5 grade
Solving the simplest equations
Solving simple equations typically involves isolating the variable on one side of the equation. Remember to perform the same operation to both sides of the equation to maintain equality.
Tests by topic
Equations
These tests help build a secure understanding of the topic and its solution methods. Choose a test for your grade and practise at your own pace.
Tests by topic
Tests for this topic
6 grade
Solving equations
The process of solving an equation typically involves several steps, including rearranging the equation, isolating or revealing the unknowns, performing operations on the equations, and determining the final value.
8 grade
Systems of linear equations
Dynamic tasks on solving and checking systems, determining the number of solutions and modelling word problems.
9 grade
Quadratic equations
Dynamic incomplete and complete quadratic equations, discriminants, root counts and word modelling.
9 grade
Systems with a quadratic equation
Dynamic line-parabola systems, intersections, substitution and contextual modelling.
10 grade
Rational equations
This test focuses on solving rational equations and determining permitted variable values. Students clear denominators, check possible solutions and apply rational equations to word problems and practical situations.
10 grade
Systems of equations
This test covers systems containing linear, quadratic and rational equations. Students use substitution or elimination, verify ordered pairs and interpret the meaning of a solution both algebraically and graphically.
11 grade
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.
11 grade
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.
11 grade
Irrational equations
This test develops methods for equations containing square and cube roots. Tasks require students to determine the domain, raise both sides to a power and check for extraneous solutions introduced during transformation.
11 grade
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.
11 grade
Logarithmic equations
This test focuses on solving several types of logarithmic equations. Tasks apply logarithm properties and the fundamental identity, establish domain restrictions and reject invalid solutions.
12 grade
Trigonometric identities and equations
This test applies fundamental trigonometric identities and methods for solving equations. Students write general solutions, use periodicity and select the values that belong to a specified angular interval.