Pure 1 course · All short practice · Notes & examples

Maths4U Original · 9709 Pure 1

Factorisation and valid roots

Check a short answer, use a hint, then study the reasoning. These checks assess the final answer; use the exam-style problems to practise written explanations.

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Recall · M4U-P1-QP-QUADRATICS-FACTORISATION-01

zero product

Maths4U Original · Short practice

For \(x^2+x-20=0\), enter the positive root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Method · M4U-P1-QP-QUADRATICS-FACTORISATION-02

non-unit factorisation

Maths4U Original · Short practice

For \(3x^2-8x-3=0\), enter the negative root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Apply · M4U-P1-QP-QUADRATICS-FACTORISATION-03

do not divide away a root

Maths4U Original · Short practice

Solve \(x(x-6)=0\). Which is the complete real solution set?

Choose one answer.

Check understanding · M4U-P1-QP-QUADRATICS-FACTORISATION-04

excluded denominator

Maths4U Original · Short practice

Solve \(\frac{x^2-9}{x-3}=0\).

Choose one answer.

Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-01

zero product

Maths4U Original · Short practice

For \(x^2-2x-15=0\), enter the positive root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-02

non-unit factorisation

Maths4U Original · Short practice

For \(3x^2-7x-6=0\), enter the negative root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-03

do not divide away a root

Maths4U Original · Short practice

How many distinct real roots does \(x(x+7)=0\) have?

Enter one number or fraction. Round decimals to at least six decimal places when needed.

Fresh review variant · M4U-P1-QP-VAR-QUADRATICS-FACTORISATION-04

excluded denominator

Maths4U Original · Short practice

Solve \(\frac{x^2-16}{x-4}=0\). Enter the admissible root.

Enter one number or fraction. Round decimals to at least six decimal places when needed.