Linear and quadratic inequalitiesEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

What must you do to the sign when multiplying or dividing an inequality by a negative number?
What are critical values?
Solution of (x-a)(x-b)<0 with a<b?
Solution of (x-a)(x-b)0 with a<b?
Solve x^2<9.
Why is -2<x<4 one interval but 'x<-2 or x4' two?
What does 'and' give for two solution sets?
What does 'or' give for two solution sets?
Why should you not multiply \frac6x<x+1 by x?
How does \frac ax<b become a polynomial inequality?
How do you read f(x)<g(x) from graphs?
When are critical values included in the solution?
Solve x^2-5x+6<0.

Exam questions on Linear and quadratic inequalities

Consider the inequality $3x-7>5x+1$ , where $x$ is a real number.
Find the set of values of $x$ for which $3x-7>5x+1$ or $2x+6>0$ .2 marks
The function $f(x)=x^2-2x-8$ is defined for real $x$ .
Find the set of values of $x$ for which $f(x)<0$ and $2x-1>0$ .2 marks
A rectangular patio has width $x$ m and length $(x+6)$ m. Its area must be less than $55$ m $^2$ , and its width must be greater than $2$ m.
Show that $x^2+6x-55<0$ and hence find the range of possible values of $x$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).