its fraction of 360° gives 300 × 0.144 = 43.2, which rounds to 43.
- (a) 2.5 × 10⁷ — Method: place the decimal point so that the coefficient is at least 1 and less than 10, then count the places it has moved. Working: the digits give a coefficient of 2.5, and the decimal point travels from the end of 25,000,000 until it sits between the 2 and the 5, a move of 7 places. Answer: 2.5 × 10⁷. The distractors: 25 × 10⁶ is the same area but not in standard form, because the coefficient must be less than 10; 2.5 × 10⁸ comes from counting the eight digits of 25,000,000 instead of the seven places the decimal point moves; 2.5 × 10⁻⁷ comes from making the index negative because the decimal point was carried to the left.
- (d) 26 — Method: expand both brackets, treating the second as multiplication by −2 so that both of its terms change sign, then collect like terms. Working: 2(a + 6) = 2a + 12 and −2(a − 7) = −2a + 14, so the expression becomes 2a + 12 − 2a + 14; the a terms give 2a − 2a = 0, so no term in a survives, and the numbers give 12 + 14 = 26. Answer: 26. The distractors: −2 comes from expanding the second bracket as −2a − 14, so that the numbers give 12 − 14; 4a − 2 comes from adding 2(a − 7) instead of subtracting it, giving 2a + 12 + 2a − 14; 13 comes from multiplying the 2 over only the first term of each bracket, giving 2a + 6 − 2a + 7.
- (c) 150% — Percentage = (180,000 ÷ 120,000) × 100 = 150%.
- (b) circumference — The distance all the way around the outside edge of a circle is called the circumference. The diameter is a straight line across the circle through the centre, so it is a length through the circle, not around it. The radius is a straight line from the centre to the edge, again a length across, not around. The area is the amount of surface inside the circle, a region, not a length at all.
- (c) 32 — Method: a power tells you how many times to multiply the base by itself. Working: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Answer: 32. (10 comes from multiplying the base by the power, 2 × 5, instead of using repeated multiplication. 25 comes from swapping the base and the power and working out 5² instead. 16 comes from using one fewer 2, effectively working out 2⁴.)
- (a) False — 4(2x − 3) = 8x − 12, not 8x − 3. — Expand the bracket by multiplying both terms by 4: 4 × 2x = 8x and 4 × (−3) = −12, so 4(2x − 3) = 8x − 12, which is not 8x − 3 — the student is wrong. Saying 4(2x − 3) = 8x − 3 comes from multiplying only the 2x by 4 and copying the −3 across unchanged. Saying 4(2x − 3) = 2x − 12 comes from multiplying only the −3 by 4 and leaving 2x unmultiplied. Claiming it is true because both expressions are linear ignores that equivalence depends on the actual coefficients, not the type of expression.
- (c) 2/7 — Method: each number in a ratio counts parts, so the whole is all the parts added together, and the fraction wanted is the cement parts over that total. Working: the mix has 5 + 2 = 7 parts altogether, and 2 of those parts are cement, so the cement is 2/7 of the mix. Answer: 2/7. The distractors: 2/5 comes from writing the cement parts over the sand parts, comparing one part with the other part instead of with the whole; 5/7 comes from writing the sand parts over the total, which answers about the wrong material; 7/2 comes from writing the total over the cement parts, turning the fraction upside down.
- (a) x⁶ — Method: work through the powers in order — multiplying powers of the same base means adding indices, and dividing powers of the same base means subtracting indices. Working: first, x⁵ × x³ = x⁸ (adding 5 and 3); then x⁸ ÷ x² = x⁶ (subtracting 2 from 8). x⁴ comes from swapping the two rules — subtracting for the multiplication, 5 − 3 = 2, and then adding for the division, 2 + 2 = 4. x¹⁰ comes from adding all three indices, 5 + 3 + 2 = 10, treating the division the same as a multiplication. 6x comes from correctly reaching a total index of 6 but then writing it as a coefficient of x instead of as its power. Answer: x⁶.
- (d) 600 g — Find the flour used for one person: 240 ÷ 6 = 40 g per person. Then scale up to 15 people: 40 × 15 = 600 g. Dividing 240 by 15 and then multiplying by 6 gives 96 g — that uses the ratio the wrong way round, scaling down instead of up. Stopping at 40 g only gives the amount for one person, not for 15. Adding 15 − 6 = 9 to 240 gives 249 g, which treats the number of people and the grams of flour as if they were the same kind of quantity — proportion means scaling, not adding. The recipe needs 600 g of flour.
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.