11+ Algebra Basics: Missing Numbers, Equations and Worked Answers

Original learning material for families preparing for 11-plus exams taken in 2027. These examples are not official exam questions; check your school’s current assessment guidance for the skills and format it uses.

Algebra gives a name to a number you do not yet know, or a quantity that can vary. If a box plus seven equals nineteen, you already know how to find the missing value. Writing x + 7 = 19 records the same problem with a letter instead of a box.

Know what the symbols are saying

An expression has no equals sign telling you what it must equal. You can evaluate it when given a value, or sometimes simplify it. An equation gives a relationship you can use to find an unknown. Do not try to “solve x” in 3x + 5 unless you are given more information.

Worked example: substitute a value

Find the value of 4a + 3 when a = 6. Replace the letter with six: 4 × 6 + 3 = 24 + 3 = 27. Multiplication happens before addition here. The expression is not 46 + 3, because writing a number next to a letter indicates multiplication.

Brackets can change the result. With a = 6, the expression 4(a + 3) gives 4 × (6 + 3) = 4 × 9 = 36. Compare 27 and 36: the first expression adds three once; the second adds three inside each of four groups.

Worked example: solve and keep the balance

Solve 5x + 8 = 43. Subtract eight from both sides: 5x = 35. Divide both sides by five: x = 7. The point of doing the same thing to each side is to preserve equality. You are changing the equation into a simpler equivalent one, not merely moving symbols around.

Now substitute seven into the original equation: 5 × 7 + 8 = 35 + 8 = 43. This confirms the value satisfies the equation. If you check only the final line x = 7, you have not checked the original relationship.

Worked example: reverse a function machine

A machine multiplies an input by four, then subtracts nine. Its output is 31. Undo the last step first: 31 + 9 = 40. Undo multiplying by four: 40 ÷ 4 = 10. The input is ten. Checking forwards gives 10 × 4 − 9 = 31.

The order matters. Dividing 31 by four before adding nine would reverse the individual operations in the wrong order. A useful question is: “What was the last thing done to the number?” That is the first thing to undo.

Form an equation from a short story

A workshop charges £6 to enter and £3 for each model made. If a visitor pays £24 altogether, let m be the number of models. The charge is 6 + 3m = 24. Subtract six to get 3m = 18, then divide by three: m = 6. Check the answer as a cost: £6 + six lots of £3 = £24.

Keep the meaning of the letter clear. Here m counts models; it does not mean money. Labelling a variable prevents a numerical answer from being attached to the wrong quantity in a longer problem.

Eight algebra questions with answers

Three mistakes to watch for

• Subtracting the coefficient: in 5x = 35, undo multiplication by dividing by five, not subtracting five.
• Checking a changed equation but not the original: a slip in an earlier line can survive a check of only the last step.
• Forgetting brackets: 2(x + 4) includes two lots of four; it is not the same expression as 2x + 4.

Where this fits in preparation

These beginner skills can support multi-step word problems. For more original question practice, try the fresh maths set, which includes equations alongside other skills, or return to the Maths hub. A practice score is not a prediction of an entrance-exam result.

The DfE mathematics programme includes algebraic missing-number work and simple formulae in Year 6. It is a curriculum reference, not a guarantee that a particular 11-plus test uses these question types. Source checked 21 October 2026. No educator endorsement or official-paper affiliation is claimed.