You know the drill, GCSE Higher students, practice makes perfect, right?! Well, it certainly helps a huge amount and these manipulating and simplifying algebraic expressions questions are a great way to prepare for exams.

GCSE Maths courses place a heavy emphasis on algebra. Like it or not, the topic consumes a mammoth 30% of the mark on higher-level papers and you’ll do yourself a huge favour by practising how to manipulate and simplify algebraic expressions effectively.

So, where to start?

Diagnose your stronger areas and your areas in need of improvement with suitable practice questions like those in the quiz below. Use the questions below to find gaps in your knowledge. The quiz will tell you exactly what you need to cover in your revision from this list of topics:

– Index Laws (Algebraic)
– Changing the Subject of a Formula
– Forming Expressions
– Simplifying Algebraic Fractions
– Adding and Subtracting Fractions
– Multiplying and Dividing Fractions
– Algebraic Proof

Manipulating and Simplifying Algebraic Expressions Questions – Test Yourself with this Diagnostic Quiz!

Ready to test your knowledge?

Simplify \[(3p^4)^2\]

\[3p^8\]

\[6p^8\]

\[9p^6\]

\[9p^8\]

Hint

Which of the following is an expression for the perimeter of the rectangle?

\[5x+3\]

\[5x+5\]

\[10x+6\]

\[10x+10\]

Hint

Make \(x\) the subject of \(y=mx+c\).

\[x=\frac{y-c}{m}\]

\[x=\frac{y+c}{m}\]

\[x=m(y-c)\]

\[x=m(y+c)\]

Hint

Fully simplify \[\frac{x^2+6x}{x^2+4x-12}\]

\[\frac{6x}{4x-12}\]

\[\frac{3x}{2x+6}\]

\[-\frac{3}{4}\]

\[\frac{x}{x-2}\]

Hint

Simplify \[\frac{12x^6y^3}{4x^2y^9}\]

\[3x^3y^3\]

\[3x^4y^5\]

\[\frac{3x^3}{y^3}\]

\[\frac{3x^4}{y^6}\]

Hint

Write \(\frac{8}{2x-3} - \frac{5}{x+7}\) as a single fraction in its simplest form.

\[\frac{3}{x-10}\]

\[\frac{3}{2x^2+11x-21}\]

\[\frac{71-2x}{2x^2+11x-21}\]

\[\frac{x-10}{2x^2+4x+21}\]

Hint

Rohit is four times as old as Kane. Ellyse is six years younger than Rohit. Given that Kane is \(x\) years old, write an expression for the mean of their ages.

\[\frac{x+2}{3}\]

\[\frac{3x+2}{3}\]

\[2x-2\]

\[3x-2\]

Hint

Simplify the expression below, giving your answer in the form \(\frac{ax+b}{cx+d}\). \[\frac{3x-15}{2x+3} \div \frac{x^2-x-20}{2x^2-9x-18}\]

\[\frac{3x+18}{x+4}\]

\[\frac{3x-18}{x+4}\]

\[\frac{3x-3}{x-4}\]

\[\frac{x-3}{3x+12}\]

Hint

Fully simplify \[\frac{4x-3}{3x+2} \times \frac{3x-4}{2x+1} \]

\[\frac{12x^2-25x+12}{6x^2+7x+2}\]

\[\frac{12x^2+25x-12}{6x^2+7x+2}\]

\[\frac{12x^2-25x-12}{6x^2+7x+2}\]

\[\frac{12x^2+25x+12}{6x^2+7x+2}\]

Hint

Given that \(n\) is an integer, which of these expressions is always a multiple of 5?

\[5(n+\frac{1}{2})\]

\[5n+4\]

\[n+5\]

\[5(n+1)\]

Hint

Rearrange the formula below to make \(a\) the subject. \[\frac{a}{b} = \frac{3a+7}{5b-2}\]

\[a=\frac{3ab+7b}{5b-2}\]

\[a=\frac{7b}{2b-2}\]

\[a=\frac{7}{2}-\frac{7b}{2}\]

\[a=\frac{7}{2b-2}\]

Hint

Given \(n\) is an integer, which pair of expressions represent two, consecutive numbers.

\(n + 1\) and \(n - 1\)

\(2n + 1\) and \(2n - 1\)

\(2n\) and \(2(n +1)\)

\(n\) and \(n+1\)

Hint

Fully simplify \[\frac{15x+6}{3x^2+18}\]

\[\frac{5x+2}{x^2+6}\]

\[\frac{5x}{12}\]

\[\frac{5x+2}{x+6}\]

\[\frac{1}{x+3}\]

Hint

Rearrange the formula below to make \(u\) the subject. \[v^2=u^2+2as\]

\[u^2=v^2+2as\]

\[u^2=v^2-2as\]

\[u=\sqrt{v^2-2as}\]

\[u=\sqrt{v^2+2as}\]

Hint

Write the expression below as a fraction in its simplest form. \[\frac{3}{2a+5} + \frac{7}{3a+4}\]

\[\frac{10}{5a+9)}\]

\[\frac{23a+47}{(2a+5)(3a+4)}\]

\[\frac{10}{(2a+5)(3a+4)}\]

\[\frac{23a+47}{5a+9}\]

Hint

Time's up

We’re not only tests here at Beyond. You can find a great selection of blogs here and you can find our main Daily Maths Revision Page here! You can also subscribe to Beyond for access to thousands of secondary teaching resources. You can sign up for a free account here and take a look around at our free resources before you subscribe too.