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Year 10 Mathematics
Linear equations and inequalities
Chapter 8
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RESTS ON
Solve a one-step linear equation
CH 2
Factor numerators and denominators, cancel common factors rather than terms, retain the original excluded values, and present the remaining numerator and denominator in a consistent form
CH 10
Decimal place value
CH 1
Identify the intercept and slope in y = a + bx, including its edge shapes
CH 6
Unitary method
CH 2
Convert between units
CH 1
Linear equations and expressions
Equations with brackets and fractions
Formula substitution and rearrangement
Linear inequalities
Intersections of linear graphs
Simultaneous equations by substitution
Simultaneous equations by elimination
Solve two-step linear equations by inverse operations in reverse order
Recognise whether an equation is linear from the power on its unknowns
Translate a described situation into a linear equation in one unknown
Turn an equation's exact solution into the answer the situation demands
Check a claimed solution or point by substituting into the original equation
Signed numbers
Multiplication and division
Solve an equation containing algebraic fractions by clearing the lowest common denominator
Multiply, divide, add or subtract algebraic fractions by using reciprocals where required, constructing the lowest common denominator and simplifying the exact result without losing restrictions
Solve equations with a scaled bracket by expanding or dividing first
Solve equations with unknowns on both sides by collecting them onto one side
Solve equations with the unknown inside a fraction by clearing the denominator first
Multiply and divide fractions
Substitute all given values into a formula and solve the resulting linear (or simple squared/root) equation for the one remaining unknown, isolating it by inverse operations in reverse order
Make a nominated variable the subject of a formula by applying equivalent inverse operations to the whole of both sides, including undoing a squared or square-root term correctly; recognise that a square root does not distribute over a sum
Substitute known values into a formula and evaluate it correctly
Isolate a nominated subject in a linear literal equation by applying equivalent operations to the whole of both sides and simplifying only valid common factors
Rounding
Translate between a one-variable linear inequality and its number-line representation: read the boundary value, open/closed endpoint and ray direction from a drawn number line, and draw/match the line for a solved inequality
Solve a one-variable linear inequation, reversing the order relation exactly when multiplication or division by a negative value occurs
State whether the boundary is included and identify which side of a one- or two-variable linear boundary satisfies the inequation, using an exact test point where useful
Read the point of intersection of two graphed lines
Recognise from equal slopes that a system has no solution or every point
Solve a pair of simultaneous linear equations for the shared (x, y)
Read coordinates off a graphed line respecting its axis scales
Solve a pair of simultaneous linear equations by the named substitution method: identify or make a subject, substitute that expression into the other equation with brackets, solve the resulting single-variable equation, back-substitute for the second variable, and check in the unused equation
Choose the efficient algebraic or graphical method for a pair of simultaneous equations (substitution when one variable is the subject, elimination when matching/opposite coefficients exist, graphing for a described visual comparison) from the equations' structure
Solve a practical simultaneous pair and answer the question asked
Translate a two-condition description into a pair of equations in two unknowns
Build and read a total formula from two unit rates
Solve a pair of simultaneous linear equations by the named elimination method: decide add or subtract, multiply equation(s) to form a matching coefficient pair, combine to eliminate one variable, solve, back-substitute, and check