Home / 11 Plus guide / Question types / Maths 11 Plus maths: every question type 13 topics. Each one below shows an exam-standard question to try and the kinds of question inside the topic; open a topic to see it from foundation upwards.
Every question here is written by Prism in the style of the tests. None is copied from a real paper, and a fresh one is drawn each time a child practises.
Digits, columns, rounding and ×/÷ by 10, 100, 1000.
Exam standard
Question 1 Aim for about 60 seconds
At night the temperature was -4°C. By midday it was 8°C. How many degrees did it rise?
A 13°C B 12°C C 22°C D 4°C E 8°C
Show the worked answer
Answer: B, 12°C
How to work it out From -4°C up to 0°C is 4 degrees, then up to 8°C is 8 more: 4 + 8 = 12 degrees.
Why the other options are wrong A (13°C): This is 1°C more than the correct answer, so the last step of the working is out by one.C (22°C): This is 10°C more than the correct answer, so the tens column is out. Recheck the working.D (4°C): This is the difference between 4 and 8. The rise crosses 0°C, so add them.E (8°C): This is the midday temperature itself, not the rise from -4°C. Written methods and order of operations (BIDMAS).
The missing digit Which calculation Place the brackets Check with the inverse Decimal times decimal The quick way
Exam standard
Question 2 Aim for about 60 seconds
Find the missing number that makes both sides equal.
85 + 309 = ? + 299
A 75 B 10 C 95 D 394 E 85
Show the worked answer
Answer: C, 95
How to work it out The left side is 85 + 309 = 394. So ? + 299 = 394, and ? = 394 − 299 = 95. A quicker way: 299 is 10 less than 309, so ? must be 10 more than 85. Why the other options are wrong A (75): The right side's number is 10 smaller, so the missing number must be 10 bigger, not smaller.B (10): This is only the difference between 309 and 299.D (394): This is the total of the left side. The right side already has 299 in it, so the missing number is smaller.E (85): This assumes 309 and 299 are the same; they differ by 10. Fractions of amounts, simplifying, comparing and adding.
Between two fractions Of what is left The one that is not equivalent What is left in the jug Largest of fractions, decimals and percentages
Exam standard
Question 3 Aim for about 60 seconds
Hamza ran 31 10 13 4 67 20
A 32 10 B 67 20 C 31 10 D 33 10 E 13 4
Show the worked answer
Answer: C, 31 10
How to work it out Change each to a decimal (or to twentieths): 31 10 13 4 67 20 The smallest is 31 10 Why the other options are wrong A (32 10 32 10 B (67 20 67 20 D (33 10 33 10 E (13 4 13 4 Percentages of amounts, discounts, and FDP conversions.
Which is larger Up then down A percentage of a percentage Percentage change Which method works The rest
Exam standard
Question 4 Aim for about 60 seconds
Which list is in order from smallest to largest?
7 10
A 68%, 7 10 B 0.65, 68%, 7 10 C 7 10 D 0.65, 7 10 E 7 10
Show the worked answer
Answer: B, 0.65, 68%, 7 10
How to work it out Change them all to the same form, such as decimals: 7 10 Smallest to largest: 0.65, 68%, 7 10 Why the other options are wrong A (68%, 7 10 7 10 7 10 C (7 10 7 10 7 10 D (0.65, 7 10 7 10 7 10 E (7 10 Sharing in a ratio, recipes and scaling.
Simplest form Which mix is stronger What must be true of a ratio Map scales Best buy From a fraction to a ratio
Exam standard
Question 5 Aim for about 60 seconds
1 kg is about 2.2 lbs. About how many kilograms are there in 35.2 lbs?
A 77 kg B 17 kg C 16 kg D 15 kg E 33 kg
Show the worked answer
Answer: C, 16 kg
How to work it out Each kilogram is 2.2 lbs, so divide: 35.2 ÷ 2.2 = 16. Check: 16 × 2.2 = 35.2. Why the other options are wrong A (77 kg): This multiplies by 2.2 again. Changing pounds to kilograms makes the number smaller.B (17 kg): 17 kg is about 37 lbs, not 35.2. Multiply back by 2.2 to check.D (15 kg): 15 kg is about 33 lbs, not 35.2. Multiply back by 2.2 to check.E (33 kg): This takes away 2.2 instead of dividing by it. Solving equations, substitution and “think of a number”.
Which expression Two facts, two unknowns Undo a formula Which equation What must be true of a and b Which rule fits the pattern
Exam standard
Question 6 Aim for about 60 seconds
The volume of a triangular prism is V = 1 2
A 33 cm³ B 324 cm³ C 27 cm³ D 648 cm³ E 162 cm³
Show the worked answer
Answer: B, 324 cm³
How to work it out Put the numbers into the formula: 1 2 Half of 18 is 9, and 9 × 3 × 12 = 324 cm³. Why the other options are wrong A (33 cm³): This adds the lengths instead of multiplying them.C (27 cm³): This leaves out l = 12.D (648 cm³): This forgets the 1 2 E (162 cm³): This halves twice. Linear, square, Fibonacci-style and growing-difference patterns.
Two sequences woven together Two rules taking turns Dividing sequences Triangle numbers The tenth or twentieth term A gap in the middle Which number breaks the rule Which rule explains it Find the first term
Exam standard
Question 7 Aim for about 60 seconds
What is the next number in the sequence?
2, 5, 14, 41, 122, ?
A 365 B 364 C 203 D 366 E 367
Show the worked answer
Answer: A, 365
How to work it out Write the gaps between the numbers to find the rule. Multiply by 3, then take away 1, so the next number is 365. Why the other options are wrong B (364): This is one less than the next term. Check the rule: multiply by 3, then take away 1.C (203): This adds the last gap, 81, again to 122, but the gaps in this sequence are not the same each time.D (366): This is one more than the next term. Check the rule: multiply by 3, then take away 1.E (367): This is two more than the next term. Check the rule: multiply by 3, then take away 1. Area, perimeter, compound shapes and angle facts.
Exam standard
Question 8 Aim for about 60 seconds
A, B and C are three corners of a rectangle. What are the coordinates of the fourth corner, D?
−4 −4 −3 −3 −2 −2 −1 −1 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 x y A B C A (0, −1) B (3, 2) C (−1, 0) D (−1, −1) E (2, −1)
Show the worked answer
Answer: D, (−1, −1)
How to work it out D is above A and level with C. So it has A's x-coordinate (−1) and C's y-coordinate (−1): (−1, −1). Why the other options are wrong A ((0, −1)): D must be directly above A, so its x-coordinate is −1, not 0.B ((3, 2)): This carries on past C instead of finding the missing corner.C ((−1, 0)): This uses the width for the height; the sides of a rectangle can differ.E ((2, −1)): Check which corner is missing: it must be above A. Time calculations, unit conversions, speed-distance-time.
Which is longest When to leave Tiles on a floor Read the scale Which unit The due date
Exam standard
Question 9 Aim for about 60 seconds
Dev must be at the Library by 09:10. What is the latest bus Dev can catch from the Station?
Row Bus 1 Bus 2 Bus 3 Bus 4 Station 08:10 08:39 09:14 09:28 Market 08:22 08:51 09:26 09:40 Library 08:35 09:04 09:39 09:53 Park 08:40 09:09 09:44 09:58
A 09:14 B 08:39 C 08:10 D 09:04 E 08:45
Show the worked answer
Answer: B, 08:39
How to work it out Look along the Library row for the last time at or before 09:10: 09:04, which is Bus 2. That bus leaves the Station at 08:39. Why the other options are wrong A (09:14): That bus reaches the Library at 09:39, which is too late.C (08:10): This bus works, but a later one also arrives in time.D (09:04): This is when the bus reaches the Library, not when it leaves the Station.E (08:45): 08:45 is not a time any bus leaves the Station. Multi-step problems in real contexts.
Exam standard
Question 10 Aim for about 60 seconds
Honey is sold in jars: 250 g for £0.70, 400 g for £1.36, 500 g for £1.86, 1000 g for £3.10. Which jar is the best value?
A The 400 g jar B The 250 g jar C The 500 g jar D They are all the same value E The 1000 g jar
Show the worked answer
Answer: B, The 250 g jar
How to work it out Compare the price of the same amount, 100 g: 250 g jar £0.28 per 100 g, 400 g jar £0.34 per 100 g, 500 g jar £0.37 per 100 g, 1000 g jar £0.31 per 100 g. The cheapest per 100 g is the 250 g jar. The biggest jar is not always the best value. Why the other options are wrong A (The 400 g jar): It costs £0.34 per 100 g, more than the 250 g jar at £0.28.C (The 500 g jar): It costs £0.37 per 100 g, more than the 250 g jar at £0.28.D (They are all the same value): The jars cost different amounts for the same 100 g.E (The 1000 g jar): It costs £0.31 per 100 g, more than the 250 g jar at £0.28. Mean, median, mode, range and reading charts.
Exam standard
Question 11 Aim for about 60 seconds
The table shows how many customers bought each flavour of sweets on each day. Each customer bought 3 packs. How many packs of cherry sweets were sold on Monday?
Row Grape Cherry Lemon Monday 28 18 33 Tuesday 18 32 28 Wednesday 33 24 22 Thursday 19 11 16 Friday 22 21 26
A 21 B 96 C 18 D 54 E 237
Show the worked answer
Answer: D, 54
How to work it out Find Monday in the Cherry column: 18 customers. Each bought 3 packs: 18 × 3 = 54 packs. Why the other options are wrong A (21): This adds 3 instead of multiplying.B (96): This reads the wrong row: check the day.C (18): This is the number of customers; each one bought 3 packs.E (237): This uses every flavour on that day, not just one. Primes, HCF, LCM, squares and cubes.
What must be true of a number How many factors Tell without dividing Nearest square root Consecutive numbers Odd one out
Exam standard
Question 12 Aim for about 60 seconds
Which set contains only cube numbers?
A 16, 64, 125 B 27, 64, 125 C 64, 81, 125 D 27, 65, 125 E 27, 64, 144
Show the worked answer
Answer: B, 27, 64, 125
How to work it out A cube number is a number times itself three times: 3 × 3 × 3 = 27; 4 × 4 × 4 = 64; 5 × 5 × 5 = 125. So the set is 27, 64, 125. Why the other options are wrong A (16, 64, 125): 16 is 4 × 4, a square number, not a cube number.C (64, 81, 125): 81 is 3 × 27, not a cube.D (27, 65, 125): 65 is one more than the cube number 64, so it is not a cube.E (27, 64, 144): 144 is 12 × 12, a square number, not a cube number. Find out where your child stands today Prism starts with a free assessment across maths, English, verbal and non-verbal reasoning, then builds a weekly plan for your target schools. Parents follow progress free.
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