11+ Algebra Practice
(GL Assessment)

Algebra accounts for roughly 3 to 6 questions on a typical GL 11+ maths paper, around 6 to 12 percent, but its true reach is wider because sequences, missing-number problems, and function machines all rely on algebraic thinking without being labelled "algebra". (GL does not publish official topic weightings, so these figures are careful estimates from practice-paper analysis, flagged here for honesty.)

For many parents, "algebra" sounds advanced for a ten-year-old. In the 11+ it is gentler than it sounds: substituting a value into an expression, solving a simple equation, following a number machine, or continuing a sequence. Every question is multiple choice with five options, and a child who understands the idea can usually reach the answer in under a minute.

The biggest barrier is rarely the maths itself. It is the idea that a letter stands for a number, and that the equals sign means "both sides balance", not "the answer is". Get those two ideas secure and 11+ algebra becomes very approachable.

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What the GL 11+ Tests on Algebra

Every question is multiple choice with five options (A to E), spanning D1 to D3. Based on practice-paper analysis (GL publishes no official weightings, so treat the order as indicative), GL tests:

  • Substituting values into expressions (the most frequent type)
  • Solving one-step equations (4x = 28, x + 15 = 42)
  • Solving two-step equations (3x + 5 = 20)
  • Function or number machines, forwards and backwards
  • Continuing linear sequences and finding a distant term
  • "Think of a number" word problems
  • Finding the rule (nth term) of a sequence
  • Shape or picture equations, and pairs of unknowns

These map directly onto the Year 6 curriculum: using simple formulae, generating linear sequences, expressing missing-number problems with letters, and finding pairs of numbers that satisfy an equation with two unknowns. D3 questions occasionally stretch into early Year 7 territory.

Function Machines and Algebra vs Sequences: How to Tell Them Apart

Sequences and algebra both hunt for hidden numbers, but in different ways. A sequence gives a run of numbers and asks you to spot the rule and continue it. A function machine and an equation instead hide one unknown value, which you find by reversing the operations. One extends a pattern; the other pins down a single number.

Comparing Function Machines, Algebra and Sequences
Question type What it tests What it looks like The classic mix-up
Function MachinesThis page Following a chain of operations forwards, or reversing them to find a missing input. Boxes joined by arrows showing operations like "x 3" then "+ 2". For example, "Input 5, multiply by 3, add 2, output ___" Working the steps forwards when the output is given, not realising a missing input means reversing them.
AlgebraThis page Finding an unknown value in an equation, by substitution or by reversing the operations around it. A calculation containing a letter to find, or a "think of a number" story. For example, "If 4n - 3 = 25, what is n?" Hunting for a term-to-term pattern as in a sequence, instead of isolating the unknown letter.
Sequences Spotting the rule that links a run of numbers, then continuing it or finding a later term. A list of numbers with a gap or an arrow at the end. For example, "What comes next? 2, 6, 12, 20, ___" Trying to "solve for a letter" as in an equation, instead of finding the term-to-term rule.

If you are given a run of numbers and asked what comes next, it is a sequence; if a single unknown is hidden inside a calculation or a letter, it is algebra.

Sample Algebra Questions

Five questions drawn from PrepStep’s algebra bank, spanning Foundation to Challenging. Tap “Show worked explanation” to see the full method after you’ve had a go. The correct answer is highlighted on each question so you can check immediately.

Question 1 Foundation

Emma thinks of a number, adds 7, and gets 15. What number did Emma think of?

  1. 15
  2. 8✓
  3. 7
  4. 1
  5. 9
Show worked explanation

Let Emma's number be x. So x + 7 = 15. To find x, subtract 7 from both sides: x = 15 - 7 = 8. Emma thought of 8. ✓

Question 2 Foundation

Jack is j years old. His sister Sophie is 3 years younger. Which expression shows Sophie's age?

  1. j + 3
  2. 3j
  3. j - 3✓
  4. j ÷ 3
  5. 3 - j
Show worked explanation

If Jack is j years old and Sophie is 3 years younger, then Sophie's age = j - 3. ✓

Question 3 Intermediate

A number machine multiplies by 3 then adds 2. If you put 5 into the machine, what comes out?

5
Input
× 3
+ 2
?
Output
  1. 13
  2. 15
  3. 17✓
  4. 19
  5. 21
Show worked explanation

Input = 5. First multiply by 3: 5 × 3 = 15. Then add 2: 15 + 2 = 17. Output = 17. ✓

Question 4 Intermediate

Lily thinks of a number, multiplies it by 4, then adds 5 to get 29. What was Lily's number?

  1. 6✓
  2. 5
  3. 7
  4. 19
  5. 29
Show worked explanation

Let the number be x. So 4x + 5 = 29. First subtract 5: 4x = 24. Then divide by 4: x = 6. Lily's number was 6. ✓

Question 5 Challenging

Lucy is n years old. Her mum is 28 years older. In 5 years' time, how old will Lucy's mum be?

  1. n + 23
  2. n + 33✓
  3. n + 28
  4. n + 5
  5. 28n + 5
Show worked explanation

Lucy's mum is now n + 28. In 5 years she'll be (n + 28) + 5 = n + 33 years old. ✓

Common Mistakes to Avoid

Common mistake 1 of 4

Misreading the equals sign.

Tip: Many children think "=" means "write the answer". In 8 + 4 = __ + 5 the answer is 7, not 12. Both sides must weigh the same.

Common mistake 2 of 4

Reading "3a" as "3 and a".

Tip: The hidden multiplication sign trips children up; 3a means 3 times a. When substituting a = 5, that is 15, not 8 and not 35.

Common mistake 3 of 4

Reversing a number machine in the wrong order.

Tip: To undo "times 3 then add 5", subtract 5 first, then divide by 3. List the steps and reverse them bottom to top.

Common mistake 4 of 4

Translating words backwards.

Tip: "5 less than a number" is n minus 5, not 5 minus n. GL deliberately offers both, so slow, careful translation matters more than speed here.

About these questions

Every PrepStep 11+ question is original, written to mirror the style and difficulty of the GL Assessment 11+ and grounded in a library of real past-paper patterns, with a worked explanation for each one. PrepStep is built by Ben Jackson, its founder and a parent who has taken one child through the 11+ with another preparing now. Last reviewed: August 2026.

Frequently Asked Questions

Does the GL 11+ test algebra?

Yes, though lightly. Practice-paper analysis suggests roughly 3 to 6 algebra questions per paper, covering substitution, simple equations, function machines, and sequences. Many other "number" questions also use algebraic thinking, so the reasoning shows up more often than the raw count implies.

What kind of algebra is on the 11+ exam?

Year 6 level algebra: substituting a value into an expression, solving one-step and two-step equations, following number machines forwards and backwards, continuing sequences, and simple "think of a number" problems. It does not require advanced techniques, just secure understanding of letters as numbers.

Is 11+ algebra hard for a 10-year-old?

Usually less hard than parents expect. The maths is gentle; the real hurdles are conceptual, mainly understanding that a letter represents a number and that the equals sign means "balance". Once those click, most children handle 11+ algebra confidently.

What is the most common algebra mistake in the 11+?

Treating the equals sign as "the answer goes here" rather than as a balance, and misreading "3a" as "3 and a" instead of "3 times a". GL builds wrong answers directly around these two misconceptions.

How do I teach my child algebra for the 11+?

Start with missing-number problems (7 + ? = 12) before introducing letters, use a balance-scale picture for equations, and practise function machines both forwards and backwards. Building from arithmetic they already understand removes most of the anxiety around the word "algebra".

What is the difference between sequences and algebra in the 11+?

In a sequence, GL gives you several numbers in a row and you work out the rule that links them, then continue it, for example finding what follows 4, 7, 10, 13. In algebra, including function machines, one value is unknown and you reverse the steps to find it, for example solving 3n plus 4 equals 19. Sequences extend a pattern; algebra pins down one hidden number.

Explore the other GL Assessment maths topics, each with free sample questions and worked explanations.

All maths topics Percentages Decimals Place Value Fractions Long Division Long Multiplication Ratio & Proportion Negative Numbers Prime Numbers & Factors Area & Perimeter Volume Angles & Shapes Sequences Data Handling Speed, Distance & Time Free 11+ practice papers & tests All GL question types explained

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