Mathematics · Pearson Edexcel 9MA0 · Topic 2

Algebra and functions

The algebra toolkit: indices, surds, quadratics, simultaneous equations, inequalities, polynomials, graph sketching, functions, transformations and partial fractions.

11 sub-topics
5 in Year 12, 3 in Year 13
193 practice questions
11 animated lessons

Practice questions (193) Lessons Worksheets All Edexcel Mathematics topics

What the specification says

Every sub-topic Pearson Edexcel can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

2.1Laws of indices for all rational exponentsY12
2.2Surds and rationalising the denominatorY12
2.3Quadratic functions: discriminant, completing the square, solvingY12
2.4Simultaneous equations, one linear and one quadraticY12
2.5Linear and quadratic inequalitiesY12
2.6Polynomials, the factor theorem and algebraic divisionY13
2.7Graphs of cubics, quartics, reciprocals and modulus functionsY13
2.8Composite and inverse functionsY13
2.9Transformations of y = f(x)Y13
2.10Partial fractionsY13
2.11Functions in modellingY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 193 questions in this topic, free, no account needed.

Algebra and functions

Easy

Equal roots · Year 12 · 3 marks

The equation $x^2 + kx + 9 = 0$ has equal roots. Find the possible values of $k$ .
(3)

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Equal (repeated) roots happen when the discriminant is zero. $b^2 - 4ac = 0$
Here $a = 1$ , $b = k$ and $c = 9$ . $k^2 - 4 \times 1 \times 9$ ${}= 0$ ${}\Rightarrow k^2$ ${}= 36$
Square-rooting gives two answers: positive and negative. $k = 6$ or $k = -6$

Total3

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Algebra and functions

Not needed for Year 12Medium

Partial fractions · Year 13 · 3 marks

Express $\dfrac{5x + 1}{(x - 1)(x + 2)}$ in partial fractions.
(3)

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Write it as $\dfrac{A}{x - 1}$ ${}+ \dfrac{B}{x + 2}$ and multiply through. $5x + 1 = A(x + 2) + B(x - 1)$
Choose values of $x$ that make one bracket zero. $x = 1$ : $6 = 3A \Rightarrow A = 2$ ; $x = -2$ : $-9 = -3B \Rightarrow B = 3$
$\dfrac{2}{x - 1}$ ${}+ \dfrac{3}{x + 2}$

Total3

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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Algebra and functions

Hard

Roots and the discriminant · Year 12 · 5 marks

Find the values of $k$ for which $kx^2 + 4x + (k - 3) = 0$ has two distinct real roots.
(5)

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Two distinct real roots means the discriminant is positive. $b^2 - 4ac > 0$ : $16 - 4k(k - 3) > 0$
Divide by $-4$ , which reverses the inequality. $k^2 - 3k - 4 < 0$
Critical values $-1$ and $4$ ; a ∪ shape is negative between them. $(k - 4)(k + 1) < 0$ , so $-1 < k < 4$
If $k = 0$ the equation is not a quadratic and has only one root. $-1 < k < 4$ , $k \ne 0$

Total5

MMethod mark: for a correct method, even with a slip.
AAccuracy mark: for a correct answer from a correct method.
BIndependent mark: for a correct fact or result on its own, with no method needed.

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