11 Plus Mathematics Syllabus
11+ Maths goes well beyond the typical Year 5 curriculum. Children must combine accurate calculation with strong problem-solving, often working with multi-step word problems under time pressure. Most boards test mental arithmetic speed, application of fractions/decimals/percentages, geometry and measurement, and reasoning about data. Confidence with times tables up to 12×12 is the foundation everything else is built on.
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Typically 45–60 minutes (varies by board)
Format at a glance
Multiple-choice or short-answer; some boards use mental maths sections
Number & Place Value
Reading, writing, ordering and comparing numbers up to 10,000,000. Negative numbers, rounding and Roman numerals.
Place value to millions and decimals
Negative numbers
Rounding to nearest 10/100/1000 or decimal place
Roman numerals to 1000
Identify the value of a digit in a number.
In the number 4,728,316, what is the value of the digit 7?
Reading from the right: 6 (units), 1 (tens), 3 (hundreds), 8 (thousands), 2 (ten thousands), 7 (hundred thousands), 4 (millions). The 7 sits in the hundred-thousands column.
Round whole numbers and decimals to a given degree of accuracy.
Round 47.658 to one decimal place.
Look at the next digit (5). Since 5 rounds up, 47.6|58 becomes 47.7.
Order and calculate with negative numbers.
The temperature was -3°C and rose by 8°C. What is the new temperature?
Adding 8 to -3 on a number line: -3 + 8 = 5.
Read and write Roman numerals up to 1000 (M).
Which year is represented by MCMXCIV?
M = 1000, CM = 900 (1000 - 100), XC = 90 (100 - 10), IV = 4 (5 - 1). Total: 1000 + 900 + 90 + 4 = 1994.
Factors, Multiples & Prime Numbers
Identifying factors, multiples, prime numbers, prime factorisation, and finding the highest common factor (HCF) and lowest common multiple (LCM).
Factors of a number (whole numbers that divide it exactly)
Multiples (the times-table of a number)
Prime numbers (exactly two factors: 1 and itself)
Prime factorisation
Highest Common Factor (HCF) and Lowest Common Multiple (LCM)
Find all the whole-number factors of a given number.
Which of the following is NOT a factor of 24?
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The number 9 does not divide 24 exactly (24 ÷ 9 = 2 remainder 6), so it is NOT a factor.
A prime number has exactly two factors — 1 and itself. Note: 1 is not prime.
Which of these is a prime number?
21 = 3 × 7, 27 = 3 × 9, 33 = 3 × 11 — all have factors other than 1 and themselves. 29 has only two factors (1 and 29), so it is prime.
A multiple of a number is the result of multiplying it by any whole number.
Which number is a common multiple of 4 and 6?
Multiples of 4: 4, 8, 12, 16, 20, 24, 28... Multiples of 6: 6, 12, 18, 24, 30... 24 appears in both lists. (12 is the lowest common multiple, but 24 is the only common multiple in the options.)
The largest number that divides exactly into two or more numbers.
What is the HCF of 18 and 24?
Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The largest factor in both lists is 6.
Powers, Squares & Cubes
Squaring and cubing numbers, square and cube roots, and recognising powers of 10 and their use in standard calculations.
Square numbers (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...)
Cube numbers (1, 8, 27, 64, 125...)
Square root and cube root
Powers of 10
A square number is a number multiplied by itself (n × n).
What is 12² (12 squared)?
12² means 12 × 12 = 144.
A cube number is a number multiplied by itself, then by itself again (n × n × n).
What is 4³ (4 cubed)?
4³ means 4 × 4 × 4 = 16 × 4 = 64.
The square root of a number is the value that, multiplied by itself, gives the number.
What is √81?
9 × 9 = 81, so √81 = 9.
Four Operations
Addition, subtraction, multiplication and division — including long methods and the order of operations.
Column addition and subtraction
Long multiplication (up to 4-digit × 2-digit)
Short and long division
BIDMAS / order of operations
Multiply a 3- or 4-digit number by a 2-digit number using the column method.
Calculate 246 × 34
246 × 4 = 984. 246 × 30 = 7,380. 984 + 7,380 = 8,364.
Divide a multi-digit number by a one- or two-digit divisor.
Calculate 462 ÷ 14
14 × 33 = 14 × 30 + 14 × 3 = 420 + 42 = 462. So 462 ÷ 14 = 33.
Apply the correct order: Brackets, Indices, Division/Multiplication, Addition/Subtraction.
What is 6 + 4 × (8 - 3)²?
Brackets first: (8 - 3) = 5. Indices: 5² = 25. Multiplication: 4 × 25 = 100. Addition: 6 + 100 = 106.
Fractions, Decimals & Percentages
Equivalence, ordering, calculations and conversions between fractions, decimals and percentages.
Equivalent fractions and simplification
Adding and subtracting fractions with different denominators
Multiplying and dividing fractions
Converting between forms
Finding a percentage of an amount
Simplify or recognise fractions of equal value.
Which fraction is equivalent to 12/18?
Divide both numerator and denominator by their highest common factor, 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3.
Add or subtract fractions with different denominators by finding a common denominator.
Calculate 2/3 + 1/4
Common denominator is 12: 2/3 = 8/12 and 1/4 = 3/12. 8/12 + 3/12 = 11/12.
Multiply numerators and denominators directly. Cancel common factors first to simplify.
Calculate 3/5 × 10/9
Cancel: 3 and 9 share a factor of 3 (3 → 1, 9 → 3); 5 and 10 share a factor of 5 (5 → 1, 10 → 2). Now 1/1 × 2/3 = 2/3.
To divide by a fraction, multiply by its reciprocal (flip it upside down).
Calculate 2/3 ÷ 4/5
Flip the second fraction and multiply: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6 (in simplest form).
Convert between mixed numbers (e.g. 2¾) and improper fractions (e.g. 11/4).
Convert 3⅖ to an improper fraction.
Multiply the whole number by the denominator: 3 × 5 = 15. Add the numerator: 15 + 2 = 17. Keep the same denominator: 17/5.
Find a new amount after a percentage rise or fall.
A coat costs £80. In a sale, the price is reduced by 25%. What is the sale price?
25% of £80 = £20 (one quarter). Sale price = £80 − £20 = £60.
Find a given percentage of a number.
What is 15% of £240?
10% of £240 = £24. 5% = half of 10% = £12. 10% + 5% = £24 + £12 = £36.
Convert between fractions, decimals and percentages.
Express 0.375 as a fraction in its simplest form.
0.375 = 375/1000. Divide top and bottom by 125: 375 ÷ 125 = 3, 1000 ÷ 125 = 8 → 3/8.
Ratio & Proportion
Sharing in a given ratio, scaling up and down, and using direct proportion in real-life problems.
Simplifying ratios
Sharing an amount in a ratio
Direct proportion (recipes, scale)
Best-buy comparisons
Divide both sides of the ratio by their highest common factor to write it in simplest form.
Simplify the ratio 18 : 24 to its lowest terms.
The HCF of 18 and 24 is 6. Divide both sides by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. So the simplified ratio is 3 : 4.
Divide an amount in a given ratio.
£60 is shared between Alex and Bea in the ratio 2:3. How much does Bea receive?
Total parts: 2 + 3 = 5. One part = £60 ÷ 5 = £12. Bea gets 3 × £12 = £36.
Scale a recipe up or down using a unitary method.
A recipe for 4 people uses 200g of flour. How much flour is needed for 10 people?
For 1 person: 200 ÷ 4 = 50g. For 10 people: 50 × 10 = 500g.
Compare two products to determine which is better value.
A 250ml bottle costs £1.50 and a 600ml bottle costs £3.30. Which is the better value?
Cost per 100ml: £1.50 ÷ 2.5 = £0.60 vs £3.30 ÷ 6 = £0.55. The 600ml is cheaper per 100ml.
Algebra & Sequences
Solving simple equations, recognising sequences, function machines and using letters to represent unknowns.
Simple linear equations
Function machines
Number sequences and the nth term
Substituting values into expressions
Find the value of an unknown letter.
Solve: 3x + 7 = 22
Subtract 7: 3x = 15. Divide by 3: x = 5.
Apply a series of operations to an input or work backwards from an output.
A function machine doubles a number then subtracts 3. The output is 17. What was the input?
Work backwards: add 3 (17 + 3 = 20), then halve (20 ÷ 2 = 10).
Identify the rule of a sequence and find the next term or a specific term.
Find the next number in the sequence: 2, 6, 12, 20, 30, ...
Differences: 4, 6, 8, 10. The next difference is 12, so the next term is 30 + 12 = 42.
For a sequence with a constant difference, find a rule in the form an + b that gives any term.
What is the rule for the nth term of the sequence 5, 8, 11, 14, 17, ...?
The common difference is 3, so the rule begins "3n". Check: when n = 1, 3(1) + 2 = 5 ✓ matches the first term. So the rule is 3n + 2.
Translate a worded relationship into an algebraic expression.
A pencil costs p pence. A pen costs 5 pence more. Write an expression for the cost of three pens.
One pen costs (p + 5) pence. Three pens cost 3 × (p + 5) = 3(p + 5) pence.
Replace letters with numbers to evaluate an expression.
If a = 4 and b = 3, what is the value of 2a² - b?
2 × 4² - 3 = 2 × 16 - 3 = 32 - 3 = 29.
Measurement
Length, mass, capacity, time, money and unit conversion — using both metric and (some) imperial units.
Converting metric units (mm/cm/m/km, g/kg, ml/l)
Reading and using time (12- and 24-hour)
Money calculations and change
Imperial conversion approximations (mile ≈ 1.6 km, kg ≈ 2.2 lb)
Convert between metric units.
How many millilitres are there in 2.4 litres?
1 litre = 1,000 ml, so 2.4 × 1,000 = 2,400 ml.
Calculate elapsed time, working with 12- and 24-hour clocks.
A train leaves at 14:35 and arrives at 17:10. How long is the journey?
From 14:35 to 17:00 is 2 hours 25 minutes. Add another 10 minutes to reach 17:10 → 2 hours 35 minutes.
Calculate totals, change and best-value purchases.
Sara buys 3 books at £4.75 each. She pays with a £20 note. How much change does she receive?
3 × £4.75 = £14.25. Change: £20.00 - £14.25 = £5.75.
Speed, Distance & Time
Calculating any one of speed, distance or time when given the other two. A frequent topic in CSSE, ISEB and harder independent-school papers.
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
Converting between units (mph ↔ km/h, minutes ↔ hours)
Average speed for journeys with multiple legs
Find the speed when distance and time are given.
A cyclist travels 60 km in 3 hours. What is her average speed?
Speed = Distance ÷ Time = 60 ÷ 3 = 20 km/h.
Find the distance when speed and time are given.
A train travels at 80 km/h for 2½ hours. How far does it travel?
Distance = Speed × Time = 80 × 2.5 = 200 km.
Find the time taken when speed and distance are given.
A car travels 270 miles at an average speed of 60 mph. How long does the journey take?
Time = Distance ÷ Speed = 270 ÷ 60 = 4.5 hours, which is 4 hours and 30 minutes.
Find the overall average speed when a journey has more than one leg.
Sam drives 90 km in 1.5 hours, then a further 60 km in 1 hour. What is his average speed for the whole journey?
Total distance = 90 + 60 = 150 km. Total time = 1.5 + 1 = 2.5 hours. Average speed = 150 ÷ 2.5 = 60 km/h. (Note: it is NOT simply the average of the two speeds.)
Geometry — 2D Shapes & Angles
Properties of polygons, types of triangle and quadrilateral, angle rules and circle parts.
Properties of triangles and quadrilaterals
Regular and irregular polygons
Angles on a line, around a point, in a triangle, in a quadrilateral
Parts of a circle (radius, diameter, circumference)
Use the rule that angles in a triangle add to 180°.
Two angles of a triangle are 47° and 73°. What is the size of the third angle?
Angles in a triangle sum to 180°. 180° - 47° - 73° = 60°.
Use the rule that angles on a straight line sum to 180°.
Three angles meet on a straight line: 35°, 85° and x°. What is x?
180° - 35° - 85° = 60°.
Recognise the number of sides, angles and lines of symmetry of common polygons.
A regular hexagon has interior angles of:
Sum of interior angles = (6 - 2) × 180° = 720°. Divide by 6 sides: 720° ÷ 6 = 120°.
Use the rule that angles in a quadrilateral sum to 360°.
Three angles of a quadrilateral are 80°, 95° and 110°. What is the fourth angle?
Angles in a quadrilateral sum to 360°. 360° − 80° − 95° − 110° = 75°.
Use the rule that angles meeting at a point sum to 360°.
Four angles meet at a point: 90°, 75°, 110° and x°. What is x?
360° − 90° − 75° − 110° = 85°.
Identify and use the radius (centre to edge), diameter (twice the radius) and circumference (perimeter).
A circle has a diameter of 14 cm. What is its radius?
The radius is half the diameter: 14 ÷ 2 = 7 cm.
Geometry — 3D Shapes
Identifying 3D solids, counting faces, edges and vertices, and recognising nets.
Faces, edges, vertices of common solids
Nets of cubes, cuboids, prisms and pyramids
Cross-sections
Count the faces, edges and vertices of a 3D shape.
A square-based pyramid has how many edges?
4 edges around the square base + 4 edges going up to the apex = 8.
Identify which 2D net folds into which 3D shape.
How many faces does the net of a cube have?
A cube has 6 square faces, so its net is made of 6 connected squares.
Perimeter, Area & Volume
Calculating perimeter, area of rectangles/triangles/parallelograms/trapeziums, and volume of cuboids.
Perimeter of compound shapes
Area = base × height (rectangles/parallelograms)
Area of triangle = ½ × base × height
Volume of cuboid = length × width × height
Add up the lengths of every side of the shape.
A rectangle has length 9 cm and width 4 cm. What is its perimeter?
Perimeter of a rectangle = 2 × (length + width) = 2 × (9 + 4) = 2 × 13 = 26 cm.
Multiply length by width.
A rectangular garden is 12m long and 8m wide. What is its area?
Area = length × width = 12 × 8 = 96 m².
Use the formula ½ × base × height.
A triangle has base 14 cm and perpendicular height 9 cm. What is its area?
Area = ½ × 14 × 9 = ½ × 126 = 63 cm².
Multiply length × width × height.
A box measures 5cm × 4cm × 3cm. What is its volume?
Volume = 5 × 4 × 3 = 60 cm³.
Split a complex shape into simple rectangles or triangles, then combine areas.
An L-shape is made by removing a 3cm × 2cm rectangle from the corner of a 6cm × 5cm rectangle. What is the area of the L-shape?
Whole rectangle: 6 × 5 = 30 cm². Removed corner: 3 × 2 = 6 cm². Remaining L-shape: 30 - 6 = 24 cm².
Symmetry & Transformation
Lines of symmetry, rotational symmetry, translations, reflections, rotations and enlargements.
Lines of symmetry in 2D shapes
Order of rotational symmetry
Reflection in a mirror line
Translation by a vector
Count the lines of symmetry of a shape.
How many lines of symmetry does a regular pentagon have?
A regular pentagon has one line of symmetry from each vertex to the midpoint of the opposite side — five in total.
Find the order of rotational symmetry.
What is the order of rotational symmetry of a square?
A square fits onto itself 4 times during a complete 360° rotation (every 90°).
Slide a shape by a given vector — written as (right/left, up/down).
A point at (2, 3) is translated 4 right and 2 down. What are its new coordinates?
4 right adds 4 to the x-coordinate: 2 + 4 = 6. 2 down subtracts 2 from the y-coordinate: 3 − 2 = 1. New point: (6, 1).
Flip a point or shape across a mirror line.
The point (5, 3) is reflected in the y-axis. What are its new coordinates?
Reflection in the y-axis (the vertical axis) flips the sign of the x-coordinate; the y-coordinate stays the same. (5, 3) → (−5, 3).
Turn a point around a centre by a given angle.
The point (4, 0) is rotated 90° clockwise about the origin. What are its new coordinates?
90° clockwise about the origin sends (x, y) → (y, −x). So (4, 0) → (0, −4). Visualise the point on the positive x-axis moving down to the negative y-axis.
Coordinates
Reading and plotting points in all four quadrants, and finding midpoints.
Plotting (x, y) coordinates
All four quadrants (positive and negative)
Midpoint of a line segment
Identify the coordinates of a point on a grid.
A point is 3 units left of the y-axis and 4 units below the x-axis. What are its coordinates?
Left of y-axis = negative x. Below x-axis = negative y. So the point is (-3, -4).
Find the midpoint of two coordinates.
Find the midpoint of (2, 6) and (8, 14).
Midpoint = ((2 + 8)/2, (6 + 14)/2) = (10/2, 20/2) = (5, 10).
Statistics & Data
Reading and interpreting tables, bar charts, line graphs and pie charts. Calculating mean, median, mode and range.
Reading tables and graphs
Mean, median, mode, range
Pie charts (fractions of 360°)
Frequency tables
Add the values and divide by how many there are.
Find the mean of 6, 9, 11, 14 and 15.
Sum = 6 + 9 + 11 + 14 + 15 = 55. Mean = 55 ÷ 5 = 11.
Find the middle value when the data is in order.
Find the median of: 12, 4, 8, 7, 15, 9.
Order: 4, 7, 8, 9, 12, 15. With six values, the median is the mean of the 3rd and 4th: (8 + 9) ÷ 2 = 8.5.
The mode is the most frequent value; the range is the largest minus the smallest.
For the data 5, 7, 7, 9, 12, 15, find the range.
Range = largest - smallest = 15 - 5 = 10. (Mode = 7.)
Find a fraction of 360° to represent a category.
In a survey of 60 children, 25 chose football. What angle of the pie chart represents football?
Each child is 360° ÷ 60 = 6°. 25 children = 25 × 6° = 150°.
Read information off a bar chart and answer questions about it.
A bar chart shows fruit chosen by 30 children: Apples 12, Bananas 8, Oranges 6, Grapes 4. How many MORE children chose apples than oranges?
Difference = 12 (apples) − 6 (oranges) = 6.
Read values off a line graph and interpret trends over time.
A line graph shows a plant's height each week: Week 1 = 4 cm, Week 2 = 7 cm, Week 3 = 11 cm, Week 4 = 14 cm. By how much did the plant grow between weeks 2 and 3?
Growth = height at week 3 − height at week 2 = 11 − 7 = 4 cm.
Probability
Likelihood of an event, expressed as a fraction, decimal or percentage between 0 and 1.
Sample space and outcomes
Probability scale (impossible → certain)
Probability as a fraction of total outcomes
Place an event on a scale from "impossible" (0) to "certain" (1) using fractions, decimals or words.
Which event has a probability of exactly 0.5?
A coin has 2 equally likely outcomes (heads or tails), so P(heads) = 1/2 = 0.5. The other events have probabilities 1/6, 4/52 and 5/26 respectively — none of which equals 0.5.
Express the chance of an event as a fraction.
A bag contains 3 red, 4 blue and 5 green counters. What is the probability of drawing a blue counter?
Total counters = 12. P(blue) = 4/12 = 1/3 (in simplest form).
Word Problems & Multi-Step Reasoning
Multi-step problems combining several skills — the highest-marked questions in many 11+ papers.
Reading carefully and identifying useful information
Choosing the right operation(s)
Showing working out clearly
Checking the answer is sensible
A real-world problem requiring two or more steps to solve.
A school orders 24 packs of pencils. Each pack contains 12 pencils. The pencils are shared equally between 8 classes. How many pencils does each class receive?
Total pencils: 24 × 12 = 288. Per class: 288 ÷ 8 = 36.
Use logical reasoning and simple algebra to solve.
I think of a number, double it, add 7, and the result is 25. What was my number?
Work backwards: 25 - 7 = 18. 18 ÷ 2 = 9.
Put Mathematics into practice
Use these resources to turn the syllabus into exam-ready confidence.
11 plus Mathematics — frequently asked questions
Quick answers to the questions parents ask most about 11+ Mathematics.