Topic

Mastery Objectives

Essential Knowledge

Autumn Term (1st half term)

Calculations, checking and rounding

· Estimate powers and roots of any given positive number

· Apply the product rule for counting

Indices, roots, reciprocals and hierarchy of operations

· Calculate with fractional and negative indices

· Know that a^-m = 1/a^m

· Know that a^m/n = ()^m

Factors, multiples, primes, standard form and surds

· Simplify surd expressions involving squares

· Know set notation

Algebra: the basics, setting up, rearranging and solving equations- including expanding two brackets containing surds

· Simplify and manipulate algebraic expressions (including those involving surds) by expanding products of two binomials and factorising expressions of the form ax² + bx + c

Sequences

· Find the nth term of quadratic sequences

· Recognise simple geometric progressions

Autumn Term (2^nd half term)

Averages and range

· Calculate averages from frequency tables and grouped frequency tables

Representing and interpreting data and scatter graphs

· Interpolate and extrapolate apparent trends

· Know that correlation does not indicate causation

· Know the dangers of interpolation and extrapolation

Fractions and percentages

· Change recurring decimals into their corresponding fractions

· Know the corresponding fraction for simple recurring decimals

Algebraic Fractions and solving linear equations arising from algebraic fractions

· Simplify and manipulate algebraic expressions involving algebraic fractions

Ratio and proportion

Spring Term (1st half term)

Multiplicative reasoning

· Set up and solve and interpret answers in growth and decay problems including compound interest

Polygons, angles and parallel lines

· Know the sum of interior angles of regular polygons

· Understand and use the angle properties of parallel lines and find missing angles using the properties of corresponding and alternate angles supplementary, giving reasons

· Know the formula to find the sum of interior angles in a polygon

· Know the exterior angles in a polygon sum to 360^o

· Know the angle properties of supplementary, corresponding and alternate angles

Pythagoras’ Theorem and trigonometry

· Apply Pythagoras theorem in general triangles

· Apply the trig ratios to find angles and lengths in right angled triangles, 2D only

· Know the convention for labelling the sides in a right-hand triangle

· Know the trig ratios

· Know the exact values of sinq and cosq, where q = 30, 45, 60, 90

· Know the exact values for tanq, where q = 0, 30, 45, 60

Graphs: the basics and real-life graphs

· Draw distance time graphs and velocity time graphs

Spring Term (2^nd half term)

Linear graphs and coordinate geometry

· Use the form y = mx + c to identify perpendicular lines

· Know that the gradient is calculate using y2 – y1/x2 – x1

· Know the conditions for perpendicular lines

Quadratic, cubic and other graphs

· Identify roots, intercepts, turning points of quadratic functions graphically

Solving quadratic equations and simultaneous equations

· Solve quadratic equations (including those requiring rearrangement) algebraically by factorising, by completing the square and using the quadratic formula

· Solve two linear simultaneous equations or where one is quadratic, in two variables algebraically

· Know the special case of difference of two squares

· Know the quadratic formula

Solving quadratic equations arising from algebraic fractions

Summer Term (1st half term)

Inequalities- including quadratic inequalities

· Solve linear inequalities in two variables

· Solve quadratic inequalities in one variable

· Represent the solution set to inequality on a graph

Know the conventions for representing inequalities graphically

Probability

· Calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and venn diagrams

· Know p(A or B) = p(A) + p(B)

· Know p(A and B) = p(A) x p(B)

Transformations

· Identify describe and construct similar shapes, including on coordinate axes, by considering enlargement (incl. negative scale factor)

· Describe changes and invariance achieved by rotations, reflections and translations

Know the information required to describe a transformation

Summer Term (2^nd half term)

Similarity and congruence in 2D and 3D

Apply concepts of congruence and similarity, including the relationships between length, area and volumes in similar figures

Constructions, loci and bearings

· Find and describe regions satisfying a combination of loci

· Use the standard ruler and compass constructions:

· bisect a given angle;

· construct a perpendicular to a given line from/at a given point;

· construct angles of 90°, 45°;

perpendicular bisector of a line segment