What topics are in 11 Plus maths?

Number and Place Value

Mastering number and place value forms the foundation of 11+ maths success. Exams test place value up to 10,000 and number ordering through multiple-choice and word problems. Students focus on HTU, thousands, and comparing numbers.

11+ mathematics papers from CEM and GL often include questions on partitioning numbers and ordering them from smallest to largest. Practice helps with place value charts and mental decomposition. This builds confidence for timed maths tests.

Quick diagnostic questions reveal strengths. Try these: 1) What is the value of the 7 in 4,729? 2) Order: 3,482; 3,248; 3,824. 3) Partition 5,631 into thousands, hundreds, tens, units.

Answers: 1) 700, 2) 3,248; 3,482; 3,824, 3) 5 thousands + 6 hundreds + 3 tens + 1 unit. For detailed strategies used by top-scoring students, see the sections below on place value and operations.

Place Value and Ordering

Many students miss place value questions due to weak HTU decomposition. Use the simple Partition-Expand-Compare method to build skills in eleven plus exam prep. It works well for year 6 maths.

First, partition numbers like 4,729 as 4 thousands + 7 hundreds + 2 tens + 9 units. Next, expand to compare, such as 4,000 versus 3,000 in two numbers. Finally, order using a place value grid for clarity.

Practice with this table showing the method:

Try these 5 practice questions, 45 seconds each: 1) Partition 6,345. 2) Compare 5,278 and 5,287. 3) Order 2,941; 2,419; 2,914. 4) What is 8 in 9,830? 5) Grid 7,562.

Answers: 1) 6Th + 3H + 4T + 5U, 2) 5,278 < 5,287, 3) 2,419; 2,914; 2,941, 4) 800, 5) 7 | 5 | 6 | 2. Repeat for primary school maths mastery.

Four Operations

11+ maths papers test four operations extensively. Master bus stop division and long multiplication with these shortcuts for GL maths and CEM maths. They suit non-calculator methods.

For addition, use column method with carrying: 4,867 + 3,492 = 8,359. Line up units, add right to left, carry over as needed. Check by estimating thousands.

Subtraction follows columns too, borrowing where required. For division, bus stop method: 476 ÷ 4 = 119, divide step-by-step per digit. Multiplication uses grid: 23 × 47 breaks to 20×40=800, 20×7=140, etc., totals 1,081.

Apply BODMAS for order: brackets first, like (12 + 8) × 3 = 60. Try these 8 timed questions, 3 minutes total: 1) 5,672 + 2,318. 2) 9,104 - 4,567. 3) 36 × 24. 4) 483 ÷ 3. 5) 47 × 23. 6) 728 ÷ 8. 7) (45 - 15) × 4. 8) 1,296 ÷ 9.

Mark scheme: 1) 7,990, 2) 4,537, 3) 864, 4) 161, 5) 1,081, 6) 91, 7) 120, 8) 144. Practice boosts speed for word problems and multi-step questions.

Fractions, Decimals and Percentages

Fractions appear in 18% of 11+ questions across CEM/GL. Converting between forms unlocks 40% more correct answers. Students master equivalence, conversions, and percentage calculations in this key area of 11 Plus maths.

Visual models like pie charts and bar shading build intuition for equivalent fractions. Quick mental methods, such as doubling or halving, speed up year 6 maths work. These skills appear in eleven plus exam word problems and multiple choice.

Try this quick assessment: Convert 3/4 to a decimal and 25% to a fraction. The techniques below help students gain 15-20 marks in CEM maths and GL maths. Practice with timed maths tests to build confidence.

Focus on place value for decimals and simplifying fractions using common factors. Link concepts through tables and ladders for fast recall in non-calculator methods.

Equivalent Fractions

Use the 'Multiply Top & Bottom' rule: 2/5 = 4/10 = 6/15. Multiply numerator and denominator by the same number to find equivalents. This builds 11+ mathematics fluency.

Follow the equivalence ladder step-by-step. First, find the lowest common denominator, like 3/6 = 1/2. Simplify by dividing top and bottom, as in 12/18 = 2/3 by dividing by 6.

Try the visual shading method. Shade half a rectangle for 1/2, a quarter twice for 2/4, and three sixths for 3/6. This helps with primary school maths understanding.

Practice these CEM-style multiple choice questions:

1. 1Which is equivalent to 3/5? A) 6/10 B) 2/4 C) 1/2 D) 4/7 A (multiply by 2).
2. 2Simplify 8/12: A) 2/3 B) 4/6 C) 1/2 D) 3/4 A (divide by 4).
3. 35/10 equals: A) 1/2 B) 1/5 C) 2/5 D) 5/2 A (divide by 5).
4. 4Equivalent to 4/6: A) 2/3 B) 1/2 C) 8/12 D) A and C D (both simplify to 2/3).
5. 5Visual: Shade 3/8 matches: A) 6/16 B) 1/2 C) 9/24 D) A and C D (ladders match).
6. 67/14 simplifies to: A) 1/2 B) 7/2 C) 3/7 D) 1/7 A (divide by 7).

Decimal-Fraction Conversions

Convert 0.75 to 3/4 using place value: tenths 7/10, hundredths 5/100, total 75/100 = 3/4. This method works for 11+ topics like money and measures.

Use this two-way conversion chart for quick reference.

Key methods: Decimal to fraction by writing over powers of 10, like 0.625 = 625/1000 = 5/8. Percentage to fraction: 35% = 35/100 = 7/20 by simplifying.

Try these 7 practice problems in a 90-second timer using GL mark scheme: full marks for correct form and simplification.

1. 10.4 as fraction: 2/5
2. 260% as fraction: 3/5
3. 30.2 as percentage: 20%
4. 41/5 as decimal: 0.2
5. 50.8 as fraction: 4/5
6. 675% as decimal: 0.75
7. 73/8 as decimal: 0.375

Measurement

Measurement questions test practical application in the eleven plus exam with real-world contexts like fencing costs. They focus on perimeter and area formulas alongside unit conversions. Common pitfalls include forgetting to square units for area.

Students often practise converting metres to centimetres or kilograms to grams. For example, calculate the perimeter of a 5m × 3m rectangle: add 2(5 + 3) = 16 metres. Quick checks like this build confidence in timed maths tests.

In 11 Plus maths, expect multi-step problems involving length, weight, or capacity. Use metric units mainly, but imperial units like miles or pounds may appear in GL maths papers. Always double-check units in answers.

Practice with speed distance time questions or money problems sharpens skills. Year 6 maths covers 12-hour and 24-hour clocks for time conversions. These topics appear across CEM maths and multiple choice maths formats.

Perimeter, Area, Volume

Memorise formulas: rectangle P=2(l+w), A=l×w; triangle A=½bh. These appear in most 11+ papers for primary school maths. Quick recall helps in reasoning questions and word problems.

Example one: Trapezium area uses average of parallel sides times height, like ½(5 + 9) × 6 = 42 units². Check units match the question. Example two: Cuboid volume 6×4×3=72cm³ requires multiplying all dimensions.

Word problem: A field measures 20m by 15m with a 5m gate. Fencing costs £10 per metre. Perimeter is 2(20+15)=70m minus 5m gate equals 65m, so £650 total. Practice unit checks to avoid errors.

• Rectangle 10cm × 8cm: Perimeter 36cm, area 80cm².
• Triangle base 7cm, height 4cm: Area 14cm².
• Cuboid 5×3×2cm: Volume 30cm³.
• Trapezium parallels 4m and 10m, height 5m: Area 35m².
• Circle radius 3cm: Area 9π cm², circumference 6π cm.

Geometry

Geometry covers 15% of marks through shape identification, angle calculations, and transformations. In the 11 Plus maths exam, pupils identify properties of 2D and 3D shapes and measure angles. Expect drawing and reasoning questions, such as naming angles in a triangle for diagnostics.

Questions often ask children to spot differences between shapes like parallelograms and rhombuses. They must reason why a figure cannot be a certain polygon. Practice with year 6 maths resources builds confidence for eleven plus exam timed tests.

GL maths and CEM maths papers include multiple choice on nets and symmetry. Pupils draw lines of symmetry or calculate missing angles on parallel lines. Regular drills on primary school maths topics ensure quick recognition under pressure.

Focus on non-calculator methods for angle sums in triangles and quadrilaterals. Word problems mix geometry with arithmetic operations. This prepares for multi-step reasoning in 11+ topics.

2D and 3D Shapes

Know properties: Quadrilateral 4 sides, triangle 3 sides, properties table helps identify shape questions. In 11 Plus maths, compare 2D shapes like circles and polygons with their 3D equivalents. Practice spotting nets for solids such as cuboids.

Example one: Identify if a net forms a cuboid by checking opposite faces match. Example two: Calculate interior angle of a regular pentagon using formula. Reasoning question: Why can't this shape be a square? It lacks equal sides and right angles.

Try these identification tasks: Name the shape with five equal sides. Spot the net for a pyramid. Draw a heptagon. Explain why a rectangle is a parallelogram. These build skills for maths topics in multiple choice maths.

Angles and Symmetry

Angles on a line equal 180°, at a point 360°, essential for geometry reasoning questions. Master rules for angles in a triangle sum to 180° and quadrilaterals to 360°. Use these in 11+ mathematics for quick calculations.

Methods include co-interior angles on parallel lines sum to 180°. Count lines of symmetry in shapes like isosceles triangles. Practice with compass and protractor for accurate drawings in reasoning questions.

Solve: Find missing angle if two in triangle are 50° and 60°. Draw symmetry lines on a parallelogram. Calculate reflex angle opposite 70°. Use perpendicular lines at 90° for bearings. These prepare for timed maths tests and word problems.

Statistics and Probability

Data interpretation appears in every 11+ paper. Students must extract correct values from four chart types: bar charts, pie charts, line graphs and tables. This tests primary school maths skills in year 6 maths.

Calculate averages like mean, median and mode from data sets. Probability questions ask about likely, unlikely, impossible or certain events. Practice reading scales accurately to build confidence for CEM maths or GL maths papers.

A common error is misreading pie chart percentages. Remember each pie chart represents 360 degrees as 100%. Use these skills in multiple choice maths and timed maths tests.

Word problems often combine data handling with arithmetic operations. Experts recommend practising with real eleven plus exam questions. This prepares you for reasoning questions in 11 Plus maths.

Graphs and Tables

Read the scale first rule prevents most data errors. Practice with real exam graphs in 11+ mathematics. Start by identifying intervals on each chart type.

For bar charts, note the scale between bars, such as every 10 units. Pie charts use 360° = 100%, so each 10% equals 36°. Line graphs show trends over time, like rises or falls between points.

Tables require scanning rows and columns for values. Calculate averages by adding totals and dividing. Try this: in a table of scores, find the mean average for a class.

• Bar chart question: How many more in 2020 than 2019?
• Pie chart: What percentage is apples if slice is 90°?
• Line graph: Describe trend from 2018 to 2021.
• Table: Median sales from five values.

These appear across 12 questions in papers, often worth 1-2 marks each. Use non-calculator methods for speed in problem solving.

Algebra and Problem Solving

Algebra tests logical thinking through patterns and equations. It makes up 25% of reasoning marks for top CEM scores. Students solve for unknown values in the eleven plus exam.

Simple equations like 3x + 2 = 11 ask pupils to find x = 3. They balance both sides using inverse operations. Practice non-calculator methods to build speed for timed maths tests.

Sequences involve spotting patterns, such as 2, 5, 8... where the nth term is 3n - 1. Multi-step word problems combine algebra with arithmetic operations. Checking answers by substitution helps avoid errors.

CGP 11+ practice paper analysis shows students gain marks with these techniques. Focus on year 6 maths skills like BODMAS and balancing equations. Regular practice boosts confidence in GL maths and CEM maths papers.

Simple Equations

Simple equations in 11 Plus maths require isolating the unknown. Start by subtracting or adding terms on both sides. Use inverse operations like division after multiplication.

For 3x + 2 = 11, subtract 2 to get 3x = 9, then divide by 3. Always check by plugging the answer back in. This builds problem solving skills for multiple choice maths.

Practice with negative numbers and fractions too. Non-calculator methods keep mental maths sharp. Experts recommend daily drills for primary school maths mastery.

Sequences and Patterns

Sequences test number patterns in 11+ topics. Identify the rule, like adding 3 each time in 2, 5, 8, 11. Find the nth term formula for extended lists.

For 2, 5, 8..., the nth term is 3n - 1. Work backwards from terms to spot the pattern. Use tables to organise thinking in reasoning questions.

Reverse sequences or quadratic patterns appear in harder papers. Practice describing rules in words first. This aids multi-step problems in year 6 maths.

Multi-Step Word Problems

Multi-step word problems mix algebra with everyday scenarios. Read carefully to extract key numbers and operations. Set up equations from the context.

A problem like "Twice a number plus 5 is 17" becomes 2x + 5 = 17. Solve step by step, showing working. Estimation helps check reasonableness.

Combine with ratio or percentages for CEM maths challenge. Break into smaller parts. Non-calculator strategies like number bonds speed up solutions.

Exam-Style Questions

Try these 10 questions to practise algebra and problem solving. Four focus on equations, three on sequences, three on reasoning. Use pencil and paper for timed practice.

• Solve: 4x - 3 = 9. What is x?
• If 2y + 5 = 13, find y.
• Solve for z: 3(z + 1) = 12.
• What value of w makes 5w = 20 + 5 true?
• Continue the sequence: 3, 7, 11, 15,... What is the 6th term?
• Find the nth term for 1, 4, 7, 10...
• Sequence: 5, 10, 15,... What is the 10th term?
• A shop sells apples at 3 for £2. How many can you buy for £8? Set up an equation.
• Tom is x years old. In 5 years, he will be three times as old as now. Solve for x.
• Find the next two terms: 2, 6, 18, 54... Explain the rule.

Answers: 1. x=3, 2. y=4, 3. z=3, 4. w=5, 5. 24, 6. 3n-2, 7. 50, 8. 12 apples (let n=number, 2/3 n=8 so n=12), 9. x=2.5 (but check integer context), 10. 162, 486 (multiply by 3). Review mistakes to improve.