11+ Maths Curriculum
Ages 9–11
GL & CEM Assessment
11+ Algebra & Equations
Master balancing linear equations, two-way function machines, substitution and symbol puzzles with visual step-by-step methods.
11+ EXAM WEIGHTING
Core Topic: 3–5 Marks
Algebra frequently separates top scorers in grammar school entrance exams (GL & CEM). Mastering inverse operations and symbol replacement guarantees quick, confident marks.
✓ Balance Scale Inverse Method
✓ Working Backwards from Output
✓ Symbol Elimination Puzzles
11+ Algebra & Equation Explorer
Interactive Tool
💡
Golden Rule of Algebra: An equation is like a balance scale. Always do the exact same inverse operation to both sides to isolate x!
Core 11+ Method
Solve Equations with Balance Physics
Rule: Keep the scale level by applying the same inverse operation to both pans.
LEFT PAN: Variable & Constants
⚖️ Adjust x to balance
RIGHT PAN: Target Weight
Left Weight: 0
Right Weight: 0
EQUATION:
2x + 6 = 18
Coefficient of x (piles)
2
Constant added/subtracted
+6
Target Right Pan Total
18
🎯 Student Guess for x
x = ?
Adjust the slider to balance the scale or use the Step buttons!
11+ EXAM PRESETS:
Two-Step Machine
Function Machines & Inverse Arithmetic
Input (n)
6
Starting Value
➔
Operation 1
× 3
Mid: 18
➔
Operation 2
+ 5
Final step
➔
Output
23
Result
Input Value (n)
6
Operation 1
Operation 2
🔄 Working Backwards (Exam Technique):
To find the starting input from an output of 23: reverse Op 2 (23 - 5 = 18), then reverse Op 1 (18 ÷ 3 = 6).
11+ FUNCTION CHALLENGES:
11+ Favourite
Simultaneous Symbol & Fruit Equations
Method: Compare equations to eliminate one variable immediately.
GIVEN PROBLEM:
🍎 +
🍎 +
🍌
=
22
🍎 +
🍌
=
15
11+ EXAM PUZZLES:
Pattern Master
Sequences & Deriving the nth Term
Shortcut: nth Term = (Difference × n) + (Zero-th Term)
SEQUENCE TERMS:
Difference: +3
General Rule (nth Term Formula)
3n + 1
Multiplier = 3 (the jump). Zero term = 4 - 3 = +1.
Calculate Term at n = 20
61
3(20) + 1 = 61
First Term (a)
4
Common Difference (d)
+3
Find Nth Term at n =
20
11+ EXAM SEQUENCES:
Live Practice
11+ Algebra Speed Drill
Streak: 0
Score: 0 / 0
LINEAR EQUATION
Solve for x: 3x + 7 = 28
11+ Algebra Methods & Exam Traps
Master these proven methods and avoid the standard pitfalls that trip up candidates in GL Assessment and CEM papers.
1
The 4 Core 11+ Algebra Methods
1. The Balance Scale Method (Inverse Operations):
Whatever operation is attached to the variable, undo it with the opposite operation on both sides:
• Undo addition with subtraction (+5 → −5)
• Undo multiplication with division (×3 → ÷3)
Example:
Whatever operation is attached to the variable, undo it with the opposite operation on both sides:
• Undo addition with subtraction (+5 → −5)
• Undo multiplication with division (×3 → ÷3)
Example:
4x + 7 = 31 ⇒ 4x = 24 ⇒ x = 6.
2. Reversing Function Machines (Working Backwards):
When given the final output of a multi-stage machine, write out the operations in reverse order, inverting each arithmetic sign as you go.
When given the final output of a multi-stage machine, write out the operations in reverse order, inverting each arithmetic sign as you go.
3. Symbol Elimination & Substitution:
When two equations feature icons or objects (e.g. 2 Apples + 1 Banana = 22; 1 Apple + 1 Banana = 15), subtract Equation 2 from Equation 1 to find the value of 1 Apple instantly (
When two equations feature icons or objects (e.g. 2 Apples + 1 Banana = 22; 1 Apple + 1 Banana = 15), subtract Equation 2 from Equation 1 to find the value of 1 Apple instantly (
22 − 15 = 7). Then substitute back!
4. The nth Term Sequence Rule:
For any linear sequence (e.g.
1. Find the step difference:
2. Subtract difference from 1st term to find the zero-term adjustment:
3. Formula:
For any linear sequence (e.g.
4, 7, 10, 13…):1. Find the step difference:
+3 ⇒ 3n.2. Subtract difference from 1st term to find the zero-term adjustment:
4 − 3 = +1.3. Formula:
3n + 1.
2
11+ Common Algebra Traps & Fixes
⚠️ Trap 1: The Minus-Before-x Sign Error:
In
Fix: Add
In
15 − 2x = 7, students often write 2x = 15 + 7 = 22.Fix: Add
2x to both sides first: 15 = 7 + 2x ⇒ 8 = 2x ⇒ x = 4.
⚠️ Trap 2: Reversing Order of Operations:
When solving
When solving
3x + 5 = 26, do not divide by 3 first! Always peel off additions/subtractions before division/multiplication.
⚠️ Trap 3: The Multiplied Letter Confusion:
In
In
4a, if a = 5, the answer is 4 × 5 = 20, never 45!
⚠️ Trap 4: Bracket Distributive Oversight:
In
In
3(x + 4) = 27, remember that 3 multiplies both terms inside (3x + 12 = 27), OR divide both sides by 3 immediately (x + 4 = 9 ⇒ x = 5).
PRACTICE ARENA
11+ Algebra & Numbers Practice Test
Test your understanding with authentic 11+ multiple-choice exam questions covering linear equations, function machine inverses, and number series.
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📄
11+ General Maths & Algebra Worksheet
Printable PDF worksheet with balanced equation challenges, function tables, and detailed answer sheet.
More 11+ Maths Topics
Explore interactive labs and practice tests across the TestLife 11+ Maths curriculum.
🔢
Arithmetic Lab
Operations & Long Methods
📐
BODMAS & Operations
Order of Operations & Brackets
📊
Word Problems & Bar Models
Dynamic ratio & money explorer
🍰
Fractions Explorer
Visualiser & four operations
🏷️
Number & Place Value
Rounding, decimals & values
⚖️
Ratio & Proportion
Direct sharing & unitary method
Get Full Access to Every 11+ Maths Topic & Mock Exam
Join thousands of students preparing for GL Assessment and CEM 11+ exams with TestLife's adaptive practice platform, full topic coverage, and timed mock tests.
