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Algebra and equations

Build and connect the representations and methods in algebra and equations.

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  • 13 lessons
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Before you begin

Build and connect the representations and methods in algebra and equations.

Learning goals
  • Interpret algebraic notation and represented operations
  • Evaluate an algebraic expression by substitution
  • Represent a situation with algebraic expressions
  • Express and use the general term of a sequence
  • Simplify linear expressions by combining like terms
  • Solve linear equations and check the solution
  • Formulate, use and interpret a mathematical model
  • Expand and factorise algebraic expressions
  • Change the subject of a formula
  • Multiply and divide algebraic fractions with domain restrictions
  • Solve simultaneous equations by justified methods
  • Interpret and draw graphs of functions
  • Solve quadratic equations by suitable methods
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 number sequences, including nth term for simple cases such as n + 3, 2n + 1 • addition and subtraction of linear expressions • simplification of linear expressions such as −2(3x − 5) + 4x and 2x/3 − 3(x − 5)/2 • expansion of the product of two linear expressions • multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10) • changing the subject of a simple formula • finding the value of an unknown quantity in a given formula • factorisation of linear expressions ax + kay • factorisation of quadratic expressions x² + px + q. Exclude (a ± b)² = a² ± 2ab + b² and a² − b² = (a + b)(a − b), and addition/subtraction of algebraic fractions such as 1/x + 1/(x − 1).
  • 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 • graphs of linear equations in two variables ax + by = c • solving simultaneous linear equations in two variables by substitution and elimination or graphically • solving quadratic equations in one variable by formula • formulating a linear or quadratic equation in one variable or a pair of linear equations in two variables to solve problems
  • 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
  • recognising number sequences (including evaluating simple nth term like n + 3 and 2n + 1)
  • translation of simple real-world situations into algebraic expressions
  • addition and subtraction of linear expressions
  • simplification of linear expressions such as −2(3x − 5) + 4x; 2x/3 − 3(x − 5)/2
  • solving linear equations in one variable
  • formulating a linear equation in one variable to solve problems
  • recognising and representing number sequences (include finding an algebraic expression for the nth term for simple cases such as n + 3 and 2n + 1)
  • expansion of the product of two linear expressions
  • multiplication and division of simple algebraic fractions such as (3a/(4b²))(5ab/3); (3a/4) ÷ (9a²/10)
  • changing the subject of a simple formula
  • finding the value of an unknown quantity in a given formula
  • factorisation of linear expressions of the form ax + kay
  • factorisation of quadratic expressions of the form x² + px + q. Exclude: use of (a ± b)² = a² ± 2ab + b² and a² − b² = (a + b)(a − b); addition and subtraction of algebraic fractions such as 1/x + 1/(x − 1)
  • graphs of linear equations in two variables (ax + by = c )
  • solving simple fractional equations that can be reduced to linear equations such as x/3 + (x − 2)/4 = 3; 3/(x − 2) = 6
  • solving simultaneous linear equations in two variables by * substitution and elimination methods * graphical method
  • formulating a pair of linear equations in two variables to solve problems
  • solving quadratic equations in one variable by use of formula
  • formulating a quadratic equation in one variable to solve problems

Lessons

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  1. Notation, evaluation and algebraic modelsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Interpret grouped algebraic notation and define a letter before substituting a value.
  2. Read a sequence ruleG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Use the given position in a stated rule without confusing the term value with its index.
  3. Linear expressions with integer coefficientsG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Distribute every sign through a bracket and combine only like terms.
  4. Linear expressions with fractional coefficientsG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Use common denominators to combine fractional linear coefficients without losing bracket signs.
  5. Linear equations with integer coefficientsG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Apply the same reversible operation on both sides and check the answer in the original equation.
  6. Equations as balanced relationshipsG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Preserve equality through each solution step and test a candidate solution in the original equation.
  7. Sequences and nth termsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Relate a position to its term and distinguish a matching rule from evidence of a unique pattern.
  8. Common factors and formula subjectsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Reverse distribution, change a formula's subject and find an unknown value from the given quantities.
  9. Products and simple quadratic factorsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Distribute two linear factors and reverse the product for monic quadratics.
  10. Algebraic fraction products and domainsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Cancel factors rather than terms and preserve exclusions when multiplying or dividing algebraic fractions.
  11. Fractional linear equationsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Clear every denominator and check both the original domain and the solution.
  12. Simultaneous linear equationsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Construct two linear graphs, solve for their common pair and check graphical readings with algebra.
  13. Quadratic formula and modelsG1 Mathematics 2027 · Normal (Technical) Secondary 3–4 Mathematics 2022Identify coefficients, retain both possible roots and reject values only for a stated domain reason.

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