Maths practice questions
12 topics and 240 questions, each with a worked explanation. Tap an answer to check it, or open “Show answer & explanation”.
Maths in the 11+ tests whether a child can apply core arithmetic and reasoning skills quickly and accurately under time pressure, not whether they've memorised advanced formulas. Most schools draw questions from four broad areas: number work (place value, fractions, decimals, percentages), problem-solving (word problems, ratio, algebra basics), shape and measurement (geometry, angles, unit conversion), and data handling (averages, sequences). The single biggest factor separating a strong 11+ Maths score from an average one is speed of recall for times tables, number bonds and simple fraction/percentage equivalents (1/2 = 50%, 1/4 = 25%, and so on) — a child who has to work these out from scratch every time will run out of time before running out of ability. Encourage your child to always show their working, even for questions they can do in their head: partial credit isn't usually available in a multiple-choice format, but the habit of writing things down catches careless errors, which are the most common way marks are lost. Each topic below has a short explanation of the method before the practice questions — read it first if the topic feels unfamiliar, then use the questions to build speed.
Number & Place Value
Work with digit values, place columns and rounding — foundational number sense used throughout 11+ Maths papers.
How to approach this
Place value questions test whether a child understands that a digit's value depends on its position in a number — the '4' in 4,000 is worth a thousand times more than the '4' in 4. The reliable method is to write the number out and label each column (thousands, hundreds, tens, units) before answering, rather than trying to do it purely in your head.
For rounding, the rule that trips up the most children is what happens at exactly 5: round up, always — 45 rounds to 50, not 40. Example: to find the value of the '7' in 7,382, first identify its column (thousands), then multiply the digit by that column's value: 7 × 1,000 = 7,000.
What is the value of the digit 0 in 1,057 (the hundreds digit)?
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Correct answer: D. 0
The digit 0 is in the hundreds column, so its value is 0 × 100 = 0.
Round 584 to the nearest 10.
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Correct answer: A. 580
584 is closer to 580 than to the next multiple of 10, so it rounds to 580.
What is the value of the digit 0 in 3,205 (the tens digit)?
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Correct answer: D. 0
The digit 0 is in the tens column, so its value is 0 × 10 = 0.
Round 670 to the nearest 10.
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Correct answer: C. 670
670 is closer to 670 than to the next multiple of 10, so it rounds to 670.
What is the value of the digit 3 in 3,273 (the thousands digit)?
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Correct answer: B. 3000
The digit 3 is in the thousands column, so its value is 3 × 1000 = 3000.
Round 851 to the nearest 10.
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Correct answer: B. 850
851 is closer to 850 than to the next multiple of 10, so it rounds to 850.
What is the value of the digit 0 in 4,907 (the tens digit)?
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Correct answer: A. 0
The digit 0 is in the tens column, so its value is 0 × 10 = 0.
Round 926 to the nearest 10.
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Correct answer: C. 930
926 is closer to 930 than to the next multiple of 10, so it rounds to 930.
What is the value of the digit 7 in 7,154 (the thousands digit)?
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Correct answer: C. 7000
The digit 7 is in the thousands column, so its value is 7 × 1000 = 7000.
Round 496 to the nearest 10.
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Correct answer: C. 500
496 is closer to 500 than to the next multiple of 10, so it rounds to 500.
What is the value of the digit 6 in 7,496 (the units digit)?
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Correct answer: D. 6
The digit 6 is in the units column, so its value is 6 × 1 = 6.
Round 857 to the nearest 10.
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Correct answer: B. 860
857 is closer to 860 than to the next multiple of 10, so it rounds to 860.
What is the value of the digit 8 in 8,306 (the thousands digit)?
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Correct answer: A. 8000
The digit 8 is in the thousands column, so its value is 8 × 1000 = 8000.
Round 590 to the nearest 10.
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Correct answer: B. 590
590 is closer to 590 than to the next multiple of 10, so it rounds to 590.
What is the value of the digit 8 in 7,809 (the hundreds digit)?
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Correct answer: D. 800
The digit 8 is in the hundreds column, so its value is 8 × 100 = 800.
Round 494 to the nearest 10.
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Correct answer: D. 490
494 is closer to 490 than to the next multiple of 10, so it rounds to 490.
What is the value of the digit 6 in 7,206 (the units digit)?
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Correct answer: A. 6
The digit 6 is in the units column, so its value is 6 × 1 = 6.
Round 732 to the nearest 10.
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Correct answer: A. 730
732 is closer to 730 than to the next multiple of 10, so it rounds to 730.
What is the value of the digit 1 in 7,015 (the tens digit)?
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Correct answer: D. 10
The digit 1 is in the tens column, so its value is 1 × 10 = 10.
Round 611 to the nearest 10.
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Correct answer: B. 610
611 is closer to 610 than to the next multiple of 10, so it rounds to 610.
Fractions
Calculate a fraction of an amount, a staple 11+ Maths question type covering halves, thirds, quarters, fifths and eighths.
How to approach this
Finding a fraction of an amount always follows the same two-step method: divide by the denominator (the bottom number) to find one part, then multiply by the numerator (the top number) to find how many parts you need.
For example, to find 3/4 of 20: divide 20 by 4 to get 5 (this is one quarter), then multiply 5 by 3 to get 15. Children often go wrong by multiplying first and dividing second — with awkward numbers that can create fractions mid-calculation, so always divide first. It's worth memorising the most common conversions (1/2, 1/4, 1/3, 1/5, 1/8) as percentages and decimals, since 11+ papers frequently mix fraction, decimal and percentage questions on the same topic.
What is 1/2 of 28?
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Correct answer: A. 14
28 ÷ 2 = 14, then × 1 = 14.
What is 1/4 of 32?
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Correct answer: C. 8
32 ÷ 4 = 8, then × 1 = 8.
What is 3/4 of 68?
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Correct answer: D. 51
68 ÷ 4 = 17, then × 3 = 51.
What is 1/5 of 60?
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Correct answer: D. 12
60 ÷ 5 = 12, then × 1 = 12.
What is 2/5 of 100?
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Correct answer: D. 40
100 ÷ 5 = 20, then × 2 = 40.
What is 1/3 of 45?
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Correct answer: A. 15
45 ÷ 3 = 15, then × 1 = 15.
What is 2/3 of 57?
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Correct answer: C. 38
57 ÷ 3 = 19, then × 2 = 38.
What is 3/5 of 70?
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Correct answer: C. 42
70 ÷ 5 = 14, then × 3 = 42.
What is 1/8 of 104?
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Correct answer: D. 13
104 ÷ 8 = 13, then × 1 = 13.
What is 5/8 of 128?
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Correct answer: C. 80
128 ÷ 8 = 16, then × 5 = 80.
What is 1/2 of 38?
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Correct answer: A. 19
38 ÷ 2 = 19, then × 1 = 19.
What is 1/4 of 20?
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Correct answer: D. 5
20 ÷ 4 = 5, then × 1 = 5.
What is 3/4 of 16?
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Correct answer: D. 12
16 ÷ 4 = 4, then × 3 = 12.
What is 1/5 of 70?
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Correct answer: A. 14
70 ÷ 5 = 14, then × 1 = 14.
What is 2/5 of 60?
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Correct answer: D. 24
60 ÷ 5 = 12, then × 2 = 24.
What is 1/3 of 9?
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Correct answer: C. 3
9 ÷ 3 = 3, then × 1 = 3.
What is 2/3 of 45?
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Correct answer: A. 30
45 ÷ 3 = 15, then × 2 = 30.
What is 3/5 of 35?
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Correct answer: A. 21
35 ÷ 5 = 7, then × 3 = 21.
What is 1/8 of 144?
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Correct answer: C. 18
144 ÷ 8 = 18, then × 1 = 18.
What is 5/8 of 16?
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Correct answer: A. 10
16 ÷ 8 = 2, then × 5 = 10.
Decimals & Percentages
Find percentages of amounts and add decimals — skills that come up constantly in real-world style word problems.
How to approach this
Percentage-of-an-amount questions use the same logic as fractions: 'per cent' literally means 'per hundred', so finding 25% of a number is the same as finding a quarter of it. The most efficient method for tricky percentages is to build them from friendly ones: to find 15% of 40, first find 10% (divide by 10 = 4), then find 5% (half of that = 2), then add them together (4 + 2 = 6).
For adding decimals, the error to watch for is misaligning the decimal point — always line up the decimal points vertically before adding, even when doing it mentally, by imagining the columns.
What is 10% of 500?
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Correct answer: C. 50
10% of 500 = (10/100) × 500 = 50.
What is 10.8 + 1.3?
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Correct answer: D. 12.1
10.8 + 1.3 = 12.1.
What is 25% of 340?
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Correct answer: A. 85
25% of 340 = (25/100) × 340 = 85.
What is 12.8 + 1?
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Correct answer: C. 13.8
12.8 + 1 = 13.8.
What is 75% of 260?
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Correct answer: B. 195
75% of 260 = (75/100) × 260 = 195.
What is 18.5 + 0.7?
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Correct answer: B. 19.2
18.5 + 0.7 = 19.2.
What is 5% of 80?
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Correct answer: D. 4
5% of 80 = (5/100) × 80 = 4.
What is 20.4 + 1.1?
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Correct answer: D. 21.5
20.4 + 1.1 = 21.5.
What is 40% of 680?
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Correct answer: A. 272
40% of 680 = (40/100) × 680 = 272.
What is 18.3 + 0.3?
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Correct answer: C. 18.6
18.3 + 0.3 = 18.6.
What is 10% of 740?
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Correct answer: D. 74
10% of 740 = (10/100) × 740 = 74.
What is 5.5 + 0.7?
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Correct answer: C. 6.2
5.5 + 0.7 = 6.2.
What is 25% of 740?
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Correct answer: A. 185
25% of 740 = (25/100) × 740 = 185.
What is 18.9 + 1.5?
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Correct answer: C. 20.4
18.9 + 1.5 = 20.4.
What is 75% of 720?
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Correct answer: B. 540
75% of 720 = (75/100) × 720 = 540.
What is 10.7 + 0.3?
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Correct answer: A. 11
10.7 + 0.3 = 11.
What is 5% of 380?
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Correct answer: D. 19
5% of 380 = (5/100) × 380 = 19.
What is 8.7 + 0.5?
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Correct answer: B. 9.2
8.7 + 0.5 = 9.2.
What is 40% of 420?
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Correct answer: A. 168
40% of 420 = (40/100) × 420 = 168.
What is 16.8 + 0.8?
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Correct answer: D. 17.6
16.8 + 0.8 = 17.6.
Ratio & Proportion
Simplify ratios to their lowest terms using the highest common factor.
How to approach this
A ratio compares two quantities, and simplifying one works exactly like simplifying a fraction: find the highest common factor (the largest number that divides evenly into both sides) and divide both sides by it. For a ratio like 12:18, both numbers divide by 6, giving 2:3 in its simplest form.
A quick way to check you've fully simplified a ratio is to ask whether the two numbers share any common factor greater than 1 — if they do, you haven't finished. Ratio questions in the 11+ are usually testing this simplification skill directly, or asking you to scale a ratio up or down while keeping the proportion the same.
Simplify the ratio 20:16 to its simplest form.
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Correct answer: D. 5:4
Divide both sides by their highest common factor, 4: 20÷4 : 16÷4 = 5:4.
Simplify the ratio 20:12 to its simplest form.
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Correct answer: B. 5:3
Divide both sides by their highest common factor, 4: 20÷4 : 12÷4 = 5:3.
Simplify the ratio 15:5 to its simplest form.
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Correct answer: B. 3:1
Divide both sides by their highest common factor, 5: 15÷5 : 5÷5 = 3:1.
Simplify the ratio 18:24 to its simplest form.
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Correct answer: D. 3:4
Divide both sides by their highest common factor, 6: 18÷6 : 24÷6 = 3:4.
Simplify the ratio 5:20 to its simplest form.
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Correct answer: D. 1:4
Divide both sides by their highest common factor, 5: 5÷5 : 20÷5 = 1:4.
Simplify the ratio 20:16 to its simplest form.
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Correct answer: B. 5:4
Divide both sides by their highest common factor, 4: 20÷4 : 16÷4 = 5:4.
Simplify the ratio 12:6 to its simplest form.
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Correct answer: A. 2:1
Divide both sides by their highest common factor, 6: 12÷6 : 6÷6 = 2:1.
Simplify the ratio 12:9 to its simplest form.
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Correct answer: D. 4:3
Divide both sides by their highest common factor, 3: 12÷3 : 9÷3 = 4:3.
Simplify the ratio 15:6 to its simplest form.
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Correct answer: C. 5:2
Divide both sides by their highest common factor, 3: 15÷3 : 6÷3 = 5:2.
Simplify the ratio 6:2 to its simplest form.
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Correct answer: B. 3:1
Divide both sides by their highest common factor, 2: 6÷2 : 2÷2 = 3:1.
Simplify the ratio 12:4 to its simplest form.
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Correct answer: C. 3:1
Divide both sides by their highest common factor, 4: 12÷4 : 4÷4 = 3:1.
Simplify the ratio 18:18 to its simplest form.
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Correct answer: C. 1:1
Divide both sides by their highest common factor, 18: 18÷18 : 18÷18 = 1:1.
Simplify the ratio 24:12 to its simplest form.
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Correct answer: C. 2:1
Divide both sides by their highest common factor, 12: 24÷12 : 12÷12 = 2:1.
Simplify the ratio 20:10 to its simplest form.
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Correct answer: D. 2:1
Divide both sides by their highest common factor, 10: 20÷10 : 10÷10 = 2:1.
Simplify the ratio 12:24 to its simplest form.
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Correct answer: D. 1:2
Divide both sides by their highest common factor, 12: 12÷12 : 24÷12 = 1:2.
Simplify the ratio 12:9 to its simplest form.
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Correct answer: A. 4:3
Divide both sides by their highest common factor, 3: 12÷3 : 9÷3 = 4:3.
Simplify the ratio 20:20 to its simplest form.
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Correct answer: D. 1:1
Divide both sides by their highest common factor, 20: 20÷20 : 20÷20 = 1:1.
Simplify the ratio 20:8 to its simplest form.
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Correct answer: D. 5:2
Divide both sides by their highest common factor, 4: 20÷4 : 8÷4 = 5:2.
Simplify the ratio 4:6 to its simplest form.
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Correct answer: B. 2:3
Divide both sides by their highest common factor, 2: 4÷2 : 6÷2 = 2:3.
Simplify the ratio 18:12 to its simplest form.
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Correct answer: B. 3:2
Divide both sides by their highest common factor, 6: 18÷6 : 12÷6 = 3:2.
Algebra Basics
Solve simple one-step equations to find an unknown value — an early introduction to algebraic thinking.
How to approach this
At 11+ level, algebra means solving one-step equations to find a missing number, usually written with a letter like x. The method is always to do the same operation to both sides of the equation to isolate the letter: if x + 7 = 15, subtract 7 from both sides to get x = 8.
It helps to check the answer by substituting it back into the original equation — 8 + 7 does equal 15, so the answer is confirmed correct. This checking habit catches the most common mistake, which is doing the subtraction the wrong way round (calculating 15 + 7 instead of 15 − 7).
If x + 9 = 23, what is x?
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Correct answer: A. 14
Subtract 9 from both sides: x = 23 - 9 = 14.
If x + 10 = 20, what is x?
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Correct answer: A. 10
Subtract 10 from both sides: x = 20 - 10 = 10.
If x + 6 = 17, what is x?
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Correct answer: A. 11
Subtract 6 from both sides: x = 17 - 6 = 11.
If x + 13 = 28, what is x?
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Correct answer: D. 15
Subtract 13 from both sides: x = 28 - 13 = 15.
If x + 14 = 30, what is x?
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Correct answer: B. 16
Subtract 14 from both sides: x = 30 - 14 = 16.
If x + 14 = 26, what is x?
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Correct answer: C. 12
Subtract 14 from both sides: x = 26 - 14 = 12.
If x + 5 = 14, what is x?
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Correct answer: A. 9
Subtract 5 from both sides: x = 14 - 5 = 9.
If x + 4 = 10, what is x?
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Correct answer: C. 6
Subtract 4 from both sides: x = 10 - 4 = 6.
If x + 7 = 22, what is x?
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Correct answer: B. 15
Subtract 7 from both sides: x = 22 - 7 = 15.
If x + 4 = 10, what is x?
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Correct answer: B. 6
Subtract 4 from both sides: x = 10 - 4 = 6.
If x + 9 = 15, what is x?
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Correct answer: D. 6
Subtract 9 from both sides: x = 15 - 9 = 6.
If x + 3 = 23, what is x?
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Correct answer: B. 20
Subtract 3 from both sides: x = 23 - 3 = 20.
If x + 13 = 22, what is x?
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Correct answer: B. 9
Subtract 13 from both sides: x = 22 - 13 = 9.
If x + 2 = 5, what is x?
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Correct answer: B. 3
Subtract 2 from both sides: x = 5 - 2 = 3.
If x + 4 = 14, what is x?
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Correct answer: C. 10
Subtract 4 from both sides: x = 14 - 4 = 10.
If x + 8 = 10, what is x?
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Correct answer: B. 2
Subtract 8 from both sides: x = 10 - 8 = 2.
If x + 6 = 11, what is x?
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Correct answer: C. 5
Subtract 6 from both sides: x = 11 - 6 = 5.
If x + 5 = 18, what is x?
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Correct answer: B. 13
Subtract 5 from both sides: x = 18 - 5 = 13.
If x + 6 = 25, what is x?
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Correct answer: A. 19
Subtract 6 from both sides: x = 25 - 6 = 19.
If x + 10 = 12, what is x?
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Correct answer: C. 2
Subtract 10 from both sides: x = 12 - 10 = 2.
Geometry & Angles
Work out missing angles in triangles and calculate the perimeter of rectangles.
How to approach this
The single most useful fact for 11+ geometry is that angles in a triangle always add up to 180°, and angles on a straight line always add up to 180° too — most angle questions can be solved by adding up the angles you know and subtracting from 180.
For perimeter questions, remember perimeter means the total distance around the outside of a shape: for a rectangle, that's twice the length plus twice the width, not length times width, which is area — mixing these two up is the most common error in this topic.
A triangle has angles of 52° and 58°. What is the third angle?
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Correct answer: A. 70
Angles in a triangle sum to 180°, so the third angle is 180 - 52 - 58 = 70°.
What is the perimeter of a rectangle 6cm long and 12cm wide?
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Correct answer: C. 36
Perimeter = 2 × (length + width) = 2 × (6 + 12) = 36cm.
A triangle has angles of 69° and 40°. What is the third angle?
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Correct answer: C. 71
Angles in a triangle sum to 180°, so the third angle is 180 - 69 - 40 = 71°.
What is the perimeter of a rectangle 17cm long and 8cm wide?
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Correct answer: C. 50
Perimeter = 2 × (length + width) = 2 × (17 + 8) = 50cm.
A triangle has angles of 40° and 46°. What is the third angle?
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Correct answer: A. 94
Angles in a triangle sum to 180°, so the third angle is 180 - 40 - 46 = 94°.
What is the perimeter of a rectangle 4cm long and 10cm wide?
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Correct answer: A. 28
Perimeter = 2 × (length + width) = 2 × (4 + 10) = 28cm.
A triangle has angles of 74° and 58°. What is the third angle?
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Correct answer: C. 48
Angles in a triangle sum to 180°, so the third angle is 180 - 74 - 58 = 48°.
What is the perimeter of a rectangle 17cm long and 8cm wide?
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Correct answer: D. 50
Perimeter = 2 × (length + width) = 2 × (17 + 8) = 50cm.
A triangle has angles of 33° and 44°. What is the third angle?
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Correct answer: C. 103
Angles in a triangle sum to 180°, so the third angle is 180 - 33 - 44 = 103°.
What is the perimeter of a rectangle 18cm long and 3cm wide?
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Correct answer: B. 42
Perimeter = 2 × (length + width) = 2 × (18 + 3) = 42cm.
A triangle has angles of 40° and 51°. What is the third angle?
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Correct answer: C. 89
Angles in a triangle sum to 180°, so the third angle is 180 - 40 - 51 = 89°.
What is the perimeter of a rectangle 13cm long and 2cm wide?
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Correct answer: A. 30
Perimeter = 2 × (length + width) = 2 × (13 + 2) = 30cm.
A triangle has angles of 75° and 70°. What is the third angle?
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Correct answer: B. 35
Angles in a triangle sum to 180°, so the third angle is 180 - 75 - 70 = 35°.
What is the perimeter of a rectangle 5cm long and 13cm wide?
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Correct answer: D. 36
Perimeter = 2 × (length + width) = 2 × (5 + 13) = 36cm.
A triangle has angles of 70° and 89°. What is the third angle?
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Correct answer: C. 21
Angles in a triangle sum to 180°, so the third angle is 180 - 70 - 89 = 21°.
What is the perimeter of a rectangle 18cm long and 13cm wide?
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Correct answer: B. 62
Perimeter = 2 × (length + width) = 2 × (18 + 13) = 62cm.
A triangle has angles of 73° and 57°. What is the third angle?
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Correct answer: A. 50
Angles in a triangle sum to 180°, so the third angle is 180 - 73 - 57 = 50°.
What is the perimeter of a rectangle 15cm long and 6cm wide?
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Correct answer: D. 42
Perimeter = 2 × (length + width) = 2 × (15 + 6) = 42cm.
A triangle has angles of 60° and 75°. What is the third angle?
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Correct answer: D. 45
Angles in a triangle sum to 180°, so the third angle is 180 - 60 - 75 = 45°.
What is the perimeter of a rectangle 9cm long and 2cm wide?
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Correct answer: B. 22
Perimeter = 2 × (length + width) = 2 × (9 + 2) = 22cm.
Measurement
Convert between units, such as centimetres to metres or grams to kilograms.
How to approach this
Unit conversion questions test whether a child has memorised the standard conversions: 100cm in a metre, 1000g in a kilogram, 60 minutes in an hour, 1000ml in a litre. The method is always the same: work out how many of the small unit fit into one of the big unit, then multiply.
So to convert 6 hours into minutes, multiply 6 by 60 (not divide) — a useful check is to think about whether your answer should be a bigger or smaller number than you started with; minutes are smaller units than hours, so there should be more of them.
How many cm are there in 3 m?
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Correct answer: D. 300
1 m = 100 cm, so 3 m = 3 × 100 = 300 cm.
How many g are there in 2 kg?
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Correct answer: A. 2000
1 kg = 1000 g, so 2 kg = 2 × 1000 = 2000 g.
How many min are there in 9 hr?
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Correct answer: D. 540
1 hr = 60 min, so 9 hr = 9 × 60 = 540 min.
How many ml are there in 6 l?
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Correct answer: D. 6000
1 l = 1000 ml, so 6 l = 6 × 1000 = 6000 ml.
How many cm are there in 7 m?
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Correct answer: B. 700
1 m = 100 cm, so 7 m = 7 × 100 = 700 cm.
How many g are there in 8 kg?
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Correct answer: A. 8000
1 kg = 1000 g, so 8 kg = 8 × 1000 = 8000 g.
How many min are there in 9 hr?
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Correct answer: D. 540
1 hr = 60 min, so 9 hr = 9 × 60 = 540 min.
How many ml are there in 8 l?
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Correct answer: C. 8000
1 l = 1000 ml, so 8 l = 8 × 1000 = 8000 ml.
How many cm are there in 9 m?
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Correct answer: B. 900
1 m = 100 cm, so 9 m = 9 × 100 = 900 cm.
How many g are there in 7 kg?
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Correct answer: A. 7000
1 kg = 1000 g, so 7 kg = 7 × 1000 = 7000 g.
How many min are there in 9 hr?
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Correct answer: B. 540
1 hr = 60 min, so 9 hr = 9 × 60 = 540 min.
How many ml are there in 6 l?
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Correct answer: B. 6000
1 l = 1000 ml, so 6 l = 6 × 1000 = 6000 ml.
How many cm are there in 4 m?
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Correct answer: A. 400
1 m = 100 cm, so 4 m = 4 × 100 = 400 cm.
How many g are there in 9 kg?
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Correct answer: C. 9000
1 kg = 1000 g, so 9 kg = 9 × 1000 = 9000 g.
How many min are there in 3 hr?
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Correct answer: C. 180
1 hr = 60 min, so 3 hr = 3 × 60 = 180 min.
How many ml are there in 8 l?
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Correct answer: A. 8000
1 l = 1000 ml, so 8 l = 8 × 1000 = 8000 ml.
How many cm are there in 3 m?
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Correct answer: B. 300
1 m = 100 cm, so 3 m = 3 × 100 = 300 cm.
How many g are there in 9 kg?
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Correct answer: C. 9000
1 kg = 1000 g, so 9 kg = 9 × 1000 = 9000 g.
How many min are there in 9 hr?
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Correct answer: A. 540
1 hr = 60 min, so 9 hr = 9 × 60 = 540 min.
How many ml are there in 9 l?
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Correct answer: C. 9000
1 l = 1000 ml, so 9 l = 9 × 1000 = 9000 ml.
Time & Money
Calculate arrival times from a start time and a journey duration — a classic 11+ time-based word problem.
How to approach this
Time calculation questions (like working out an arrival time from a departure time and a journey length) are easiest to solve by breaking the journey into chunks of whole hours first, then adding the leftover minutes — rather than trying to add minutes directly across an hour boundary, which is where most mistakes happen.
For example, a journey of 95 minutes starting at 9:15 is easier to handle as '1 hour 35 minutes': add the hour first (10:15), then the 35 minutes (10:50). Always double-check whether your answer crosses into the afternoon if the question uses the 24-hour clock.
A train leaves at 11:00 and the journey takes 58 minutes. What time does it arrive?
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Correct answer: D. 11:58
11:00 plus 58 minutes is 11:58.
A train leaves at 09:00 and the journey takes 68 minutes. What time does it arrive?
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Correct answer: A. 10:08
09:00 plus 68 minutes is 10:08.
A train leaves at 10:00 and the journey takes 56 minutes. What time does it arrive?
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Correct answer: D. 10:56
10:00 plus 56 minutes is 10:56.
A train leaves at 11:15 and the journey takes 29 minutes. What time does it arrive?
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Correct answer: B. 11:44
11:15 plus 29 minutes is 11:44.
A train leaves at 08:45 and the journey takes 71 minutes. What time does it arrive?
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Correct answer: C. 09:56
08:45 plus 71 minutes is 09:56.
A train leaves at 10:30 and the journey takes 51 minutes. What time does it arrive?
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Correct answer: D. 11:21
10:30 plus 51 minutes is 11:21.
A train leaves at 08:30 and the journey takes 73 minutes. What time does it arrive?
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Correct answer: D. 09:43
08:30 plus 73 minutes is 09:43.
A train leaves at 09:45 and the journey takes 59 minutes. What time does it arrive?
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Correct answer: A. 10:44
09:45 plus 59 minutes is 10:44.
A train leaves at 08:15 and the journey takes 65 minutes. What time does it arrive?
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Correct answer: A. 09:20
08:15 plus 65 minutes is 09:20.
A train leaves at 10:15 and the journey takes 20 minutes. What time does it arrive?
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Correct answer: D. 10:35
10:15 plus 20 minutes is 10:35.
A train leaves at 11:45 and the journey takes 65 minutes. What time does it arrive?
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Correct answer: C. 12:50
11:45 plus 65 minutes is 12:50.
A train leaves at 11:15 and the journey takes 55 minutes. What time does it arrive?
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Correct answer: B. 12:10
11:15 plus 55 minutes is 12:10.
A train leaves at 08:30 and the journey takes 39 minutes. What time does it arrive?
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Correct answer: A. 09:09
08:30 plus 39 minutes is 09:09.
A train leaves at 10:45 and the journey takes 65 minutes. What time does it arrive?
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Correct answer: D. 11:50
10:45 plus 65 minutes is 11:50.
A train leaves at 10:15 and the journey takes 76 minutes. What time does it arrive?
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Correct answer: D. 11:31
10:15 plus 76 minutes is 11:31.
A train leaves at 11:45 and the journey takes 42 minutes. What time does it arrive?
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Correct answer: C. 12:27
11:45 plus 42 minutes is 12:27.
A train leaves at 08:45 and the journey takes 39 minutes. What time does it arrive?
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Correct answer: B. 09:24
08:45 plus 39 minutes is 09:24.
A train leaves at 11:30 and the journey takes 33 minutes. What time does it arrive?
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Correct answer: D. 12:03
11:30 plus 33 minutes is 12:03.
A train leaves at 10:00 and the journey takes 47 minutes. What time does it arrive?
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Correct answer: C. 10:47
10:00 plus 47 minutes is 10:47.
A train leaves at 11:30 and the journey takes 57 minutes. What time does it arrive?
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Correct answer: C. 12:27
11:30 plus 57 minutes is 12:27.
Data & Averages
Calculate the mean average of a small set of numbers.
How to approach this
The mean average is found by adding up all the numbers in a set, then dividing by how many numbers there are. The most common mistake is dividing by the wrong count — always count the numbers in the list before dividing, rather than assuming.
For example, the mean of 4, 9 and 14 is found by adding them (27) and dividing by 3 (the count), giving 9. It's worth sense-checking your answer: the mean should always fall somewhere between the smallest and largest number in the set — if it doesn't, a calculation has gone wrong.
What is the mean of 4, 13, 3?
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Correct answer: A. 6.7
Add the numbers: 4 + 13 + 3 = 20. Divide by 3: 20 ÷ 3 = 6.7.
What is the mean of 7, 14, 5?
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Correct answer: A. 8.7
Add the numbers: 7 + 14 + 5 = 26. Divide by 3: 26 ÷ 3 = 8.7.
What is the mean of 6, 18, 17?
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Correct answer: D. 13.7
Add the numbers: 6 + 18 + 17 = 41. Divide by 3: 41 ÷ 3 = 13.7.
What is the mean of 17, 20, 13?
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Correct answer: A. 16.7
Add the numbers: 17 + 20 + 13 = 50. Divide by 3: 50 ÷ 3 = 16.7.
What is the mean of 11, 16, 11?
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Correct answer: A. 12.7
Add the numbers: 11 + 16 + 11 = 38. Divide by 3: 38 ÷ 3 = 12.7.
What is the mean of 19, 11, 3?
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Correct answer: A. 11
Add the numbers: 19 + 11 + 3 = 33. Divide by 3: 33 ÷ 3 = 11.
What is the mean of 5, 9, 19?
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Correct answer: A. 11
Add the numbers: 5 + 9 + 19 = 33. Divide by 3: 33 ÷ 3 = 11.
What is the mean of 16, 19, 12?
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Correct answer: C. 15.7
Add the numbers: 16 + 19 + 12 = 47. Divide by 3: 47 ÷ 3 = 15.7.
What is the mean of 9, 15, 2?
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Correct answer: D. 8.7
Add the numbers: 9 + 15 + 2 = 26. Divide by 3: 26 ÷ 3 = 8.7.
What is the mean of 10, 12, 15?
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Correct answer: D. 12.3
Add the numbers: 10 + 12 + 15 = 37. Divide by 3: 37 ÷ 3 = 12.3.
What is the mean of 13, 19, 15?
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Correct answer: C. 15.7
Add the numbers: 13 + 19 + 15 = 47. Divide by 3: 47 ÷ 3 = 15.7.
What is the mean of 10, 9, 8?
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Correct answer: C. 9
Add the numbers: 10 + 9 + 8 = 27. Divide by 3: 27 ÷ 3 = 9.
What is the mean of 15, 17, 17?
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Correct answer: C. 16.3
Add the numbers: 15 + 17 + 17 = 49. Divide by 3: 49 ÷ 3 = 16.3.
What is the mean of 7, 20, 6?
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Correct answer: B. 11
Add the numbers: 7 + 20 + 6 = 33. Divide by 3: 33 ÷ 3 = 11.
What is the mean of 12, 20, 8?
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Correct answer: C. 13.3
Add the numbers: 12 + 20 + 8 = 40. Divide by 3: 40 ÷ 3 = 13.3.
What is the mean of 19, 6, 18?
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Correct answer: B. 14.3
Add the numbers: 19 + 6 + 18 = 43. Divide by 3: 43 ÷ 3 = 14.3.
What is the mean of 20, 10, 20?
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Correct answer: B. 16.7
Add the numbers: 20 + 10 + 20 = 50. Divide by 3: 50 ÷ 3 = 16.7.
What is the mean of 9, 18, 18?
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Correct answer: D. 15
Add the numbers: 9 + 18 + 18 = 45. Divide by 3: 45 ÷ 3 = 15.
What is the mean of 15, 4, 2?
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Correct answer: D. 7
Add the numbers: 15 + 4 + 2 = 21. Divide by 3: 21 ÷ 3 = 7.
What is the mean of 5, 11, 8?
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Correct answer: B. 8
Add the numbers: 5 + 11 + 8 = 24. Divide by 3: 24 ÷ 3 = 8.
Word Problems
Apply addition and subtraction to short real-world scenarios involving people and objects.
How to approach this
Word problems test whether a child can translate a story into a calculation, which is usually the hardest part — the arithmetic itself is often simple once you know what to calculate. The reliable approach is to underline the numbers in the question and circle the words that tell you the operation: 'more', 'given', 'total' usually mean addition; 'left', 'fewer', 'spent' usually mean subtraction.
Reading the question twice before writing anything down catches most misunderstandings, since 11+ word problems are often written to be slightly misleading on a first read.
Leo has 36 sweets and is given 23 more. How many sweets does Leo have now?
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Correct answer: B. 59
36 + 23 = 59.
Leo has 39 sweets and is given 25 more. How many sweets does Leo have now?
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Correct answer: A. 64
39 + 25 = 64.
Amina has 40 sweets and is given 23 more. How many sweets does Amina have now?
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Correct answer: C. 63
40 + 23 = 63.
Jack has 10 sweets and is given 23 more. How many sweets does Jack have now?
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Correct answer: D. 33
10 + 23 = 33.
Priya has 27 sweets and is given 8 more. How many sweets does Priya have now?
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Correct answer: D. 35
27 + 8 = 35.
Leo has 14 sweets and is given 22 more. How many sweets does Leo have now?
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Correct answer: D. 36
14 + 22 = 36.
Leo has 18 sweets and is given 15 more. How many sweets does Leo have now?
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Correct answer: D. 33
18 + 15 = 33.
Grace has 16 sweets and is given 23 more. How many sweets does Grace have now?
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Correct answer: A. 39
16 + 23 = 39.
Amina has 18 sweets and is given 20 more. How many sweets does Amina have now?
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Correct answer: A. 38
18 + 20 = 38.
Amina has 26 sweets and is given 20 more. How many sweets does Amina have now?
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Correct answer: A. 46
26 + 20 = 46.
Jack has 13 sweets and is given 10 more. How many sweets does Jack have now?
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Correct answer: B. 23
13 + 10 = 23.
Priya has 39 sweets and is given 22 more. How many sweets does Priya have now?
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Correct answer: B. 61
39 + 22 = 61.
Amina has 5 sweets and is given 3 more. How many sweets does Amina have now?
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Correct answer: D. 8
5 + 3 = 8.
Jack has 30 sweets and is given 18 more. How many sweets does Jack have now?
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Correct answer: A. 48
30 + 18 = 48.
Grace has 22 sweets and is given 19 more. How many sweets does Grace have now?
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Correct answer: D. 41
22 + 19 = 41.
Jack has 30 sweets and is given 5 more. How many sweets does Jack have now?
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Correct answer: B. 35
30 + 5 = 35.
Priya has 29 sweets and is given 4 more. How many sweets does Priya have now?
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Correct answer: C. 33
29 + 4 = 33.
Priya has 14 sweets and is given 22 more. How many sweets does Priya have now?
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Correct answer: D. 36
14 + 22 = 36.
Jack has 34 sweets and is given 24 more. How many sweets does Jack have now?
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Correct answer: A. 58
34 + 24 = 58.
Leo has 11 sweets and is given 23 more. How many sweets does Leo have now?
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Correct answer: B. 34
11 + 23 = 34.
Sequences
Spot the pattern in a number sequence and work out what comes next, whether it increases by a fixed amount or doubles.
How to approach this
Number sequences either add (or subtract) the same amount each time, or multiply by the same amount each time — the first job is always to work out which type you're looking at by checking the gap between the first two numbers, then confirming that same gap holds between the next pair.
If the numbers are growing very quickly (doubling, tripling), it's a multiplying sequence; if they're growing steadily by the same small amount, it's an adding sequence. Once you've identified the rule, apply it once more to find the next term, rather than trying to guess the pattern.
Find the next number: 3, 5, 7, 9, ?
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Correct answer: B. 11
The sequence adds 2 each time, so the next number is 11.
Find the next number: 3, 6, 12, 24, ?
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Correct answer: C. 48
The sequence doubles each time, so the next number is 48.
Find the next number: 6, 13, 20, 27, ?
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Correct answer: A. 34
The sequence adds 7 each time, so the next number is 34.
Find the next number: 2, 4, 8, 16, ?
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Correct answer: C. 32
The sequence doubles each time, so the next number is 32.
Find the next number: 6, 10, 14, 18, ?
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Correct answer: A. 22
The sequence adds 4 each time, so the next number is 22.
Find the next number: 5, 10, 20, 40, ?
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Correct answer: C. 80
The sequence doubles each time, so the next number is 80.
Find the next number: 10, 18, 26, 34, ?
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Correct answer: B. 42
The sequence adds 8 each time, so the next number is 42.
Find the next number: 8, 16, 32, 64, ?
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Correct answer: A. 128
The sequence doubles each time, so the next number is 128.
Find the next number: 4, 6, 8, 10, ?
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Correct answer: A. 12
The sequence adds 2 each time, so the next number is 12.
Find the next number: 2, 4, 8, 16, ?
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Correct answer: D. 32
The sequence doubles each time, so the next number is 32.
Find the next number: 1, 8, 15, 22, ?
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Correct answer: A. 29
The sequence adds 7 each time, so the next number is 29.
Find the next number: 5, 10, 20, 40, ?
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Correct answer: A. 80
The sequence doubles each time, so the next number is 80.
Find the next number: 3, 11, 19, 27, ?
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Correct answer: B. 35
The sequence adds 8 each time, so the next number is 35.
Find the next number: 4, 8, 16, 32, ?
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Correct answer: C. 64
The sequence doubles each time, so the next number is 64.
Find the next number: 3, 11, 19, 27, ?
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Correct answer: A. 35
The sequence adds 8 each time, so the next number is 35.
Find the next number: 4, 8, 16, 32, ?
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Correct answer: C. 64
The sequence doubles each time, so the next number is 64.
Find the next number: 8, 16, 24, 32, ?
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Correct answer: A. 40
The sequence adds 8 each time, so the next number is 40.
Find the next number: 7, 14, 28, 56, ?
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Correct answer: A. 112
The sequence doubles each time, so the next number is 112.
Find the next number: 8, 15, 22, 29, ?
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Correct answer: B. 36
The sequence adds 7 each time, so the next number is 36.
Find the next number: 2, 4, 8, 16, ?
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Correct answer: D. 32
The sequence doubles each time, so the next number is 32.
Mental Arithmetic
Sharpen quick addition, subtraction and multiplication under time pressure — the bread-and-butter of every 11+ Maths paper.
How to approach this
Mental arithmetic questions reward speed and number sense over method, so the biggest single improvement a child can make is fluency with times tables up to 12×12 and quick addition/subtraction of two-digit numbers.
For addition and subtraction under time pressure, rounding one number to the nearest 10 and adjusting at the end is often faster than working with the exact numbers directly — for example, 38 + 47 is easier as (40 + 47) − 2. Regular short bursts of practice build this fluency far more effectively than occasional long sessions.
What is 16 + 7?
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Correct answer: A. 23
16 + 7 = 23.
What is 39 - 34?
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Correct answer: C. 5
39 - 34 = 5.
What is 12 × 8?
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Correct answer: B. 96
12 × 8 = 96.
What is 44 + 15?
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Correct answer: D. 59
44 + 15 = 59.
What is 27 - 14?
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Correct answer: D. 13
27 - 14 = 13.
What is 11 × 3?
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Correct answer: B. 33
11 × 3 = 33.
What is 32 + 11?
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Correct answer: C. 43
32 + 11 = 43.
What is 43 - 6?
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Correct answer: C. 37
43 - 6 = 37.
What is 7 × 6?
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Correct answer: D. 42
7 × 6 = 42.
What is 38 + 36?
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Correct answer: D. 74
38 + 36 = 74.
What is 53 - 23?
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Correct answer: B. 30
53 - 23 = 30.
What is 12 × 8?
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Correct answer: C. 96
12 × 8 = 96.
What is 34 + 21?
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Correct answer: C. 55
34 + 21 = 55.
What is 41 - 22?
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Correct answer: A. 19
41 - 22 = 19.
What is 6 × 3?
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Correct answer: B. 18
6 × 3 = 18.
What is 43 + 27?
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Correct answer: B. 70
43 + 27 = 70.
What is 44 - 21?
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Correct answer: D. 23
44 - 21 = 23.
What is 5 × 4?
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Correct answer: C. 20
5 × 4 = 20.
What is 40 + 17?
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Correct answer: B. 57
40 + 17 = 57.
What is 46 - 44?
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Correct answer: B. 2
46 - 44 = 2.