Year 10 Curriculum - Maths
Topic |
Mastery Objectives |
Essential Knowledge |
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Autumn Term (1st half term) |
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Calculations, checking and rounding |
· Estimate powers and roots of any given positive number · Apply the product rule for counting |
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Indices, roots, reciprocals and hierarchy of operations |
· Calculate with fractional and negative indices |
· Know that a-m = 1/am · Know that am/n = ( |
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Factors, multiples, primes, standard form and surds |
· Simplify surd expressions involving squares |
· Know set notation |
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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 |
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Sequences |
· Find the nth term of quadratic sequences |
· Recognise simple geometric progressions |
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Autumn Term (2nd half term) |
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Averages and range |
· Calculate averages from frequency tables and grouped frequency tables |
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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 |
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Fractions and percentages |
· Change recurring decimals into their corresponding fractions |
· Know the corresponding fraction for simple recurring decimals |
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Algebraic Fractions and solving linear equations arising from algebraic fractions |
· Simplify and manipulate algebraic expressions involving algebraic fractions |
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Ratio and proportion |
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Spring Term (1st half term) |
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Multiplicative reasoning |
· Set up and solve and interpret answers in growth and decay problems including compound interest |
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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 360o · Know the angle properties of supplementary, corresponding and alternate angles |
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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 |
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Graphs: the basics and real-life graphs |
· Draw distance time graphs and velocity time graphs |
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Spring Term (2nd half term) |
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Linear graphs and coordinate geometry |
· Use the form y = mx + c to identify perpendicular lines
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· Know that the gradient is calculate using y2 – y1/x2 – x1 · Know the conditions for perpendicular lines |
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Quadratic, cubic and other graphs |
· Identify roots, intercepts, turning points of quadratic functions graphically |
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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 |
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Solving quadratic equations arising from algebraic fractions |
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Summer Term (1st half term) |
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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 |
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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) |
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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 |
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Summer Term (2nd half term) |
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Similarity and congruence in 2D and 3D |
Apply concepts of congruence and similarity, including the relationships between length, area and volumes in similar figures |
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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 |
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