1
Complete the square
Not checkedRewrite \(x^2+2x-5\) in the form \((x+p)^2+q\).
Cambridge 9709 · Pure Mathematics 1
Practise completing the square
Check your answers and use feedback to improve.
Maths4U Original: notes, examples & two exam-style problems
Your practice progress
10 questions to work through
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How to enter answers
Use integers, fractions such as -3/2, or decimals rounded to six decimal places. Keep the sign inside the bracket. For equations, work on paper first, then choose an answer.
Start with a unit coefficient
2
Complete the square
Not checkedRewrite \(x^2-10x+20\) in the form \((x+p)^2+q\).
3
Complete the square
Not checkedRewrite \(x^2-4x+1\) in the form \((x+p)^2+q\).
Keep the outside coefficient
4
Complete the square with a coefficient
Not checkedRewrite \(6x^2+12x-3\) in the form \(a(x+b)^2+c\).
5
Complete the square with a coefficient
Not checkedRewrite \(3x^2-6x-15\) in the form \(a(x+b)^2+c\).
6
Complete the square with a coefficient
Not checkedRewrite \(3x^2+5x+1\) in the form \(a(x+b)^2+c\).
Handle a negative square
7
Complete the square
Not checkedRewrite \(6-8x-x^2\) in the form \(q-(x+p)^2\).
8
Complete the square with a coefficient
Not checkedRewrite \(5-2x-2x^2\) in the form \(c-a(x+b)^2\).
Use the form to solve equations
9
Solve by completing the square
Not checkedSolve \(x^2+6x+1=0\) by completing the square. Give your answers in surd form.
10
Solve by completing the square
Not checkedSolve \(x^2-3x-2=0\) by completing the square. Give your answers in surd form.
Practice complete
You have completed the guided set
Explain why the correction term is needed without looking at the notes. Return in a couple of days and try the questions again.
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