| 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 ∝ x²
- 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
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