Algebra and equations
Explore expressions, linear equations and rational-expression restrictions. Other algebra methods are still being prepared.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Find this activity in your course
Before you begin
Explore expressions, linear equations and rational-expression restrictions. Other algebra methods are still being prepared.
Learning goals
- Interpret algebraic notation and represented operations
- Evaluate an algebraic expression by substitution
- Represent a situation with algebraic expressions
- Simplify linear expressions by combining like terms
- Expand and factorise algebraic expressions
- Express and use the general term of a sequence
- Solve linear equations and check the solution
- Formulate, use and interpret a mathematical model
- Change the subject of a formula
- Multiply and divide algebraic fractions with domain restrictions
- Calculate and simplify algebraic fractions with restrictions
- Add and subtract algebraic fractions with domain restrictions
- Solve simultaneous equations by justified methods
- Interpret and draw graphs of functions
- Solve quadratic equations by suitable methods
- Solve inequalities and represent their solution sets
Syllabus statements covered
- using letters to represent numbers • interpreting notations: ab as a × b; a/b as a ÷ b or a × (1/b); a² as a × a, a³ as a × a × a, a²b as a × a × b, …; 3y as y + y + y or 3 × y; 3(x + y) as 3 × (x + y); (3 + y)/5 as (3 + y) ÷ 5 or (1/5) × (3 + y) • evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic expressions • recognising and representing patterns/relationships by finding an algebraic expression for the nth term • addition and subtraction of linear expressions • simplification of linear expressions such as −2(3x − 5) + 4x and 2x/3 − 3(x − 5)/2 • use brackets and extract common factors • factorisation of linear expressions ax + bx + kay + kby • expansion of the product of algebraic expressions • changing the subject of a formula • finding the value of an unknown quantity in a given formula • use of (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², a² − b² = (a + b)(a − b) • factorisation of quadratic expressions ax² + bx + c • multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10) • addition and subtraction of algebraic fractions with linear or quadratic denominator such as 1/(x − 2) + 2/(x − 3); 1/(x² − 9) + 2/(x − 3); 1/(x − 3) + 2/(x − 3)²
- solving linear equations in one variable • solving simple fractional equations that reduce to linear equations, such as x/3 + (x − 2)/4 = 3 and 3/(x − 2) = 6 • solving simultaneous linear equations in two variables by substitution and elimination or graphically • solving quadratic equations in one variable by factorisation, formula, completing the square for y = x² + px + q, or graphically • solving fractional equations that reduce to quadratics, such as 6/(x + 4) = x + 3 and 1/(x − 2) + 2/(x − 3) = 5 • formulating equations to solve problems • solving linear inequalities in one variable and representing the solution on the number line
- using letters to represent numbers
- interpreting notations: ab as a × b; a/b as a ÷ b or a × (1/b); a² as a × a, a³ as a × a × a, a²b as a × a × b, …; 3y as y + y + y or 3 × y; 3(x + y) as 3 × (x + y); (3 + y)/5 as (3 + y) ÷ 5 or (1/5) × (3 + y)
- evaluation of algebraic expressions and formulae
- translation of simple real-world situations into algebraic expressions
- recognising and representing patterns/relationships by finding an algebraic expression for the nth term
- addition and subtraction of linear expressions
- simplification of linear expressions such as −2(3x − 5) + 4x; 2x/3 − 3(x − 5)/2
- use brackets and extract common factors
- concept of equation
- solving linear equations in one variable
- solving simple fractional equations that can be reduced to linear equations such as x/3 + (x − 2)/4 = 3; 3/(x − 2) = 6
- formulating a linear equation in one variable to solve problems
- expansion of the product of algebraic expressions
- changing the subject of a formula
- finding the value of an unknown quantity in a given formula
- use of: • (a + b)² = a^2 + 2ab + b^2 • (a − b)² = a^2 − 2ab + b^2 • a^2 − b^2 = (a + b)(a − b)
- factorisation of linear expressions of the form ax + bx + kay + kby
- factorisation of quadratic expressions ax^2 + bx + c
- multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10)
- addition and subtraction of algebraic fractions with linear or quadratic denominator such as 1/(x − 2) + 2/(x − 3); 1/(x² − 9) + 2/(x − 3); 1/(x − 3) + 2/(x − 3)²
- concept of equation and inequality
- solving simple inequalities in the form ax + b ≤ c and ax + b < c and representing the solutions on the number line
- graphs of linear equations in two variables (ax + by = c)
- solving simultaneous linear equations in two variables by: • substitution and elimination methods • graphical method
- solving quadratic equations in one variable by factorisation
- formulating a pair of linear equations in two variables to solve problems
- solving quadratic equations in one variable by: • use of formula • completing the square for y = x^2 + px + q • graphical method
- solving fractional equations that can be reduced to quadratic equations such as 6/(x + 4) = x + 3; 1/(x − 2) + 2/(x − 3) = 5
- solving linear inequalities in one variable (including simultaneous inequalities) and representing the solution on the number line
- formulating a quadratic equation in one variable to solve problems
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Notation, evaluation and algebraic modelsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Interpret grouped algebraic notation and define a letter before substituting a value.
- Expressions and equivalenceG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Distinguish an expression from an equation and justify equivalent algebraic forms.
- Read a sequence ruleG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use the given position in a stated rule without confusing the term value with its index.
- Linear expressions with integer coefficientsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Distribute every sign through a bracket and combine only like terms.
- Linear expressions with fractional coefficientsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use common denominators to combine fractional linear coefficients without losing bracket signs.
- Linear equations with integer coefficientsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Apply the same reversible operation on both sides and check the answer in the original equation.
- Equations as balanced relationshipsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Preserve equality through each solution step and test a candidate solution in the original equation.
- Sequences and nth termsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Relate a position to its term and distinguish a matching rule from evidence of a unique pattern.
- Common factors and formula subjectsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Reverse distribution, change a formula's subject and find an unknown value from the given quantities.
- Products and simple quadratic factorsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Distribute two linear factors and reverse the product for monic quadratics.
- Identities and general quadratic factorsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Derive useful identities by distribution and verify every factorisation by expansion.
- Four-term common factorsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Group terms to expose a matching complete factor and verify it by expansion.
- Algebraic fraction products and domainsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Cancel factors rather than terms and preserve exclusions when multiplying or dividing algebraic fractions.
- Algebraic fraction sumsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Choose a common denominator, retain excluded values and simplify only complete factors.
- Formulae and restrictionsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Rearrange formulae and simplify rational expressions while retaining nonzero-denominator restrictions.
- Fractional linear equationsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Clear every denominator and check both the original domain and the solution.
- Simultaneous linear equationsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Construct two linear graphs, solve for their common pair and check graphical readings with algebra.
- Zero products and quadratic equationsG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Set a factored quadratic equal to zero and retain every factor alternative.
- Quadratic formula and modelsG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Identify coefficients, retain both possible roots and reject values only for a stated domain reason.
- Completing the square and fractional quadraticsG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Choose an exact quadratic method and distinguish solving from rewriting a function.
- Linear inequalitiesG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021 · Express Secondary 3–4 Mathematics 2022Reverse the order relation when multiplying or dividing by a negative number.
- Simultaneous linear inequalitiesG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Intersect conditions required together and retain the correct strict or inclusive endpoints.
No lessons match your search. Try a shorter phrase, or show all lessons.