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Grade Ladder – Algebra
9
  • Solve quadratic equations arising from algebraic fractions
  • Know how to use a composite function
  • Estimate area under a quadratic graph by dividing it into trapezia
  • Estimate the gradient of a quadratic or non-linear graph at a given point by sketching the tangent
  • Find the equation of a tangent to a circle at a given point
  • Interpret coordinates for trigonometric graphs
  • Plot graphs of the exponential function y = 〖ab〗^x
  • Use iteration with simple converging sequences
8
  • Find the inverse of a linear function
  • Plot graphs of exponential functions
  • Recognise, sketch and interpret graphs of trigonometric functions
  • Know how to transform graphs
  • Find the gradient of the radius that meets the circle at a given point
  • Find the nth term of a quadratic sequence
  • Solve linear/x²+y²=r² simultaneous equations
7
  • Solve quadratic equations by using the quadratic formula
  • Expand two or more brackets
  • Factorise harder quadratics, including difference of two squares
  • Use function notation
  • Deduce turning points by completing the square
  • Sketch a graph of a quadratic
  • Find the equation of the line through two given points
  • Find the equation of the line through one point with a given gradient
  • Find the gradient of perpendicular lines
  • Give equations of lines parallel and perpendicular to the given line
  • Solve quadratic inequalities
  • Manipulate algebraic expressions with surds and algebraic fractions
  • Solve linear/quadratic simultaneous equations
  • Solve linear/non-linear simultaneous equations graphically
  • Set up equations to solve direct or inverse proportion problems
6
  • Solve linear equations with fractional coefficients
  • Solve quadratics by completing the square
  • Expand double brackets (ax ± b)(cx ± d)
  • Change the subject of a more complex formula (square roots and fractions)
  • Identify and interpret gradient from an equation in the form ax+b=c
  • Recognise, sketch and interpret cubic and reciprocal graphs
  • Find the midpoint of a line using a formula
  • Solve linear inequalities graphically
  • Solve two simultaneous inequalities algebraically
  • Answer simple proof and ‘show that’ questions
  • Continue a quadratic sequence and use the nth term to generate terms
  • Continue geometric progression and find term to term rule, including negative, fraction and decimal terms
  • Simplify expressions involving brackets and powers
  • Use expressions of the form y ∝
  • Identify direct proportion from a table of values
5
  • Solve quadratic equations by factorising
  • Change the subject of a formula (including subject on both sides)
  • Find the equation of a straight-line from its graph
  • Interpret distance-time graphs and calculate speed
  • Interpret gradient as rate of change
  • Identify and interpret roots, intercepts and turning points of a quadratic graph
  • Given the coordinates of points A and B, calculate the length of AB
  • Plot and draw graphs of straight lines without using a table of values
  • Solve more complex linear inequalities
  • Use algebra to support and construct arguments
  • Recognise and use simple geometric progressions
  • Use function machines to find terms of sequence
  • Solve linear simultaneous equations algebraically and graphically
  • Write a ratio as a linear function
4
  • Solve more complex equations (including negatives and division)
  • Use systematic trial and improvement
  • Form and solve an equation
  • Expand double brackets
  • Understand the meaning of an identity and use the sign
  • Find an unknown that is not the subject of the formula
  • Rearrange simple equations
  • Find the gradient of a line
  • Identify parallel lines from their equations
  • Plot the graphs of linear functions in the form y=mx+c
  • Plot and recognise quadratics
  • Solve simple linear inequalities
  • Find and use the nth term of an arithmetic sequence
  • Simplify simple expressions involving index notation
  • Understand and use compound measures (density, speed, pressure)
  • Solve problems involving variables in direct and inverse proportion
3
  • Solve equations with ‘x’s on both sides
  • Solve equations involving brackets
  • Expand and simplify a single bracket
  • Substitute positive integers into expressions involving small powers
  • Identify an Identity
  • Factorise linear expressions
  • Change the subject of a formula in one step
  • Know what is meant by the gradient of a straight line
  • Draw velocity-time graphs
  • Find the coordinates of the midpoint of a line from a given graph
  • Recognise that equations of the form y=mx+c lead to straight line graphs
  • Write down whole number values that satisfy an inequality
  • Use algebra to describe the nth term in an arithmetic sequence.
  • Understand the use of small, positive powers in algebra
2
  • Solve two-step equations
  • Construct equations from real life situations
  • Substitute into more complex formulae (involving brackets and more than one operation)
  • Substitute positive and negative integers into simple formulae
  • Select an expression/ equation/ formula from a list
  • Generate coordinates from functions
  • Use graphs to solve distance-time problems.
  • Interpret information from a complex real life graph
  • Find the coordinates required to complete a shape
  • Plot and draw graphs of straight lines using a table of values
  • Draw the next term in a pattern sequence
  • Recognise cube numbers and Fibonacci-type sequences
  • Know how to find the nth term for linear sequences
1
  • Substitute integers into equations and formulae
  • Construct expressions from worded descriptions
  • Multiply a single positive term over a bracket
  • Create expressions from worded examples
  • Complete a number machine
  • Plot a simple distance-time graph
  • Read coordinates in all four quadrants
  • Draw graphs of y=a, x=a, y=x and y=-x
  • Show inequalities on a number line
  • Generate terms in a sequence given term-to-term rule or position-to-term rule
  • Use arithmetic operations with algebra
  • Multiply together two simple algebraic expressions
W3
  • Substitute into simple formulae
  • Use function machines
  • Simplify by collecting like terms
  • Find inputs and outputs of functions
  • Interpret line graphs
  • Read values from straight-line graphs
  • Draw, label and scale axes
  • Use inequality notation >, <, ≥, and ≤
  • Generate terms of a simple sequence
  • Know square and triangle numbers
W2
  • Find outputs of simple functions
  • Read coordinates in the first quadrant