Linear and quadratic simultaneous equations · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

A line and a quadratic curve — objective 1

Maths4U Original · Short practice

A curve is \(y = x^{2} - 34 x + 341\) and a line is \(y = 2 x + 18\).

Find the smaller intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

A line and a quadratic curve — objective 1

Maths4U Original · Short practice

A curve is \(y = x^{2} - 36 x + 397\) and a line is \(y = 3 x + 19\).

Find the smaller intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

A line and a quadratic curve — objective 2

Maths4U Original · Short practice

A curve is \(y = x^{2} - 36 x + 397\) and a line is \(y = 3 x + 19\).

Find the larger intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

A line and a quadratic curve — objective 2

Maths4U Original · Short practice

A curve is \(y = x^{2} - 41 x + 457\) and a line is \(y = x + 20\).

Find the larger intersection x-coordinate.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

A line and a quadratic curve — objective 3

Maths4U Original · Short practice

A curve is \(y = x^{2} - 41 x + 457\) and a line is \(y = x + 20\).

Find the y-coordinate of the left intersection.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

A line and a quadratic curve — objective 3

Maths4U Original · Short practice

A curve is \(y = x^{2} - 43 x + 521\) and a line is \(y = 2 x + 21\).

Find the y-coordinate of the left intersection.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

A line and a quadratic curve — objective 4

Maths4U Original · Short practice

A curve is \(y = x^{2} - 43 x + 521\) and a line is \(y = 2 x + 21\).

Find the area between the two graphs.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

A line and a quadratic curve — objective 4

Maths4U Original · Short practice

A curve is \(y = x^{2} - 41 x + 505\) and a line is \(y = 3 x + 22\).

Find the area between the two graphs.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →