AQA · Mathematics · 8300
GCSE Maths: Frequency Trees
Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Frequency Trees (Corbettmaths Video 376), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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50 children audition; 18 are boys; 15 get roles, 8 of them girls. What fraction of boys got a role?
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7/18. Boys with a role = 15 − 8 = 7, out of 18 boys.
200 students, 102 in Year 11; 182 did homework; 14 Year 10s didn't. What percentage of Year 11 did homework?
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About 96.1% (98/102). Year 10: 98 students, 84 did it, so 182 − 84 = 98 Year 11s did it.
60 buses: 7 of 50 Saturday buses late, 2 of 10 Sunday buses late. Which day has the higher chance of a late bus?
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Sunday: 2/10 = 20% vs Saturday 7/50 = 14%. Compare proportions, not raw counts.
144 candidates; 1st-attempt pass:fail = 2:1; 2nd-attempt pass:fail = 5:7. How many pass on their 2nd attempt?
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20. 48 fail the first attempt; 48 × 5/12 = 20 pass the second.
135 students each study one language; German = 2 × Spanish; Spanish = French + 5. How many study Spanish?
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35. 2S + S + (S − 5) = 135 → 4S = 140 → S = 35 (German 70, French 30).
80 children, 36 girls; 9 failed a test; 39 boys passed. Probability a random boy failed?
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5/44. There are 44 boys; 44 − 39 = 5 failed.
160 driving tests; 108 had 10+ hours of lessons, 29 of those failed; 104 passed overall. P(passed | under 10 hours)?
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25/52. Passed with 10+ hours = 79, so 104 − 79 = 25 passed out of the 52 with under 10 hours.
533 students; 255 in Year 8; 85 of the 165 at football training are Year 7. Which year had the higher attendance percentage?
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Year 8: 80/255 ≈ 31.4% vs Year 7: 85/278 ≈ 30.6%. More Year 7s attended, but a smaller proportion.
300 people: 105 under 50 (2/3 back Purple), 195 aged 50+ (3/5 back Yellow). Which party did most prefer?
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Yellow: 152 (35 + 117) vs Purple 148 (70 + 78).
390 cinema-goers: standard £7, 3D £9, vouchers give 10% off; 110 saw 3D; 84 used vouchers; 237 standard viewers had no voucher. Total takings?
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£2883.00 = 237×£7 + 43×£6.30 + 69×£9 + 41×£8.10.
In a two-attempt test frequency tree, how do you find how many passed on the 2nd attempt?
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Subtract the number who passed on the 1st attempt from the total who passed (either attempt).
In a frequency tree, what must the values on the branches leaving a node add up to?
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The value at that node (the parent frequency) — each split is a partition of the group.
How is the profit from a paid game calculated?
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Profit = total money taken from players − total prize money paid out.
Given a game's profit, total prizes paid and number of players, how do you find the entry cost?
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Entry cost = (profit + total prize money) ÷ number of players.
240 students each study one language; French = Spanish + 40, German = 2 × Spanish. How many study Spanish?
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50. Let Spanish = S: S + (S + 40) + 2S = 240 → 4S = 200 → S = 50.
If twice as many Year 10 as Year 11 students study French, what fraction of French students are in Year 10?
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Two thirds (2/3) — the ratio Year 10 : Year 11 is 2 : 1.
If 60% of students studying Spanish are in Year 11, what percentage are in Year 10?
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40% — the two year groups make up 100% of the Spanish students.
How do you find the value of one part when 552 marbles are shared in the ratio 3 : 20?
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Divide by the total number of parts: 552 ÷ (3 + 20) = 552 ÷ 23 = 24 marbles per part.
552 marbles shared between Bag A and Bag B in the ratio 3 : 20 gives Bag A ? marbles.
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72
How do you use a pie chart to find the number of items in one category?
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Multiply the total for that chart by the category's fraction of 360° (or its percentage).
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