KS4 Course Outline: Mathematics

Transcription

1 6+ Topic Index Sheet, Autumn Term Year 10 D Factorise an expression eg. 6a+8 = 2(3a+4); a 2-3a = a(a - 3) 104 C Factorise an expression with 2 or more factors eg. 4x 3 + 6xy = 2x(2x 2 +3y) 104 D Write expressions using algebra, and solve problems 106 C 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 D use alternate and corresponding angles to give reasons for sizes of angles between parallel lines and a transversal 67 D understand angle properties in quadrilaterals giving reasons for answers 36 D 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 of the two interior opposite angles 68,69 C understand that the sum of exterior angles of a regular polygon is and that the each pair of exterior and interior angles lie on a straight line. 70 B understand large and small numbers written using standard form 135 C find the prime factor decomposition of a number; find the HCF and LCM for a pair of numbers; solve problems involving HCF/LCM 95, 96 Understand and be able to use Venn Diagrams D Use non-calculator (written) methods for adding, subtracting, multiplying and dividing whole numbers and/or decimals D Revise non-calculator and calculator techniques with percentages C Use percentage multipliers to find percentage changes D understand simple interest A use a percentage multiplier raised to a power for compound percentage changes 137 B recognise and calculate reverse percentage change problems 138 understand simplie index numbers and chain base index numbers Draw and interpret population pyramids for continuous data Draw and interpret Choropleth maps Draw and interpret multiple/composite bar charts and vertical line graphs C Draw and interpret frequency polygons, bar charts D Construct stem and leaf tables (& a scale); interpret these, and calculating the median 89 D 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 Draw a line of best fit by eye and passing through the point representing the mean of each variable; use this to predict other results D calculate the mean from a frequency table and identify the median or mode) 133a C grouped frequency tables: calculate an estimate of the mean, using midpoints; identify the modal group and estimates of the median 133b Understand relative merits of each of the three measures of central tendency

2 Topic Index: Higher Tier (6+), Spring Term Year 10 D Perform and describe rotations and reflections 74,75 C translate a shape using a column vector 77 D,C,A Perform and describe enlargements using integer (D), fractional (C) and negative scale factors (A) B Perform combinations of transformations, and describe a single transformation D 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 D estimate the answer to a calculation by rounding the numbers to 1sf 101 C, A find the upper and lower bounds for a number (C); use these in calculations (A) E/D revise methods for calculating area and perimeter of 2D shapes including triangle, parallelogram and rhombus; extend to compound shapes (D) 33a-d 73 D/C revise area and circumference of circles; extend to compound shapes (C) C 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 D Draw graphs of linear functions using a table of values. Eg y = 3x C/B Draw 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 C find the nth term of a linear sequence E,D,C 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 C Form and solve linear equations in a variety of contexts: eg. The perimeter of a shape with lengths given algebraically 106 B complete a cumulative frequency table, draw a cumulative frequency graph and use this to estimate the median and the interquartile range 151 B Draw and interpret a box plot 152 Find median, IQR from ungrouped data B Use statistics, such as two box plots to compare two sets of data 152 Identify positive and negative skews from a box plot Identify outliers, calculate deciles, percentiles and interdecile/interpercentile range Draw and compare step polygons 105, 108-9

3 Topic Index: Higher Tier (6+) Summer Term Year 10 C Calculate the volume of a prism, such as a cuboid, triangular prism or cylinder. 122 C Calculate the surface area of the shapes above, given appropriate measurements 121 A Extend knowledge of volume and surface area to spheres and cones 177 C 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' C 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 Plot points as time series and draw a trend line by eye calculate and use appropriate moving averages; plot moving averages, identify and discuss seasonal variation by visual inspection. Extension: establish a trend line from moving averages and calculate its equation Extension: Find the equation of a 'line of best fit' from a scattergraph in the form y=ax+b and interpret a and b C Use trial and improvement to solve a quadratic or a cubic equation 110 D/C Add, subtract, multiply and divide fractions with or without a calculator (C grade questions generally involve mixed numbers eg 3⅕ + 4⅜) 56, E/D Understand 'best value' and solve best value problems in a variety of contexts 64 C Understand and apply Pythagoras' Theorem when calculating unknown lengths in right angled triangles in 2D; solve problems where a right angled triangle needs to be identified. C Understand coordinates in three dimensions 120 A Extend Pythagoras' Theorem to work in 3D. 174 D Identify solids from drawings of their plans and elevations, and use a given solid to draw a plan view and front and side elevations 81 A Draw a histogram; understand the difference between a histogram and a bar chart C Criticise questions used in questionnaires, and write suitable corrections 134 Understand the terms quantitative, qualitative, discrete, continuous, primary, secondary when describing data A Understand the terms: population, census, sample, random sample generate random samples; select a stratified sample; understand bias and need to minimise this understand and use systematic,quota, cluster and convenience sampling Understand relative merits of various sampling methods; understand use of a control group mock-controlled assessment, post Year 10 exam. 118, 119

4 Year 11 Topic Index: GCSE (6+), Autumn Term D,C Revise angle facts, including parallel lines, and interior and exterior angles B Learn and apply angle facts in circles and tangents to circles 150 D Understand the sum of probabilities for mutually exclusive events is 1; Know that if the probability of an event occurring is p, the corresponding probability of it not occuring is 1-p; be able to find a missing probability from a table C Understand experimental probability and relative frequency 132 C C Find probabilities by considering relative frequency in experimental data including 2-way tables Produce and understand how to use a sample space diagram 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). 90, B Use tree diagrams to calculate probabilities of combinations of independent events; use tree diagrams with or without replacement D/C Use a formula connecting distance, speed, time; read info. from distance-time graphs (C grade involves calculating speeds). Read information from a variety of 'real-life' graphs B Solve a pair of simultaneous equations using an algebraic method 142 D understand that some fractions can be represented by terminating decimals whereas others result in recurring decimals 58 A Change recurring decimals into fractions 155 A calculate quantities that are directly proportional to one another, or which vary in indirect proportion 159 D-B revise statistical measures and diagrams, such as those met in Autumn term of Year D 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 SOHCAHTOA 147 MOCK EXAM Revise a range of topics at your teacher's discretion, including a selection of A and A* topics relevant to the mock exams Following mock exam; statistics controlled assessment 117, 126

5 Grade just maths Year 10/11 Topic Index: GCSE CD borderline Topic EFG D C B A-A* D 1 Two way tables 85 D 2 Scatter graphs 87 D 3 Stem and leaf 89 C 4 Product of prime factors, HCF, LCM 95,96 C 5 Trial and improvement 110 D 6 Questionnaires D 7 Averages from a table 133 C 8 Averages from grouped data 133 B 9 Cumulative Frequency 151 B 10 Box Plots 152 B 11 Cumulative Frequency and Box Plots C 12 Frequency Polygons 88 A 13 Histograms 181 C 14 :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 C 18 Straight line graphs 113 C/B 19 Quadratic/Cubic graphs D 20 Enlargements 76 D 21 Reflections 75 D 22 Rotations 74 D 23 Reflections and rotations 74/75 D 24 Translations 77 D/C 25 Ratio - sharing D 26 Proportion, recipes 62 D 27 Percentage of an amount C 28 Probability from a table 90,91 B 29 Probability tree diagrams D 30 Plans and elevations 81 C 31 Circles - area and circumference C 32 Surface area and volume of prisms 121-2

6 D 33 Use of a calculator 63 D 34 Exchange rates 64 D/C 35 Estimation 101 C/B/A 36 Index laws C/B 37 Inequalities D 38 alternate and corresponding angles 67 C 39 expand and simplify C 40 Sequences and nth term 112