Further Mathematics · Pearson Edexcel 9FM0 · Option FP1 · Topic 7

Inequalities

Solving inequalities that involve fractions and the modulus function, by algebra and with sketches.

1 sub-topic
Taught in Year 12
23 practice questions
1 animated lesson

Practice questions (23) Lessons Worksheets All Edexcel Further 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.

7.1InequalitiesY12

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Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 23 questions in this topic, free, no account needed.

Inequalities

Easy

A modulus inequality · Year 12 · 1 mark

What is the solution of $|x - 4| < 4$ ?
(1)

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The distance of $x$ from 4 is less than 4.A: $0 < x < 8$

Total1

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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Inequalities

Medium

Multiplying an inequality · Year 12 · 1 mark

Why is it wrong to solve $\dfrac{x + 1}{x - 2} > 3$ by multiplying both sides by $x - 2$ ?
(1)

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Multiply by $(x - 2)^2$ , which is never negative, or collect everything on one side as a single fraction. $B$ : $x - 2$ could be negative, which would reverse the inequality

Total1

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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Inequalities

Hard

An inequality with a rational function · Year 12 · 6 marks

Use algebra to find the set of values of $x$ for which $\frac{20}{x} > x - 1$ .
(6)

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Do not multiply by $x - b$ : its sign is unknown. Collect on one side. $\frac{20}{x} - (x - 1) > 0$
One fraction. $\frac{20 - x(x - 1)}{x} > 0$
Factorise the numerator. $\frac{-(x + 4)(x - 5)}{x} > 0$
Roots of the numerator and of the denominator. $\text{critical values: } -4, 0, 5$
Test the sign in each interval, or sketch. $x < -4 \text{ or } 0 < x < 5$

Total6

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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