About this topic
Before you begin
Simplify expressions, interpret sequences and rearrange formulae, then solve linear, simultaneous and quadratic equations with domain checks.
Learning goals
- Evaluate an algebraic expression by substitution
- Represent a situation with algebraic expressions
- Interpret algebraic notation and represented operations
- Express and use the general term of a sequence
- Simplify linear expressions by combining like terms
- Formulate, use and interpret a mathematical model
- Solve linear equations and check the solution
- Expand and factorise algebraic expressions
- Change the subject of a formula
- Multiply and divide algebraic fractions with domain restrictions
- Solve a first-degree equation by a specified expansion or denominator-clearing step, preserving original exclusions
- Solve a system of linear equations completely, including systems with no or infinitely many solutions
- Solve simultaneous equations by justified methods
- Interpret and draw graphs of functions
- Apply the quadratic formula with signed coefficients, both branches and the complete real solution set
- 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
Choose a lesson
Work through them in order.
- Not startedNotation, evaluation and algebraic modelsNextInterpret grouped algebraic notation and define a letter before substituting a value.
- Not startedRead a sequence ruleNextUse the given position in a stated rule without confusing the term value with its index.
- Not startedLinear expressions with integer coefficientsNextDistribute every sign through a bracket and combine only like terms.
- Not startedLinear expressions with fractional coefficientsNextUse common denominators to combine fractional linear coefficients without losing bracket signs.
- Not startedLinear equations with integer coefficientsNextApply the same reversible operation on both sides and check the answer in the original equation.
- Not startedEquations as balanced relationshipsNextPreserve equality through each solution step and test a candidate solution in the original equation.
- Not startedSequences and nth termsNextRelate a position to its term and distinguish a matching rule from evidence of a unique pattern.
- Not startedCommon factors and formula subjectsNextReverse distribution, change a formula's subject and find an unknown value from the given quantities.
- Not startedProducts and simple quadratic factorsNextDistribute two linear factors and reverse the product for monic quadratics.
- Not startedAlgebraic fraction products and domainsNextCancel factors rather than terms and preserve exclusions when multiplying or dividing algebraic fractions.
- Not startedFractional linear equationsNextClear every denominator and check both the original domain and the solution.
- Not startedSimultaneous linear equationsNextConstruct two linear graphs, solve for their common pair and check graphical readings with algebra.
- Not startedQuadratic formula and modelsNextIdentify coefficients, retain both possible roots and reject values only for a stated domain reason.
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