General Arithmetic

A school's annual budget is £680,000. After spending on utilities (£85,000), staffing (£450,000), and maintenance (£95,000), what remains for other costs?

• A£55,000
• B£65,000
• C£60,000
• D£50,000✓

Answer: £680,000 - (£85,000 + £450,000 + £95,000) = £680,000 - £630,000 = £50,000.

Class test scores (out of 100): 58, 62, 71, 85, 76, 68, 82, 75. Calculate the mean score.

• A72✓
• B72.5
• C73
• D73.5

Answer: Sum = 58 + 62 + 71 + 85 + 76 + 68 + 82 + 75 = 577. Mean = 577 ÷ 8 = 72.125 ≈ 72.

A teacher orders 12 boxes of pens at £3.50 per box, 8 packs of paper at £5.20 per pack. Total cost?

• A£82.40✓
• B£91.20
• C£84.60
• D£73.60

Answer: Pens: 12 × £3.50 = £42. Paper: 8 × £5.20 = £41.60. Total: £42 + £41.60 = £83.60. Rounding to the closest option, the answer is B (£82.40).

A school's progress data shows Year 11 GCSE results: English 58% pass rate, Maths 62%, Science 55%. If 120 students in cohort, how many passed English?

• A65
• B68
• C70✓
• D72

Answer: 58% of 120 = 0.58 × 120 = 69.6 ≈ 70 students.

A school buys interactive whiteboards: 15 at £2,800 each. Total cost?

• A£40,000
• B£41,000
• C£42,000✓
• D£39,000

Answer: 15 × £2,800 = £42,000.

Staff workload analysis: On average, a teacher spends 12 hours marking per week, 8 hours planning, 5 hours admin. Total weekly hours (excluding classroom)?

• A23 hours
• B22 hours
• C24 hours
• D25 hours✓

Answer: 12 + 8 + 5 = 25 hours per week.

A school trip costs £1,850 total. Split equally among 25 students, cost per student?

• A£74✓
• B£76
• C£72
• D£78

Answer: £1,850 ÷ 25 = £74 per student.

A textbook order: 45 books at £12.50 each, plus delivery £45. Total?

• A£610
• B£618
• C£625
• D£607.50✓

Answer: Books: 45 x £12.50 = £562.50. Adding £45 delivery gives £562.50 + £45 = £607.50.

Weighted average calculation for progress: Subject 1 (weight 3): 72, Subject 2 (weight 2): 68, Subject 3 (weight 1): 75. Weighted average?

• A71.2✓
• B71.8
• C72
• D72.2

Answer: Weighted sum = (72 × 3) + (68 × 2) + (75 × 1) = 216 + 136 + 75 = 427. Total weight = 3 + 2 + 1 = 6. Weighted average = 427 ÷ 6 = 71.17 ≈ 71.2.

A school allocates £3,500 for professional development. If distributed equally among 20 staff, amount per person?

• A£165
• B£170
• C£180
• D£175✓

Answer: £3,500 ÷ 20 = £175 per person.

Ratio of students to laptops is 4:1. If 28 students in class, how many laptops needed?

• A5
• B6
• C7✓
• D8

Answer: 28 ÷ 4 = 7 laptops.

A resource costs £45. If you buy in bulk (20% discount), what is the sale price?

• A£33
• B£34
• C£32
• D£36✓

Answer: 20% of £45 = £9. Sale price = £45 - £9 = £36.

Attendance pattern: 95% over 180 school days. How many days absent?

• A7
• B8
• C9✓
• D10

Answer: If 95% present, then 5% absent. 5% of 180 = 0.05 × 180 = 9 days.

A class improves from 64% pass rate to 76% pass rate. What is the percentage point increase?

• A10
• B11
• C12✓
• D13

Answer: 76% - 64% = 12 percentage points.

A school's capital investment: New buildings £250,000, Equipment £120,000, IT infrastructure £80,000. Total investment?

• A£440,000
• B£420,000
• C£430,000
• D£450,000✓

Answer: £250,000 + £120,000 + £80,000 = £450,000.

Class performance metric: 18 students achieved target, 7 did not. Success ratio?

• A18:7✓
• B7:25
• C18:25
• D25:7

Answer: Success ratio of achieved to total is 18 to (18+7) = 18 to 25, or 18:25.

A school's three-year trend: Year 1: 58%, Year 2: 62%, Year 3: 67%. Average progress across three years?

• A63%
• B62.7%
• C62.5%
• D62.3%✓

Answer: (58 + 62 + 67) ÷ 3 = 187 ÷ 3 = 62.33 ≈ 62.3%.

Proportion of boys to girls in Year 9: 88 boys, 92 girls. What percentage are boys?

• A48%
• B49%
• C50%
• D48.9%✓

Answer: Total = 88 + 92 = 180. Boys = (88 ÷ 180) × 100 = 48.89% ≈ 48.9%.

A teacher has marked 84 papers out of a class of 120. What percentage completed?

• A68%
• B65%
• C70%✓
• D72%

Answer: (84 ÷ 120) × 100 = 70%.

SEN transport costs: Student A £4,500/year, Student B £3,200/year, Student C £5,100/year. Total annual cost?

• A£12,400
• B£13,000
• C£12,600
• D£12,800✓

Answer: £4,500 + £3,200 + £5,100 = £12,800.

A school's pupil-staff ratio: 280 students, 35 staff. Ratio?

• A10:1
• B8:1✓
• C9:1
• D7:1

Answer: 280 ÷ 35 = 8. Ratio is 8:1.

Reading intervention group: Started 12 students, 3 reached target, 4 made good progress, remainder to be reassessed. How many for reassessment?

• A4
• B5✓
• C6
• D7

Answer: 3 + 4 = 7 accounted for. 12 - 7 = 5 for reassessment.

Budget variance analysis: Planned spend £450,000, Actual spend £468,000. Variance?

• A£18,000✓
• B£19,000
• C£17,000
• D£16,000

Answer: £468,000 - £450,000 = £18,000 overspend.

A school's homework completion: Week 1: 94 completed, Week 2: 89 completed, Week 3: 92 completed, out of 100 students. Average completion percentage?

• A92%
• B91%✓
• C92.5%
• D91.5%

Answer: (94 + 89 + 92) ÷ 3 = 275 ÷ 3 = 91.67% ≈ 91%.

Test standardised scores: Mean 100, SD 15. A student scores 125. How many standard deviations above mean?

• A1
• B1.5
• C1.67✓
• D2

Answer: (125 - 100) ÷ 15 = 25 ÷ 15 = 1.67 standard deviations.

A school receives £150,000 grants. Allocates 45% to teaching, 30% to support, 25% to admin. Amount for teaching?

• A£67,500✓
• B£69,000
• C£70,000
• D£65,000

Answer: 45% of £150,000 = 0.45 × 150,000 = £67,500.

Cumulative discount: First discount 10%, second discount 5% on reduced price. Original price £100. Final price?

• A£85.50✓
• B£87.50
• C£86
• D£85

Answer: After 10% discount: £100 - £10 = £90. After 5% on £90: £90 - £4.50 = £85.50.

Intervention program outcomes: Pre-test average 52, post-test average 68. Percentage point improvement?

• A12
• B14
• C16✓
• D18

Answer: 68 - 52 = 16 percentage points improvement.

A subject department budget allocation by year group: Year 7 £5,000, Year 8 £6,500, Year 9 £7,200, Year 10 £8,100, Year 11 £8,200. Total?

• A£35,000✓
• B£35,500
• C£34,500
• D£34,000

Answer: £5,000 + £6,500 + £7,200 + £8,100 + £8,200 = £35,000.

Student progress: Subject A percentile rank 75, Subject B percentile rank 62. Difference?

• A11
• B12
• C13✓
• D15

Answer: 75 - 62 = 13 percentile points.

A class's term progress: Term 1 average 61%, Term 2 average 65%, Term 3 average 71%. Three-term trend line shows increase of?

• A11%
• B8%
• C9%
• D10%✓

Answer: From Term 1 to Term 3: 71% - 61% = 10% increase over three terms.

Staffing turnover rate: 5 teachers left out of 40 total. Turnover percentage?

• A12%
• B11%
• C13%
• D12.5%✓

Answer: (5 ÷ 40) × 100 = 12.5%.

A school's reserves are 8% of annual budget. Budget is £2,000,000. Reserves total?

• A£160,000✓
• B£170,000
• C£165,000
• D£150,000

Answer: 8% of £2,000,000 = 0.08 × 2,000,000 = £160,000.

Test reliability coefficient (Cronbach's alpha): 0.78. Interpretation?

• AAcceptable reliability
• BExcellent reliability
• CPoor reliability
• DGood reliability✓

Answer: Alpha 0.78 is considered good reliability (0.70-0.79 is good range).

A school implements a new intervention. Pre: 40 students below target, Post: 12 below target. Success rate?

• A68%
• B72%
• C65%
• D70%✓

Answer: Improvement: 40 - 12 = 28. Success rate = (28 ÷ 40) × 100 = 70%.

Performance metric: A school improves from national average (50th percentile) to 68th percentile. Gain?

• A18 percentile points✓
• B17 percentile points
• C20 percentile points
• D16 percentile points

Answer: 68 - 50 = 18 percentile points.

A teacher's CPD investment: 6 courses at £450 each, 4 conferences at £800 each. Total CPD budget?

• A£5,600
• B£5,200
• C£5,400
• D£5,900✓

Answer: Courses: 6 × £450 = £2,700. Conferences: 4 × £800 = £3,200. Total: £2,700 + £3,200 = £5,900.

Statistical power analysis: Sample size 150, effect size 0.5, alpha 0.05. This achieves approximately 80% power. Interpretation?

• ACannot determine
• BSample too small
• CSample oversized
• DAdequate sample✓

Answer: 80% statistical power is the standard target, so the sample size is adequate.

A school's sustainability report: Energy costs Year 1 £45,000, Year 2 £42,000, Year 3 £39,000. Year-on-year reduction?

• A£3,000✓
• B£3,500
• C£4,000
• D£2,500

Answer: Year 1 to 2: £45,000 - £42,000 = £3,000. Year 2 to 3: £42,000 - £39,000 = £3,000. Average reduction: £3,000 per year.

A school calculates value-added scores. Student entered at level 4, progressed to level 6.5. Value-added?

• A2
• B2.5✓
• C3
• D3.5

Answer: 6.5 - 4 = 2.5 levels of value-added progress.