Pure 1 course · All short practice · Notes & examples

Maths4U Original · 9709 Pure 1

Linear and quadratic simultaneous equations

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-SIMULTANEOUS-01

substitution

Maths4U Original · Short practice

For \(y=x+2\) and \(y=x^2\), enter the larger x-coordinate of intersection.

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

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

line and quadratic

Maths4U Original · Short practice

For \(y=2x+3\) and \(x^2+y^2=9\), one intersection is \((0,3)\). Enter the other x-coordinate.

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

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

discriminant of intersection

Maths4U Original · Short practice

How many intersections do \(y=x+1\) and \(y=x^2+2\) have?

Choose one answer.

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

line and parabola tangency

Maths4U Original · Short practice

The line \(y=4x+k\) is tangent to \(y=x^2\). Find \(k\).

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

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

substitution

Maths4U Original · Short practice

For \(y=x+6\) and \(y=x^2\), enter the larger intersection x-coordinate.

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

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

line and quadratic

Maths4U Original · Short practice

For \(y=x+4\), \(x^2+y^2=16\), one intersection has \(x=0\). Find the other x-coordinate.

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

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

discriminant of intersection

Maths4U Original · Short practice

How many intersections do \(y=2x-1\) and \(y=x^2+1\) have?

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

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

line and parabola tangency

Maths4U Original · Short practice

The line \(y=6x+k\) is tangent to \(y=x^2\). Find \(k\).

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

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