Mathematics 4024 · O Level · Algebraic manipulation

Algebraic manipulation — practice question

(a)[1]

Evaluate the expression $\sqrt[3]{\dfrac{543}{28.6 - 1.35}}$.

(b)[1]

Factorise completely the expression $9p^2 - 6pq$.

(c)[1]

Expand the brackets, then simplify $(3a + b)^2$.

(d)[3]

Express in its simplest single-fraction form $\dfrac{4}{2t + 1} - \dfrac{3}{3t + 1}$.

(e)[2]

Find the integer values of $n$ for which $4(2-n) > 17$ and $n > -6$.

(f)[3]

Abebi, Bella and Chuku share $112$. Abebi gets $x$. Bella gets $12$ less than Abebi. Chuku gets twice Bella's amount. Form an equation in $x$ and solve it to find how much Chuku gets.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Approximately $2.71$, or $2.711\ldots$.

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