Quadratic and non-linear simultaneous equationsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

What is the first step in solving a line and a parabola algebraically?
After finding x, how do you find y?
How should the final answers be written?
Solve y=x+2 and y=x^2.
What does the discriminant b^2-4ac tell you here?
What does b^2-4ac0 mean for line and curve?
What does b^2-4ac=0 mean for line and curve?
What does b^2-4ac<0 mean for line and curve?
What is the graphical meaning of the solutions of f(x)=g(x)?
Solve x+y=7 and xy=12.
How do you rearrange x+y=10 before substituting?
A solution gives a negative length. What do you do?
Why is a graphical solution only approximate?

Exam questions on Quadratic and non-linear simultaneous equations

Consider the line $y=x+2$ and the curve $y=x^2$ .
The line is replaced by $y=2x-1$ . Show that this new line meets the curve $y=x^2$ at exactly one point, and state the coordinates of that point.2 marks
Consider the line $y=3x-4$ and the curve $y=x^2-4x+8$ .
The line is changed to $y=2x-2$ . Show that it does not meet the curve $y=x^2-4x+8$ .2 marks
A rectangular patio has length $x$ m and width $y$ m. Its perimeter is $20$ m and its area is $21$ m $^2$ .
Show that $x^2-10x+21=0$ .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).