Unit 1: Number, Algebra, Data Handling

Transcription

1 Year 10 Set 3 Textbook: AQA Higher Modular This syllabus was written as a MODULAR syllabus it will need to be re-ordered to account for the fact that this is now a LINEAR course. There is, in particular, no need to do all the statistics work initially. Ma Chapter Exercise Topic lessons notes Unit 1: Number, Algebra, Data Handling 2 18 All Algebra 1 3 Roles of letters in algebra. Understand equation, formula, identity & expression. Extend to equation of a straight line, y=mx+c and word equations written in symbolic form, such as F=2C+30 to roughly convert temperature & compare it with F=9C/5 2 7 All Number 1 4 Integers, understand, order and calculate using them. Understand simple instances of BODMAS, round to nearest 10, 100, 1000,.., multiply & divide whole numbers by given multiple of 10, check calculations by rounding & by reverse calculation. Extend to directed number work with 2+ operations or decimals. 4 1 All Collecting data 5 Designing a questionnaire, Primary & secondary data, discrete & continuous data, stratified sample, data collection sheets, bias, justifying appropriate sampling schemes (including random & systematic), problems with data collection (non-response, missing & anomalous data) Extend to other sampling schemes such as cluster & quota sampling All Probability 1 3 Listing equally likely outcomes & mutually exclusive events, calculating probability of an event not happening. Use sample space diagrams for 2 events eg 2 dice 3 and 4 All Displaying data Review pictogram & bar chart. Bar charts, histogram (equal intervals), frequency polygons, stem & leaf diagrams. Understand the difference between a bar chart & a histogram. Histograms. Draw a histogram from a frequency table. Complete a frequency table from a histogram. Understand frequency density. Extend to using computers to draw graphs and 23 All Algebra 2 3/4 Straight line graphs 1. Draw linear graphs from tabulated data. Interpret linear graphs, including conversion & distance time- graphs.

2 2 10 All Number 2 3 Decimals. Order decimals. Round to given or appropriate number of d.p s or s.f s. Use decimals in real life situations eg. Best buys. Extend to multiplying decimal by decimal (>2 d.p s) 4 2 All Averages 1 3 Find the mean, median, mode & range of an ungrouped frequency distribution. Mean from frequency table using sum of fx/sum of f. Discuss implication of a rogue value on the range and averages All Shape and space 1 3 Lines & Angles. Review types of angle. Estimate angles. Measure & draw angles to the nearest degree. Draw & measure line to nearest mm. Use angle properties to calculate unknown angles (at a point, straight line, vert opp) 4 3 All Displaying data 2 3/4 Draw and interpret pie charts. Choose an appropriate way to display discrete, continuous & categorical data. Compare distributions shown in charts & graphs 2 22 and 23 All Algebra 3 3/4 Draw & interpret straight line graphs in the form y=mx+c, Understand lines are parallel when they have the same value of m. Find the gradient & intercept of a straight line graph. 2 8 All Number 3 4 Fractions. Simplest form & equivalent fractions. Common denominators. Add & subtract fractions. Improper fractions & mixed numbers. Common recurring decimals as fractions. Simple fractions as %. 4 6 All Probability 2 6 Know the probability of A or B is P(A) + P(B) and A and B is P(A) x P(B). Draw & use tree diagrams to solve problems (including non-replacement). Relative probability. 2 2 All Averages 2 5 Grouped data. Modal class. Median using (n+1)/2. Use mid-point of equal class intervals to find estimate for mean. Know advantages & disadvantages for different measures of average All Algebra 3 5/6 Curved graphs. Plot & recognise quadratic, cubic, reciprocal, exponential & circular functions. Use the graphs to find approx solutions to equations. Match equations to graphs & sketch graphs of given functions All Number Percentage. Write % as decimals or fractions in their simplest form. Write one number as a % of another. Calculate % or fraction of given amount. Find % increase/decrease, include using multiplier (decrease by 20% x 0.8, increase by 20% x 1.2). Simple & compound interest. 4 3 All Displaying data Scatter diagrams & correlation. Draw a scatter diagram. Understand & distinguish between positive, negative & zero correlation using line of best fit. Draw line

3 of best fit by eye & use to predict values. Find equation of line of best fit & use to predict values. 2 3 All Number Ratio & scale. Understand that the ratio eg 1:2, represents 1/3 & 2/3 of a quantity. Divide quantities in a given ratio. Solve word problems involving ratio. 4 5 All Median and IQR 4-6 Find median & quartiles for large sets of ungrouped data. Draw a cumulative frequency table & curve for grouped data. Use curve to find estimates of median & quartiles & to solve problems eg how many greater than a particular value. Draw box plots. Compare diagrams & box plots to make references about distributions All Shape and Space Estimate lengths, volume & capacity, weights. Convert between metric & imperial units and between metric units. Decide on appropriate units to use in reallife problems. Read measurements from instruments. Recognise measurements to given degree of accuracy maybe up to half that unit in either direction. Unit 1 examination in March of Y10 (Calculator) Unit 2: Number, Algebra, Geometry 2 11 All Factors and multiples 3 18 All Algebraic manipulation (also in Unit 3) 3/4 Know odd, even, prime, find factors & multiples of nos, find powers roots of nos with and without calculators trial & improvement, HCF, LCM & prime factor decomposition 6 Simplify terms, products & sums, expand & factorise expressions with one pair brackets & with >1 pair of brackets, factorise quadratic expression (incl diff of 2 squares), simplify algebraic fracs All Laws of indices 3/4 Use index notation & laws for mult & div of integer powers, to simplify & calculate value of numerical expressions involving mult & div of integers, fractional & negative powers, use inverse ops involving 1/n, recall n^0=1 & n^-1=1/n for positive integers, the corresponding rule for negative integers, n^0.5=root n & n^third=cube root n for any positive no n 2 20 All Formulae (Also in Unit 3) 3 30 All Lines and angles 5/6 Substitute nos (+ & -) into simple algebraic formulae & formulae involving powers, find solution to prob by writing eqn & solving it, change subject of formula, generate formula from given info 4 Definitions & names of polygons, properties of triangles & quads, geometric proof, angles associated with parallel lines, calc & use sums of interior & exterior angles of quads, pentagons & hexagons & regular polygons, understand inscribed reg polygons 2 12 All Standard Form 3 Understand standard form convention, convert nos to & from standard form, calculate with nos in standard form with & without calc, round nos in standard form to

4 3 32 & 37 All Area, Perimeter and Volume 2 13 All Ratio & Scale 2 21 All Patterns & sequences 2 15 All Exact answers & surds 2 22 All Straight line graphs 3 31 All Circle geometry and theorems 2 3 All Estimating & reading scales 2 38 All Metric, Imperial & compound units 3 30 All 3d shapes, symmetry & tessellations given no of sig figs 4/5 Use formulas to find area of triangles, parallelograms & trapeziums, calculate surface area & volume of cuboids, use formula to calculate volume of a prism. Area & circumference of a circle, volume of a cylinder. 3/4 Use ratio notation, including in simplest form, & various links to fracs notation, divide quantity in given ratio, solve word problems about ratio, including using informal strategies & unitary method of solution. Link to metric imperial module 5 Generate integer sequences (incl sqs, powers of 2 & 10, triangle nos). generate terms of seq using term-to-term & position-to-term definitions of seq, use linear expressions to describe nth term of arithmetic sequence 4/5 Simplify surds & rationalise denominators, write answers in exact form, use surds & pi in exact calcs without a calc. 6 Find co-ords of final point to make shape, find mid-pt of line segments, know 2-D & 3-D shapes & 3-D co-ords, y=mx + c, gradients of parallel & perpendicular lines, linear functions in practical probs. 5/6 Names & definitions of parts of a circle, angle properties of tangents, understand, prove & use circle theorems, use to find unknown angles & explain method quoting appropriate theorem(s) 4/5 Make estimates of length, volume, capacity & mass, use sensible units for measuring, read measurements from instruments (scales, analogue and digital clocks, thermometers), rounding inaccuracies (+/- half unit), convert between metric units, know common imperial units & time conversions 4 Convert units metric-metric & metricimperial, estimate answers by rounding to 1sf, upper & lower bounds & maximum/minimum possible values, use formulae for speed, change units in compound measures 3/4 Know the properties of cuboids Euler s rule, nets of solids, plans & elevations, reflective & rotational symmetry, name & construct 3-D shapes from given info, tessellation Unit 2 examination in November of Y11 (Non-Calculator) Unit 3: Number, Algebra, Geometry All Percentage problems 3/4 Percentage increase & decrease & reverse percentage, proportional change using a multiplier raised to a power such as

5 2 9 All Upper & Lower Bounds 2 8 All Using Fractions (Also in Unit 1 and 2) 2 12 All Standard Form (Also in Unit 2) 2 24 All Solving linear equations & inequalities compound interest and exponential growth & decay 3/4 Recognise inaccuracies in measurement & know min & max values. Work out max/min possible error in calculations involving measurement. Find upper & lower bounds of calculations involving perimeter, areas & volumes. Apply to compound units. 3/4 Calculate fractions of amounts, expressing answer as a fraction. Understand reciprocal as multiplicative inverse. Multiply & divide fractions by integers & fractions. Recognise terminating & recurring decimals can be written as fractions including proof. Use a calculator to solve real-life problems. 3 Convert numbers to & from standard form. Calculate with numbers in standard form with, and without, a calculator. Round numbers in standard form to a given number of sig. figs 5/6 Solve linear equations with one or more operations or involving brackets &/or variables on both sides. Solve linear inequalities and present the solution set on a number line. Form linear equations from worded problems in a variety of contexts All Changing the subject 3/4 Start by reviewing previous substitution work. Change the subject of an equation including where the subject occurs more than once. Generate formula Simultaneous Equations 2 17 All Direct & Inverse Proportion 2 28 All Trial & Improvement 4/5 Solve simultaneous equations graphically & algebraically. Draw graphs of linear inequalities in 2 variables & interpret solution set given by regions or identified with crosses 4 Solve problems using unitary method or by proportional change. Use given information to find the value of the constant of proportionality. Interpret as algebraic functions and use to find unknown values. Recognise & sketch graphs. 2/3 Use systematic trial & improvement to find approximate solutions of equations, including quadratic & cubic functions & 26 All Quadratic Functions 6/7 Generate points & plot graphs of quadratic functions & use to find approximate solutions. Factorise quadratics. Solve by factorising, completing the square & using the quadratic formula. CONSIDER SPLITTING THIS TOPIC! 2 27 Simultaneous Equations 2 5/6 Find approximate solutions of linear & quadratic graphically. Find exact solutions. Draw a circle radius r centre origin. Find approximate solutions of linear & circular graphically. Find exact solutions.

6 3 34 All Transformations 5 Transform 2-D shapes by translation, reflection, rotation & a combination of transformations & know how to describe them accurately. Know any figure is congruent to image after any of these transformation. Recognise & construct enlargements using positive & negative scale factors greater & less than one. 2/3 29 All Transforming Graphs 3 33 & 39 Constructions, Loci, Similarity and Congruence 3 35 All Pythagoras Theorem & 2d Trigonometry 3 36 All Applications of Pythagoras and Trigonometry in 3d 3 41 All Trigonometry in non-right-angled triangles 3 37 All Geometry of 3d objects 4/5 Understand notation y=f(x). Apply y=f(x)+a, y=f(ax), y=f(x+a) & y=af(x) to graph of y=f(x) for linear, quadratic, sine & cosine functions f(x). Draw sketch & describe graphs of trigonometric functions for angles of any size, including transformations involving scalings in either or both the x & y directions. 5/6 Draw 2-D shapes using a ruler & protractor. Understand SSS, SAS, ASA & RHS triangles are unique but SSA aren t. Construct perpendicular & angle bisectors, 60, 30 & 45 degree angles, regular hexagon in a circle, etc Prove geometric properties of triangles & 2 triangles are congruent formally. Construct Loci. CONSIDER SPLITTING THIS TOPIC. 6/7 Know & use Pythagoras theorem to find missing sides & the distance between 2 coordinates. Use trigonometric ratios to calculate angles & unknown lengths in RAT s. Solve problems involving bearings using Pythagoras. Solve problems involving geometric figures in which a RAT has to be extracted to solve it by Pythagoras &/or trigonometry 4/5 Calculate the diagonal through a cuboid or across the face of a cuboid. Find the angle between the diagonal of a cuboid & its base. Find the angle between a sloping edge of a pyramid & its base. 3/4 Use sine & cosine rules to solve 2-D problems. Calculate the area of a triangle using ½absinC. Use sine & cosine rules to solve 3-D problems. 5/6 Use formulae for circumference & area of circle. Solve problems involving surface areas & volumes of prisms, cylinders, cones, pyramids & more complex shapes, including segments of circles, length of chord & frustums of cones. Use surds & pi in exact calculations without a calculator. Find surface areas & volumes of compound solids constructed from spheres, hemispheres & cylinders. 3 Similar Shapes 2/3 Identify scale factors of enlargements as ratio of lengths of any 2 corresponding line segments. Understand & use the effect of enlargement on areas & volumes of shapes & solids.

7 3 40 All Vectors 5 Understand & use vector notation. Calculate, & represent graphically, the sum of 2 vectors, the difference of 2 vectors & a scalar multiple of a vector. Calculate the resultant of 2 vectors. Understand & use the commutative & associative properties of vector addition. Solve simple geometric problems in 2-D using vector methods All Compound Units 2/3 Understand & use compound methods, including density. Convert measurements of area & volume from one unit to another. Unit 3 examination in June of Y11 (Calculator)