Solving quadratic inequalities: GCSE Maths Practice
Inequalities
Solving quadratic inequalities
51 self-marking GCSE practice questions on Solving quadratic inequalities, written specifically for AQA, Pearson, OCR across Higher tier. Instant marking with full worked solutions on every question.
A few of the 51 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 14 marksGrade 7-8
Solve x2−12x+20<0. Show your working.
Show the worked solution
Factorise: the expression factorises as (x−2)(x−10)
What are the common mistakes in Solving quadratic inequalities?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Shades or selects the wrong region for a quadratic inequality
Chose the region BETWEEN the roots instead of outside them - for a "> 0" inequality with a positive x2 coefficient, the solution is outside the roots
Gives only the roots of a quadratic instead of the solution region for the inequality
Found the correct critical values but didn't go on to state the inequality region
Writes a single chained inequality for a solution set that is actually two disjoint regions
Tried to write the two separate regions as a single chained inequality, which isn't valid here - the solution is two separate ranges joined by "or"
Quick answers about Solving quadratic inequalities
How many Solving quadratic inequalities practice questions are there?
There are 51 self-marking GCSE Maths questions on Solving quadratic inequalities, written for AQA, Pearson, OCR across Higher tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Solving quadratic inequalities?
No. You can start practising Solving quadratic inequalities straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
, so it equals zero when
x=2
or
x=10
.
Since the coefficient of x2 is positive, the graph is a "u-shape" - it's below zero (negative) BETWEEN the two roots.
So the solution is 2<x<10. M1A1A2A3
Question 23 marksGrade 8-9
A rectangle has width x and length x+3, where x>0. Its area is greater than 40 cm².
Form an inequality in terms of x, and solve it to find the possible values of x.
Show the worked solution
Area =x(x+3)=x2+3x
Form the inequality: x2+3x>40
Question 33 marksGrade 8-9
A rectangular garden has width x and length x+8, where x>0. Its area is greater than 65 cm².
Form an inequality in terms of x, and solve it to find the possible values of x.
Question 45 marksGrade 8-9
(a) Solve x2−6x+8=0.
(a)(i) The smaller root.
(a)(ii) The larger root.
(b) Hence solve x2−6x+8≤0.
Question 55 marksGrade 9
Here is a rectangle with sides (3x−2) cm and (x−1) cm, and a right-angled triangle with base 2x cm and height x cm.
All measurements are in centimetres. The area of the rectangle is greater than the area of the triangle.
Find the set of possible values of x.