Test
Higher-degree rational equations
This test focuses on cubic, biquadratic and other higher-degree equations. Students factor expressions, use substitution and verify which candidate values satisfy the original equation.
Time left: 00:00:00
Sample questions
- Solve x⁴ = ___.
- Solve x³ = ___.
- Solve x⁴ − ___x² + ___ = 0.
- Solve (x − (___))(x − (___)) = 0.
- The intersection equation of a line and parabola has discriminant ___. How many real intersection points are there?
Higher-degree rational equations
A higher-degree equation can often be simplified by factorisation, grouping or a substitution such as t = x². For a rational equation, first identify every value excluded by its denominators.
Finding roots
After finding one polynomial root, factor out x − a and solve the remaining lower-degree equation. Reverse every substitution to recover all original variable values. Check every candidate in the original equation because transformations may introduce inadmissible solutions.
Related mathematics tests
Exponential equations and models
This test covers exponential equations and their use in growth and decay models. Students rewrite expressions with a common base, solve equations and interpret percentage, compound and periodic change.
Function properties and transformations
This test develops understanding of even and odd functions and common graph transformations. Students identify shifts, reflections and scaling and construct a new function formula from a given transformation.
Trigonometric functions and equations
This test covers graphs, periods, ranges and signs of sine, cosine and tangent functions. Tasks also develop solution of elementary trigonometric equations and selection of solutions within a stated interval.
Roots and rational exponents
This test focuses on nth roots and powers with rational exponents. Students apply exponent laws, determine conditions under which expressions are defined and rationalise denominators.
