Mathematics 0580 · IGCSE
Algebraic manipulation
100 practice questions on Algebraic manipulation, with worked solutions and instant marking.
First expand the brackets, then simplify $4(5w + 3) - 2(w - 1)$.
Feb/March 2017
Factorise $15c^2 - 5c$ fully.
Feb/March 2017
Expand the brackets, then simplify the expression: $4(5w + 3) - 2(w - 1)$.
Feb/March 2017
Factorise completely the expression $15c^2 - 5c$.
Feb/March 2017
$M = \begin{pmatrix}5 & 3 \\ 1 & -2\end{pmatrix}$ and $N = \begin{pmatrix}3 & -6 \\ 4 & 2\end{pmatrix}$.
Feb/March 2017
Factorise $6d^2e - 9e^2$ completely.
Feb/March 2018
Finish the statements.
Feb/March 2018
Factorise completely the expression $15k^{2}m - 20m^{4}$.
Feb/March 2018
Seven students are hoping to join the school diving club. The table below gives some information about these students.
Feb/March 2018
Rearrange $s = k - t^2$ so that $t$ is the subject.
Feb/March 2018
Factorise completely the expression $8g^2 - 4g$.
Feb/March 2019
Explain why the student is wrong.
Feb/March 2019
Factorise the expression $7k^2 - 15k$.
Feb/March 2019
Calculate $\begin{pmatrix}2 & -1 \\ 4 & 3\end{pmatrix}\begin{pmatrix}1 & 6 \\ -5 & 4\end{pmatrix}$.
Feb/March 2019
Express $y$ in terms of $x$.
Feb/March 2019
Factorise fully. $3x^2 - 12xy$.
Feb/March 2020
From $x^2 - 12x + a = (x + b)^2$, determine the values of $a$ and $b$.
Feb/March 2020
Factorise completely the expression $3x^2 - 12xy$.
Feb/March 2020
Express as one fraction in simplest form: $\frac{x+3}{x-3} - \frac{x-2}{x+2}$.
Feb/March 2020
Factorise $9t^2w - 3t$ completely.
Feb/March 2021
Factorise completely $8g-2g^2$.
Feb/March 2023
Determine the highest common factor (HCF) of $12x^{12}$ and $16x^{16}$.
Feb/March 2023
Write $8g - 2g^2$ in fully factorised form.
Feb/March 2023
Write down an expression for the area of this rectangle. Give your answer in its simplest form.
Feb/March 2023
Expand then simplify $(2p^2 - 3)(3p^2 - 2)$.
Feb/March 2023
Factorise $3x^3 - 7xy$ completely.
Feb/March 2024
Simplify the expression $4m + 7k - m + 3k$.
Feb/March 2024
Find the highest common factor (HCF) shared by $28x^5$ and $98x^3$.
Feb/March 2024
$x^2 - 16x + a$ may be expressed in the form $(x + b)^2$.
Feb/March 2024
Simplify $4m + 7k - m + 3k$ into its simplest form.
Feb/March 2024
Factorise the expression. $x^2 - x - 12$
Feb/March 2024
Kat uses a rule for finding the difference of two square numbers, $a^2 - b^2$. Her rule is to multiply the sum of $a$ and $b$ by the difference between $a$ and $b$. She demonstrates this for $17^2 - 13^2$: $17^2 - 13^2 = (17 + 13) \times (17 - 13) = 30 \times 4 = 120$.
Feb/March 2025
$X=\frac{1}{3}w^2p$
Feb/March 2025
$V=4mp^2$
Feb/March 2025
Factorise the expression $8x^2 - 2x$.
Feb/March 2025
Factorise $18a^2 - 98$ into its fully factorised form.
Feb/March 2025
Simplify $4y^2 + 3y - y^2 + 2y$.
Feb/March 2025
Factorise the expression $3w^{2} - 2w$.
May/June 2015
Factorise fully $3x^2y-5xyz$.
May/June 2015
Expand the brackets, then simplify $5(x-3)-3(x-5)$.
May/June 2015
Factorise completely the expression $9x^2 - 6x$.
May/June 2015
Factorise $yp + yt + 2xp + 2xt$ fully.
May/June 2015
Expand and simplify $x(2x + 3) + 5(x - 7)$.
May/June 2015
The matrix can be written as $M = \begin{pmatrix}3 & 1 \\ -11 & -2\end{pmatrix}$.
May/June 2015
The function is $f(x) = x^2 + 4x - 6$.
May/June 2015
Factorise $9x^2 - 6x$ completely.
May/June 2015
Factorise the quadratic $2x^2 - 5x - 3$.
May/June 2015
Simplify $7e+4e-5f-f$.
May/June 2015
Make $x$ the subject from the formula $A - x = \frac{vx}{t}$.
May/June 2015
Expanding expressions, factorising, indices, and a proof involving odd numbers.
May/June 2015
Find $A$ for $r=6.2$ cm and $l=10.8$ cm.
May/June 2015
Take $P=\begin{pmatrix}2 & 3\\1 & 4\end{pmatrix}$, $Q=\begin{pmatrix}1 & 2\\0 & 3\end{pmatrix}$, $R=\begin{pmatrix}0 & u\\1 & v\end{pmatrix}$, and $S=\begin{pmatrix}w & 3\\8 & 2\end{pmatrix}$.
May/June 2015
Using $y = \frac{qx}{p}$, write $x$ in terms of $p$, $q$ and $y$.
May/June 2016
Simplify $3f + 4f - 2f$.
May/June 2016
Factorise fully: $2a + 4 + ap + 2p$.
May/June 2016
Express $x$ in terms of $p$, $q$ and $y$.
May/June 2016
Make $p$ the subject in the formula $rp + 5 = 3p + 8r$.
May/June 2016
The expression $y = x^2 + 7x - 5$ may also be expressed in the form $y = (x + a)^2 + b$.
May/June 2016
The formula can be written as $p = 4r - 3t$.
May/June 2016
Solve for $x$ in the inequality $5x - 3 > 9$.
May/June 2016
Take $A = \begin{pmatrix}2 & 0\\ -1 & 5\\ 3 & -4\end{pmatrix}$, $B = \begin{pmatrix}1 & 3\\ -1 & 5\end{pmatrix}$, $C = \begin{pmatrix}7\\ -4\end{pmatrix}$ and $D = (2\ 5)$.
May/June 2016
Expand the brackets and simplify $7(2x + 3y) - x(14 - y)$.
May/June 2017
$A=4\pi r^2$.
May/June 2017
Factorise $12n^2 - 4mn$ completely.
May/June 2017
Factorise $14x - 21y$.
May/June 2017
Factorise completely $4x^2 - 8xy$.
May/June 2017
Factorise completely $12n^2 - 4mn$.
May/June 2017
Rearrange the formula $p = 2q^2$ so that $q$ is the subject.
May/June 2017
Factorise completely the expression $9t^2 - u^2$.
May/June 2017
Factorise the expression $14x - 21y$.
May/June 2017
Factorise the expression $4x^{2} - 8xy$ completely.
May/June 2017
Simplify the expression $\frac{4(x - 6)^{2}}{(x - 6)}$.
May/June 2017
Rearrange $x = y + \sqrt{a}$ so that $a$ becomes the subject of the formula.
May/June 2017
Find $y$ expressed in terms of $x$.
May/June 2017
Simplify the expression $5a + 6a - a$.
May/June 2017
Expand the brackets, then write the expression in its simplest form: $4(2x + 5) - 5(3x - 7)$.
May/June 2017
Solve the simultaneous equations. You must show all your working. $2x + 3y = 11$, $3x - 5y = -50$.
May/June 2017
Expand then simplify $6(2y-3)-5(y+1)$.
May/June 2018
Factorise $10 + 16w$ fully.
May/June 2018
Factorise completely the expression $4xy^2 - 6y^3$.
May/June 2018
Express $y$ as the subject in the equation $5x - 2y + 7 = 0$.
May/June 2018
Simplify $7g - g + 2g$.
May/June 2018
Expand $7(x - 8)$ to simplify the expression.
May/June 2018
Factorise $w + w^3$ into a product.
May/June 2018
Expand and simplify the expression $6(2y - 3) - 5(y + 1)$.
May/June 2018
Factorise the expression $xy + 2y + 3x + 6$ completely.
May/June 2018
Expand the expression $7(x-8)$.
May/June 2018
Write $2a+4b-ax-2bx$ in fully factorised form.
May/June 2018
Rearrange the equation to make $x$ the subject.
May/June 2018
Expand the brackets and simplify the expression $(2p+3)(3p-2)$.
May/June 2018
Factorise the expression $w + w^3$.
May/June 2018
Solve $3x = 18$.
May/June 2018
Factorise the expression $2mn + m^2 - 6n - 3m$.
May/June 2018
Find the adult ticket price.
May/June 2018
Factorise the expression $5y - 6py$.
May/June 2019
Expand the bracketed expression $x^2(x-7)$.
May/June 2019
Rearrange this formula so that $x$ is the subject. $5x^2 - 3y = 4y + 8$
May/June 2019
Rearrange $2(w + h) = P$ so that $w$ is the subject.
May/June 2019
Factorise $2x^2 - x$.
May/June 2019
Simplify the expression $4x - 12y + 10x + 25y$.
May/June 2019