- Calculating:
- Calculate with roots, and with integer indices
- Calculate with standard form a × 10n, where 1 ≤ a < 10 and n is an integer
- Use inequality notation to specify simple error intervals due to truncation or rounding
- Apply and interpret limits of accuracy
- Visualising and Constructing:
- Use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle)
- Use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line
- Construct plans and elevations of 3d shapes
- Algebraic Proficiency
- Understand and use the concepts and vocabulary of identities
- Know the difference between an equation and an identity
- Simplify and manipulate algebraic expressions by expanding products of two binomials and factorising quadratic expressions of the form x² + bx + c
- Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments
- Translate simple situations or procedures into algebraic expressions or formulae
- Proportional Reasoning:
- Solve problems involving direct and inverse proportion including graphical and algebraic representations
- Apply the concepts of congruence and similarity, including the relationships between lengths in similar figures
- Change freely between compound units (e.g. Density, pressure) in numerical and algebraic contexts
- Use compound units such as density and pressure
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- Sequences:
- Recognise and use Fibonacci type sequences, quadratic sequences
- Solving Equations and Inequalities I:
- Understand and use the concepts and vocabulary of inequalities
- Solve linear inequalities in one variable
- Represent the solution set to an inequality on a number line
- Calculating Space:
- Identify and apply circle definitions and properties, including: tangent, arc, sector and segment
- Calculate arc lengths, angles and areas of sectors of circles
- Calculate surface area of right prisms (including cylinders)
- Calculate exactly with multiples of π
- Know the formulae for: pythagoras’ theorem, a² + b² = c², and apply it to find lengths in right-angled triangles in two dimensional figures
- Geometry; Angles:
- Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
- Deduce expressions to calculate the nth term of linear sequences
- Investigating Angles:
- Understand and use alternate and corresponding angles on parallel lines
- Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs
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- Algebraic Proficiency, Visualising:
- Identify and interpret gradients and intercepts of linear functions algebraically
- Use the form y = mx + c to identify parallel lines
- Find the equation of the line through two given points, or through one point with a given gradient
- Interpret the gradient of a straight line graph as a rate of change
- Recognise, sketch and interpret graphs of quadratic functions
- Recognise, sketch and interpret graphs of simple cubic functions and the reciprocal function y = 1/x with x ≠ 0
- Plot and interpret graphs (including reciprocal graphs) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration
- Solving Equations and Inequalities II:
- Solve, in simple cases, two linear simultaneous equations in two variables algebraically
- Derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution
- Find approximate solutions to simultaneous equations using a graph
- Probability:
- Calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
- Enumerate sets and combinations of sets systematically, using tree diagrams
- Understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
- Presentation of Data:
- Interpret and construct tables, charts and diagrams, including tables and line graphs for time series data and know their appropriate use
- Draw estimated lines of best fit; make predictions
- Know correlation does not indicate causation; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing
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