KS4 Course Outline: Mathematics

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1 Topic Index: Higher tier (6+), Autumn Term Year 10 Grade Topic EFG B A-A* Factorise an expression eg. 6a+8 = 2(3a+4); a 2-3a = a(a - 3) 104 Factorise an expression with 2 or more factors eg. 4x 3 + 6xy = 2x(2x 2 +3y) 104 Write expressions using algebra, and solve problems 106 Expand and simplify the product of two brackets using FOIL eg. (2x -1)(x+4) 103b B Factorise a quadratic expression into two brackets eg x 2 + 2x - 3; difference of two squares 140a;141 use alternate and corresponding angles to give reasons for sizes of angles between parallel lines and a transversal 67 understand angle properties in quadrilaterals giving reasons for answers 36 understand proofs that the sum of angles in a triangle is 180 0, and that the exterior angle of a triangle is equal to the sum 68,69 of the two interior opposite angles understand that the sum of exterior angles of a regular polygon is and that the each pair of exterior and interior 70 angles lie on a straight line. B understand large and small numbers written using standard form 135 A convert a recurring decimal into a fraction 155 Use a decimal calculation to answer related questions. Eg. If 6.2 x 3.1 = 19.22, work out / Use non-calculator (written) methods for adding, subtracting, multiplying and dividing whole numbers and/or decimals Revise non-calculator and calculator techniques with percentages Use percentage multipliers to find percentage changes understand simple interest KS4 ourse Outline: Mathematics A use a percentage multiplier raised to a power for compound percentage changes 137 B recognise and calculate reverse percentage change problems 138 onstruct stem and leaf tables (& a scale); interpret these, and calculating the median 89 calculate the mean from a frequency table and identify the median or mode) 133a calculate an estimate of the mean from a grouped frequency table, using midpoints; identify the modal group 133b B complete a cumulative frequency table, draw a cumulative frequency graph and use this to estimate the median and the interquartile range 151 B raw and interpret a box plot 152 B Use statistics, such as two box plots to compare two sets of data 152

2 Topic Index: Higher Tier (6+), Spring Term Year 10 Grade Topic EFG B A-A* Perform and describe rotations and reflections 74,75 translate a shape using a column vector 77,,A Perform and describe enlargements using integer (), fractional () and negative scale factors (A) B Perform combinations of transformations, and describe a single transformation Understand congruence, particularly when rotating, reflecting and translating shapes B Understand where shapes are mathematically 'similar' and calculate unknown lengths in such shapes 149 E round numbers to a given number of significant figures 20 estimate the answer to a calculation by rounding the numbers to 1sf 101, A find the upper and lower bounds for a number (); use these in calculations (A) E/ revise methods for calculating area and perimeter of 2 shapes including triangle, parallelogram and rhombus; extend to compound shapes () 33a-d 73 / revise area and circumference of circles; extend to compound shapes () revise the laws for indices eg a 3 x a 4 = a 7 ; (c 2 ) 3 = c 6 ; y 0 = 1; 111 B/A extend knowledge of indices to negative powers (B) and fractional powers (A) 156 B revise standard form 135 raw graphs of linear functions using a table of values. Eg y = 3x /B raw graphs of quadratic and cubic (B) functions using a table of values: eg y = x 3-2x B Use graphs of quadratic or cubic functions to estimate solutions to equations, or coordinates of maximum and minimum points 145 Understand experimental probability and relative frequency 132 Know when to add or multiply two probabilities: if A and B are mutually exclusive, then the probability of A or B occurring is P(A) + P(B), whereas if A and B are independent events, the probability of A and B occurring is P(A) P(B) B Use tree diagrams to calculate probabilities of combinations of independent events find the nth term of a linear sequence E,, KS4 ourse Outline: Mathematics solve a wide variety of linear equations, including fractions, brackets, negative numbers and with the unknown on both sides (grades depend on complexity) and inequalities Form and solve linear equations in a variety of contexts: eg. The perimeter of a shape with lengths given algebraically , 108-9

3 KS4 ourse Outline: Mathematics Topic Index: Higher Tier (6+) Summer Term Year 10 Grade Topic EFG B A-A* alculate the volume of a prism, such as a cuboid, triangular prism or cylinder. 122 alculate the surface area of the shapes above, given appropriate measurements 121 A Extend knowledge of volume and surface area to spheres and cones 177 Understand conversions between different units of area eg m 2 into cm 2 ; similarly for units of volume 124? B understand where two shapes are 'similar', and relate this to topics such as 'enlargement' understand the general form of the graph of a straight line (y=mx + c), knowing that m stands for 'gradient' and c stands for the 'y-intercept'. 143 B Identify the gradients/equations of parallel and perpendicular lines 166 B Solve a pair of simultaneous equations using a graphical method 115 / Use a formula connecting distance, speed, time; read info. from distance-time graphs ( grade involves calculating speeds). 117, Read information from a variety of 'real-life' graphs 126 B Solve a pair of simultaneous equations using an algebraic method 142 Use trial and improvement to solve a quadratic or a cubic equation 110 / Add, subtract, multiply and divide fractions with or without a calculator ( grade questions generally involve mixed numbers eg 3⅕ + 4⅜) 56, E/ Understand 'best value' and solve best value problems in a variety of contexts 64 Understand and apply Pythagoras' Theorem when calculating unknown lengths in right angled triangles in 2; solve 118, problems where a right angled triangle needs to be identified. 119 Understand coordinates in three dimensions 120 A Extend Pythagoras' Theorem to work in Identify solids from drawings of their plans and elevations, and use a given solid to draw a plan view and front and side 81 elevations

4 KS4 ourse Outline: Mathematics Year 11 Topic Index: GSE (6+), Autumn Term Grade Topic EFG B A-A*, Revise angle facts, including parallel lines, and interior and exterior angles B Learn and apply angle facts in circles and tangents to circles 150 understand that some fractions can be represented by terminating decimals whereas others result in recurring decimals 58 A hange recurring decimals into fractions 155 find the prime factor decomposition of a number; find the HF and LM for a pair of numbers; solve problems involving 95, HF/LM 96 A calculate quantities that are directly proportional to one another, or which vary in indirect proportion 159 draw a scattergraph, a line of best fit if appropriate and comment on the type of correlation. Use the line of best fit to predict other pairs of values 87 riticise questions used in questionnaires, and write suitable corrections 134 -B revise statistical measures and diagrams, such as those met in Autumn term of Year revise area and circumference of circles 71, 72 A calculate the length of an arc and the area of a sector 178 B use trigonometry to calculate unknown lengths or angles in right angled triangles using SOHAHTOA 147 Revise a range of topics at your teacher's discretion, including a selection of A and A* topics relevant to the mock exams

5 KS4 ourse Outline: Mathematics Year 10/11 Topic Index: GSE borderline Grade just maths Topic EFG B A-A* 1 Two way tables 85 2 Scatter graphs 87 3 Stem and leaf 89 4 Product of prime factors, HF, LM 95,96 5 Trial and improvement Questionnaires Averages from a table Averages from grouped data 133 B 9 umulative Frequency 151 B 10 Box Plots 152 B 11 umulative Frequency and Box Plots Frequency Polygons 88 A 13 Histograms :Pythagoras 118 B 15 Trigonometry - calculating sides in right angled triangles 147 B 16 Trigonometry - calculating angles in right angled triangles 147 B 17 Pythagoras with trigonometry Straight line graphs 113 /B 19 Quadratic/ubic graphs Enlargements Reflections Rotations Reflections and rotations 74/75 24 Translations 77 / 25 Ratio - sharing Proportion, recipes Percentage of an amount Probability from a table 90,91 B 29 Probability tree diagrams Plans and elevations 81

6 31 ircles - area and circumference Surface area and volume of prisms Use of a calculator Exchange rates 64 / 35 Estimation 101 /B/A 36 Index laws /B 37 Inequalities alternate and corresponding angles expand and simplify Sequences and nth term 112