Progressive Algebra practice questions
Use Clevolab for progressive 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 Progressive set covers equations, inequalities, sequences, quadratics, expressions, and algebraic manipulation. 271 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
Simplify $2x+5+3-x$.
- A$x+2$Answer option
- B$3x+8$Answer option
- C$x+5$Answer option
- D$x+8$Correct answer
Why this answer is right
Combine $2x-x=x$ and $5+3=8$, giving $x+8$.
Group variable and constant parts. Compute $$2x-x=x,$$ and $$5+3=8.$$ Hence the simplified expression is $$x+8.$$
Sample question
Expand $(2x-3)^2$.
- A$4x^2-6x+9$Answer option
- B$4x^2-12x+9$Correct answer
- C$2x^2-6x+9$Answer option
- D$4x^2+12x+9$Answer option
Why this answer is right
Square a binomial: $(2x)^2-2\cdot 2x\cdot 3+3^2=4x^2-12x+9$.
Use $(a-b)^2=a^2-2ab+b^2$ with $a=2x$, $b=3$. $$(2x)^2-2(2x)(3)+3^2$$ $$=4x^2-12x+9$$
Sample question
If $f(x)=x^2$ on $x\ge0$ and $g(x)=\sqrt{x+1}$, find $(f^{-1}\circ g)(x)$.
- A$(x+1)^{1/4}$Correct answer
- B$\sqrt{x+1}$Answer option
- C$(x+1)^2$Answer option
- D$\dfrac{\sqrt{x+1}}{2}$Answer option
Why this answer is right
Since $f^{-1}(y)=\sqrt{y}$ for $y\ge0$, $(f^{-1}\circ g)(x)=\sqrt{\sqrt{x+1}}=(x+1)^{1/4}$.
On $x\ge0$, the inverse of $f(x)=x^2$ is $$f^{-1}(y)=\sqrt{y}.$$ Therefore $$(f^{-1}\circ g)(x)=f^{-1}(g(x))=\sqrt{\sqrt{x+1}}=(x+1)^{1/4}.$$ The inside is nonnegative for all $x\ge-1$.
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.