Year 10 Curriculum  Maths
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 ax^{2} + 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 righthand 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 reallife 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 
· 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 twoway 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 
