# Year 10 ALC & WPC

 Week Chapter Content Code Chapter Summary Contents 1 Ratio and proportion N11, R2, R3, R4, R5, R6, R7, R8, R9, R12 • Express proportions of amounts as fractions or percentages. • Divide a quantity in a given ratio. • Use scale factors to convert between lengths on maps and scale diagrams and the distances they represent. • Calculate percentage increase and decreases using multipliers. • Find the original amount of a quantity that has undergone a percentage increase or decrease. 2 3 4 Factors, powers and roots N4, N5, N6, N7, N8, P6 • Know and use the language of prime numbers, factors and multiples. • Write a number as a product of prime factors. • Find the HCF and LCM of a pair of integers. • Find the square or cube root of an integer. • FInd the square and cube roots of numbers and apply the laws of indices. • Simplify expressions involving surds including rationalising fractions. 5 6 Assessment Answers 7 Graphs 1 A5, A8, A9, A10, A11, A12, A14, A18, R6, R8, R14 • Find and interpret the gradient and y-intercept of a line and relate these to the equation of the line in the form y = mx + c. • Identify parallel and perpendicular lines using their equations. • Draw line graphs and quadratic curves. • Identify roots, intercepts and turning points of quadratic curves using graphical and algebraic methods. • Use graphs to solve problems involving distance, speed and acceleration. 8 9 10 11 12 Working in 3D A5, G1, G12, G13, G14, G16, G17, G19, R11, R12 • Draw and interpret plans and elevations of 3D shapes. • Calculate the volume of cuboids and right prisms. • Calculate the surface area and volumes of spheres, pyramids, cones and composite shapes. • Know and apply the relationship between lengths, areas and volumes of similar shapes. 13 14 15 Assessment 16 Handling data 2 A17, S2, S3, S4, S5, S6. • Calculate summary statistics from a grouped frequency table. • Construct and interpret cumulative frequency curves and box plots. • Plot scatter graphs and recognise correlation. • Use tables and line graphs to represent time series data. 17 18 19 Calculations 2 A4, A19, N2, N6, N7, N8, N9 • Perform calculations involving roots and indices, including negative and fractional indices. • Perform exact calculations involving fractions, surds and pi. • Work with numbers in standard form. 20 21 Assessment Answers 22 Graphs 2 A12, A13, A14, A15, A16, G9, R14 • Recognise and draw graphs of cubic and reciprocal functions. • Recognise and draw graphs of exponential functions. • Recognise and sketch graphs of trigonometric functions. • Recognise and sketch translations and reflections of graphs. • Draw and interpret graphs of non-standard functions and use them in real-life problems. • Approximate the gradient of a curve at a given point and the area under a graph. Interpret these values in real-life problems including kinematic graphs. • Recognise and use simple equations of circles and find the tangent to a circle at a point. 23 24 25 26 Pythagoras, trigonometry and vectors G1, G4, G6, G9, G11, G19, G20, G21, G22, G23, G25, N8, R12 • Use Pythagoras’ theorem to find a missing side in a right angled triangle. • Use Pythagoras’ theorem to find the distance between points on a coordinate grid. • Use trigonometric ratios to find missing lengths and angles in triangles. • Find exact values for sin theta and cos theta for key angles. • Use the sine and cosine rules to find missing lengths and angles. • Use the sine formula for the area of a triangle • Calculate with vectors and use them in geometric proofs. 27 28 29 30 Assessment 31 Probability of combined events N5, P1, P2, P4, P6, P7, P8, P9 • Use Venn diagrams to represent sets. • Use a possibility space to represent the outcomes of two experiments and to calculate probabilities. • Use a tree diagram to show outcomes of two experiments. • Calculate conditional probabilities. 32 33 34 Revision for mock examination 35 36