Algebra Substitution Question Generator
Builds a sheet of substitution questions at the level you ask for. Every expression evaluates to a whole number, including the ones that divide, so a wrong answer is a mistake in the working rather than in the rounding. Every question is computed and checked directly — not a fabricated or AI-guessed fact.
What this generator does
Generates substitution questions with answers — evaluate an expression for given values. Substitution is worth isolating from solving, because it is where sign errors and missing brackets appear, and both are invisible until the arithmetic goes wrong.
How to use this tool
- Choose a level and how many questions you want.
- Press make questions and work through the sheet.
- Show the answers to mark it, or show the working to see which part of the expression is worked out first.
- Enter a seed word to rebuild the same sheet later.
Worked examples
- Stretch level, seed round9
- 5a² − 4 when a = 8 → 316, squaring first: 8² = 64, then 5 × 64 = 320, then 320 − 4.
Common use cases
- Algebra substitution practice
- Quick maths warm-ups
- Self-testing before a maths quiz
How this generator works
An expression shape is chosen for the level — one letter, two letters, a square, a bracket or a division — and coefficients and substituted values are drawn so the result is always a whole number. The check reads the number back out of the printed answer and compares it with the value the expression was built to give, so a slip between the calculation and what is printed is caught.
Randomness and fairness
Both the expression's coefficients and the substituted values are drawn with the browser's cryptographic random number generator, and the answer is computed exactly. At stretch level negative values appear regularly rather than occasionally, since those are the ones that expose the bracket problem. Unless the generator has changed since, a seed word rebuilds the same sheet later; it is for reproducibility, not cryptographic strength, so a seeded sheet is deterministic rather than unpredictable.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Every expression evaluates to a whole number, so a substitution that would naturally leave a fraction is never presented as one.
- Expressions use at most two letters. Longer expressions with three or more variables are not produced.
- Negative values are substituted only at the stretch level, and the values themselves are always whole numbers — decimals are not substituted.
Common mistakes
- Substituting a negative without brackets
- If x = −3 then x² is (−3)², which is 9. Writing −3² gives −9, which is a different expression.
- Reading 3x as thirty-something
- 3x with x = 4 is 12, not 34. The missing sign is multiplication.
Related generators
- Simple Equation GeneratorLinear equations built to order — one step, two steps, unknowns on both sides and brackets — each with a whole-number solution.
- Expanding Brackets Question GeneratorProducts of two linear brackets to multiply out, with each of the four partial products written separately.
- Logic Simplification Challenge GeneratorDeliberately over-complicated expressions built by applying an identity backwards, with the law named and equivalence proved on every assignment.
- Eigenvalue Practice GeneratorMatrices with whole-number eigenvalues, built by conjugating a triangular matrix, with trace and determinant as the check.
- Order of Operations Question GeneratorBODMAS/PEMDAS questions built so the order genuinely changes the answer, with worked steps.
- Index Laws Question GeneratorSimplification questions on multiplying and dividing powers, in one letter or two, with the numbers and the indices handled separately.