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Cambridge IGCSE Maths: Algebra and graphs — Practice Questions & Answers
A complete tour of IGCSE 0580 algebra: manipulating expressions, solving linear and quadratic equations (including the quadratic formula), rearranging formulae, simultaneous equations, inequalities, sequences and nth terms, functions with composites and inverses, the families of graphs you must recognise, estimating gradients of curves, and direct and inverse variation.
1018 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Easy
Simplify $5x+3y-2x+4y$.
$3x+7y$
$7x+7y$
$3x+y$
$7x+3y$
Tap an answer to check it.
Why Collect like terms: $5x-2x=3x$ and $3y+4y=7y$, giving $3x+7y$.
2
Multiple choice · Easy
Expand $3(2x-5)$.
$6x-15$
$6x-5$
$6x+15$
$5x-15$
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Why Multiply each term inside the bracket by 3: $3\times 2x=6x$ and $3\times(-5)=-15$.
3
Multiple choice · Easy
Factorise fully $6x+9$.
$3(2x+3)$
$3(2x+9)$
$6(x+3)$
$3(2x+6)$
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Why The highest common factor of 6 and 9 is 3, so $6x+9=3(2x+3)$.
4
Multiple choice · Easy
Simplify $x^{3}\times x^{4}$.
$x^{7}$
$x^{12}$
$x^{1}$
$x^{34}$
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Why When multiplying powers of the same base, add the indices: $3+4=7$.
5
Multiple choice · Easy
Solve $4x-7=13$.
$x=5$
$x=1.5$
$x=3.25$
$x=20$
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Why Add 7 to both sides to get $4x=20$, then divide by 4 to get $x=5$.
6
Multiple choice · Easy
Find the nth term of the sequence $5, 8, 11, 14, \ldots$
$3n+2$
$3n$
$3n+5$
$2n+3$
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Why The common difference is 3, so the term is $3n$ plus a constant; $3(1)+2=5$, giving $3n+2$.
7
Multiple choice · Easy
Find the gradient of the line through $(1,2)$ and $(3,8)$.
$3$
$\frac{1}{3}$
$-3$
$4$
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Why Gradient $=\frac{8-2}{3-1}=\frac{6}{2}=3$.
8
Multiple choice · Medium
Expand and simplify $(x+3)(x-5)$.
$x^{2}-2x-15$
$x^{2}+2x-15$
$x^{2}-15$
$x^{2}-2x+15$
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Why Multiply out: $x^{2}-5x+3x-15=x^{2}-2x-15$.
9
Multiple choice · Medium
Factorise $x^{2}-5x+6$.
$(x-2)(x-3)$
$(x+2)(x+3)$
$(x-1)(x-6)$
$(x-2)(x+3)$
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Why Two numbers multiplying to $+6$ and adding to $-5$ are $-2$ and $-3$, giving $(x-2)(x-3)$.
10
Multiple choice · Medium
Solve $x^{2}+x-6=0$.
$x=2$ or $x=-3$
$x=-2$ or $x=3$
$x=2$ or $x=3$
$x=-2$ or $x=-3$
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Why Factorising gives $(x+3)(x-2)=0$, so $x=2$ or $x=-3$.
Key terms in Algebra and graphs
Variable: A symbol, usually a letter, representing an unknown or changing quantity.
Constant: A fixed value that does not change within a problem.
Coefficient: The numerical factor multiplying a variable in a term, such as $5$ in $5x$.
Term: A single number, variable, or product of numbers and variables within an expression.
Like terms: Terms containing the same variables raised to the same powers, which can be combined.
Expression: A combination of numbers, variables, and operations without an equals sign.
Equation: A statement that two expressions are equal, containing an equals sign.
Identity: An equation true for all values of the variable, such as $2(x+1) = 2x + 2$.
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