A-Level Algebra exam-style questions
Use Clevolab for A-Level exam-style practice in algebra. This page shows what the topic covers, what skills the current set targets, and a few real examples from the reviewed question bank.
About this topic
Clevolab treats algebra as repeated practice with explanation, not just answer checking. This page is designed to make the topic legible before you open the app.
The current A-Level set covers equations, inequalities, sequences, quadratics, expressions, and algebraic manipulation. 52 reviewed questions currently published for this page.
What you can practise
- Simplifying expressions
- Solving equations and inequalities
- Factorising and expanding
- Sequences and nth-term reasoning
- Quadratic structure
Real sample questions from the current set
These examples come from the reviewed questions currently stored for this topic. They are here so the page shows the actual flavour of Clevolab, not just a summary.
Sample question
Solve $9^x=27^{x-1}$.
- A$x=1$Answer option
- B$x=2$Answer option
- C$x=3$Correct answer
- D$x=\dfrac{3}{2}$Answer option
Why this answer is right
Write $9=3^2$ and $27=3^3$. Then $3^{2x}=3^{3(x-1)}$, so $2x=3x-3$ and $x=3$.
Express both sides with base $3$. $$9^x=(3^2)^x=3^{2x},\quad 27^{x-1}=(3^3)^{x-1}=3^{3(x-1)}.$$ Equate exponents: $2x=3x-3$, hence $x=3$. Checking confirms $9^3=27^{2}$.
Sample question
The interval defined by $|x-k|\le2$ has intersection with $[0,5]$ of length $3$. Find $k$.
- A$k=2$Answer option
- B$k=3$Answer option
- C$k=1$ or $k=4$Correct answer
- D$k\in[1,4]$Answer option
Why this answer is right
$|x-k|\le2$ is $[k-2,k+2]$. For overlap length $3$, either it starts before $0$ with $k+2=3$ giving $k=1$, or ends after $5$ with $5-(k-2)=3$ giving $k=4$.
The set $|x-k|\le2$ is the interval $[k-2,k+2]$. If it overlaps $[0,5]$ with length $3$, either only the left is cut: $k-2<0$ and $k+2\le5$ with overlap $k+2=3$, so $k=1$. Or only the right is cut: $k-2\ge0$ and $k+2>5$ with overlap $7-k=3$, so $k=4$. Thus $k=1$ or $k=4$.
Sample question
If $x+\dfrac{1}{x}=3$, find $x^2+\dfrac{1}{x^2}$.
- A$7$Correct answer
- B$5$Answer option
- C$9$Answer option
- D$11$Answer option
Why this answer is right
Square $x+\tfrac{1}{x}=3$ to get $x^2+2+\tfrac{1}{x^2}=9$. Hence $x^2+\tfrac{1}{x^2}=7$.
Use $\left(x+\dfrac{1}{x}\right)^2=x^2+2+\dfrac{1}{x^2}$. Given $x+\dfrac{1}{x}=3$, square to obtain $$x^2+2+\frac{1}{x^2}=9.$$ Thus $$x^2+\frac{1}{x^2}=9-2=7.$$
How this page fits into Clevolab
Clevolab is broader than any one exam mode. GCSE and A-level pages are useful entry points, while the wider project is about sharpening understanding through repeated topic practice.