Equations, inequalities and graphs: review · 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

Two modulus expressions — objective 1

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(4 x + 18\) and \(\displaystyle V=\)\(6 x + 37\). Consider \(\left|{4 x + 18}\right| = \left|{6 x + 37}\right|\).

Find the smaller solution.

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

Fresh review variant

Two modulus expressions — objective 1

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(2 x + 19\) and \(\displaystyle V=\)\(4 x + 39\). Consider \(\left|{2 x + 19}\right| = \left|{4 x + 39}\right|\).

Find the smaller solution.

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

Method

Two modulus expressions — objective 2

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(2 x + 19\) and \(\displaystyle V=\)\(4 x + 39\). Consider \(\left|{2 x + 19}\right| = \left|{4 x + 39}\right|\).

Find the larger solution.

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

Fresh review variant

Two modulus expressions — objective 2

Maths4U Original · Short practice

Write \(\displaystyle U=\)\(3 x + 20\) and \(\displaystyle V=\)\(5 x + 41\). Consider \(\left|{3 x + 20}\right| = \left|{5 x + 41}\right|\).

Find the larger solution.

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

Apply

Cubic sign charts — objective 3

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 27\right) \left(x - 22\right) \left(x - 20\right)\). Use a sign chart to analyse P.

Find the largest root.

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

Fresh review variant

Cubic sign charts — objective 3

Maths4U Original · Short practice

\(\displaystyle P(x)=\)\(\left(x - 26\right) \left(x - 24\right) \left(x - 21\right)\). Use a sign chart to analyse P.

Find the largest root.

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

Check understanding

Equations reducible to quadratics — objective 4

Maths4U Original · Short practice

Solve \(x^{4} - 53 x^{2} + 196 = 0\). For a substitution, write \(\displaystyle u=x^{2}\).

Find the discriminant of the quadratic in \(\displaystyle u=x^{2}\).

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

Fresh review variant

Equations reducible to quadratics — objective 4

Maths4U Original · Short practice

Solve \(x^{4} - 45 x^{2} + 324 = 0\). For a substitution, write \(\displaystyle u=x^{2}\).

Find the discriminant of the quadratic in \(\displaystyle u=x^{2}\).

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

Try written exam-style problems →