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Graph Inequalities Worksheet with Answers document sample
LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 Students will OBJECTIVE Additional Resources CHAPTER AIMS & C3 Book TOPIC learn… page: S 1 PERCENTAGES 1. Financial (a) to calculate percentage increases and decreases 2,3 Teacher File C3 Chapter 1 Calculations (b) to use a multiplying factor for such increases and decreases. Non Calculator Percentage Worksheet Non Calculator Percentage Worksheet Answers 2. Profit and (a) the relationship between cost price, selling price, 4,5 Simple / Compound Interest Interactive Loss profit and loss Percentage Cards Worksheet (b) to calculate percentage profit and loss Percentages Revision Worksheet (c) to calculate selling price. 10 Ticks Level 5 Pack 2 p28-32 10 Ticks Level 6 Pack 3 upto p18 3. Reverse (a) to perform inverse calculations to find the original 6,7 10 Ticks Level 7-8 pack 2 p19-22 Percentage cost price. Calculations 4. Interest (a) to calculate simple interest. 8,9 5. Review 10,11 Mental Test TIME SCALE: 5 lessons Page 1 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 2 ALGEBRAIC EXPRESSIONS 1. Expressions (a) revise vocabulary: variable, expression, simplify, 12,13 Teacher File C3 Chapter 2 like and unlike terms, factorise and expand Simplifying Expressions Worksheet (b) simplify simple linear expressions Collecting Like Terms Worksheet (c) factorise simple linear expressions Forming Expressions Worksheet (d) multiply a constant over a bracket. Substitution Exam Questions Worksheet 10 ticks level 5 pack 5 p8-21 2. Indices (a) the meaning of index, power, and base 14,15 10 ticks level 6 pack 1 (b) be reminded that n5 means n x n x n x n x n 10 ticks level 7-8 pack 3 p11 onwards (c) be introduced to the laws of indices 3. Expanding two (a) expand two brackets in the form (x ± a) (x ± b) 16,17 Brackets (b) simplify the result 2 (c) expand (x ± a) 4. Further (a) simplify more complicated non-linear expressions 18,19 Expressions (b) use laws of indices to simplify expressions (c) factorise simple non-linear expressions. 5. Review 20,21 Test 1,2 TIME SCALE: 6 lessons Page 2 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 3 DOING A SURVEY 1. Collecting (a) to write a questionnaire with clear and unbiased questions 22,23 Teacher File C3 Chapter 3 Information (b) to give a suitable set of responses for each question Interpreting pie charts worksheet (hard) (c) to recognise flaws in questions. Pie charts interactive Template of circles and tables 2. Displaying (a) learn to distinguish between categorical and numerical data 24,25 Scatter Graphs Interactive Data (b) revise how to draw a tally chart and a bar chart Using Excel To Draw Scatter Graphs Worksheet (c) learn to use a two-way table. Using Excel To Draw Scatter Graphs Worksheet 2 Drawing Scatter Graphs Worksheet 3. Pie Charts (a) Draw and interpret pie charts 26,27 Correlation Presentation (b) to decide when a pie chart is an appropriate display to use Questionaires Presentation 10 ticks level 6 pack 6, p11-14 4. Grouped (a) to distinguish between discrete and continuous numerical data 28,29 10 ticks level 7-8 pack 6 p35,36 Data (b) to understand and use class intervals for continuous data, expressed using inequalities (c) to make a grouped tally chart and grouped frequency chart for continuous data. (d) to make a frequency polygon 5. Scatter (a) to draw and interpret scatter diagrams 30,31 Diagrams (b) to draw a line of best fit by eye and use it to make predictions (c) the meaning of positive correlation and negative correlation 6.Review 32,33 Test 3, mental test TIME SCALE:Middle of October 7 lessons End of Half Term Page 3 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 4 EQUATIONS 1. Solving (a) to solve equations involving fractiona and decimals 34,35 Teacher File C3 Chapter 4 Equations Solving equations revision worksheet Forming equations using angle facts / perimeter 2. Solving More (a) solve equations involving negative coefficients of x 36,37 Forming equations using angle facts / perimeter Equations Forming equations: Think of a Number w/s Linear Equations Interactive 3. Forming (a) form equations using given information 38,39 Solving linear equations worksheet (hard) Equations 10 Ticks Level 6 pack 1 p6-10, 15, 16-18, 20,37-38 Trial & Improvement Game Interactive 4. Trial and (a) form equations from written information 40,41 Trial & Improvement Interactive Improvement (b) use ‘trial and improvement’ to solve equations 10 ticks level 6 pack 4 p26-30 5. Review 42,43 TIME SCALE: End of half term. 5 lessons Page 4 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 5 WORKING WITH 1. Angles (a) the meaning of adjacent and exterior with respect to angles 44,45 Teacher File C3 Chapter 5 POLYGONS (b) a demonstration and a proof that angles in a Calculating angles at a point worksheet triangle add up to 180° Target board 360 starter (c) the difference between a demonstration and a proof Target board 180 starter (d) how to use the interior angle sum of a triangle to 10 ticks level 5 pack 3, p1-6 and 17-28 prove that the interior angles of a quadrilateral add up to 360° Angle calculations worksheet (hard) 10 ticks level 6 pack 2 p23-36 2. Angles of (a) a formula for the sum of the interior 46,47 10 ticks level 6 pack 5 p27-30,39 onwards Polygons angles of a polygon with n sides 10 ticks level 7-8 pack 2 upto p12 (b) that the sum of the exterior angles of a polygon is 360°. 3. Regular Students will be reminded 48,49 Polygons (a) of polygon names (b) of the requirements for a polygon to be regular. Students will learn (c) how to construct a regular polygon (d) angle properties of regular polygons. 3. Pythagoras (a) the meaning of hypotenuse 50,51 (b) Pythagoras’ rule (c) the standard equation form of Pythagoras’ rule. 4. Using how to use Pythagoras’ rule to find a shorter side 52,53 Pythagoras rule 5. Review 54,55 TEST 4,5 TIME SCALE: End of November 6 lessons Page 5 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 6 SEQUENCES 1. Generating (a) learn the meanings of sequence, term-to-term rule, 56,57 Teacher File C3 Chapter 6 Sequences position-to-term rule and function Sequences Worksheet (b) find simple term-to-term and position-to-term Sequences Worksheet Answers rules given the sequences Sequences Presentation (c) generate sequences given their rules. 10 Ticks level 5 pack 5 p25 onwards 10 Ticks level 7-8 pack 1 p37 onwards 2. Linear (a) what a linear sequence is 58,59 Sequences (b) to find the nth term of a linear sequence. 3. Using (a) how to print a linear sequence on a spreadsheet 60,61 Spreadsheets (b) properties of the 1st and 2nd difference columns in such sequences (c) what a quadratic sequence is. 4. Spatial (a) continue a spatial pattern 62,63 Patterns (b) justify a rule for the nth term by considering spatial properties 5. Review 64,65 TIME SCALE: End of November 5 lessons 11 CIRCLES 1. Circumference (a) be reminded of the names of parts of a circle 66,67 Teacher File C3 Chapter 7 and diameter (b) discover the relationship between the diameter and Area Of Circles Worksheet circumference of a circle Area Of Circles Worksheet 2 (c) learn that two approximate values of pi are 3.14 and 22/7 Circumference and Diameter Presentation (d) learn how to calculate arc length 10 Ticks level 6 pack 5 p33-38 Area and Perimeter Circles Worksheet 2. Area of a (a) deduce the formula for the area of a circle 68,69 10 ticks level 7-8 pack 5 p7-10 Circle (b) learn how to calculate the area of a sector 3. Circle (a) learn that the locus of a point in two dimensions is 70,71 Constructions a circle and in three dimensions is a sphere (b) learn how to construct a tangent to a circle (c) learn the meanings of tangent, chord and segment (d) be reminded of loci. 4. Review 72,73 TEST 6,7 TIME SCALE: End of November 5 lessons Page 6 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 8 RATIO 1. Ratio (a) simplification of ratios 74,75 Teacher File C3 Chapter 8 (b) equivalence of ratios Ratio Review Worksheet (c) division in a given ratio Ratio & Proportion Worksheet (d) using proportion Ratio & Proportion Worksheet Answers (e) finding a missing quantity in a given ratio 10 Ticks level 5 pack 3 p9-11 10 ticks level 5 pack 2 p39 onwards 2. Ratios and (a) that there is a relationship between the ratio 76,77 10 ticks level 6 pack 4 p3-16 Similar Figures of the areas of similar figures and the ratio of their lengths 10 ticks level 7-8 pack 5 p23-28 (b) that there is a relationship between the ratio of the volumes of similar figures and the ratio of their lengths 3. Review 78,79 NB Miss out direct, inverse proportion and miss last question on test Test 8, Mental test TIME SCALE:Middle of December 4 lessons End of Term 9 SIMULTANEOUS EQUATIONS 1. Solving Pairs (a) what simultaneous equations are 80,81 Teacher File C3 Chapter 9 of Equations (b) to solve simultaneous equations graphically Simultaneous Equations Interactive (c) to solve simultaneous equations by substitution 10 Ticks Level 7-8 Pack 4 upto p12 2. Simultaneous (a) to solve simultaneous equations by elimination. 82,83 Equations 3. Simultaneous (a) to solve more simultaneous equations by elimination 84,85 Equations 4. Simultaneous (a) to solve simultaneous equations which need first to 86,87 Equations be multiplied through by a constant 5. Review 88,89 TIME SCALE: End of term. 5 lessons Page 7 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 10 FRACTIONS 1. Fractions in (a) to use the many terms associated with fractions in an 90,91 Teacher File C3 Chapter 10 Algebra appropriate way Adding Fractions Interactive (b) to add, subtract and cancel simple algebraic fractions Adding Fractions Worksheet (c) to relate fractions in algebra and arithmetic. Adding / Subtracting Fractions Interactive (Hard) Adding / Subtracting Fractions Worksheet 2. Working with (a) to add and subtract mixed numbers 92,93 Fractions Interactive (+,-,*,/) Mixed Numbers (b) to multiply and divide mixed numbers. Fractions / Ratio Worksheet Equivalent Fractions Worksheet 3. Review 94,95 Mixed Numbers Interactive Multiplying Fractions Interactive Dividing Fractions Interactive 10 ticks level 5 pack 2, p28 onward 10 ticks level 6 pack 3 10 Ticks level 7-8 pack 2 p23-28 . Test 9,10 TIME SCALE: End of term. 4 lessons 11 GRAPHS 1. Mapping (a) what a mapping diagram is and how to draw one 96,97 Teacher File C3 Chapter 11 Diagrams (b) how to recognise the identity mapping. Equation Of A Straight Line Presentation Equation Of A Straight Line Worksheet 2. Inverse (a) to find a formula for a simple inverse function 98,99 Equation Of A Straight Line Worksheet Answers Mappings Chapter Review Worksheet Chapter Review Worksheet 2 3. Straight Lines (a) how to plot a straight line graph 100- 10 ticks level 5 pack 4, p23-30 101 10 ticks level 6 pack 1 p27 onwards 4. Straight Line (a) how to find the gradient of a line 102- 10 ticks level 7-8 pack 1 p21-30 Graphs (b) to recognise the equation of a straight line 103 10 ticks level 7-8 pack 3 p29 (c) how the gradient and intercept are connected to y=mx+c 5. Curves (a) to plot a graph which results in a curve 104- (b) to predict from the equation whether a graph is a 105 straight line or a curve (c) to recognise quadratic and cubic functions 6. Review 106- 107 TIME SCALE: End of term. 6 lessons Page 8 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 12 CONSTRUCTION & LOCUS 1. Using Scale (a) use maps and scale drawings to solve real life 108- Teacher File C3 Chapter 12 Drawings problems. 109 Perpendicular To A Line Presentation Perpendicular From A Line Presentation 2. Congruence & (a) be reminded of the meaning of congruent and similar 110- Making Scale Drawings Presentation Similarity (b) learn when three measurements for a triangle 111 Bearings Presentation uniquely define it. Bearings Interactive Bearings Worksheet 3. Locus (a) be reminded about locus 112- 10 ticks level 5 pack 3 p7-11 (b) learn to solve more advanced locus problems, 113 10 ticks level 6 pack 4 p31-32 including some in three dimensions. 10 ticks level 6 pack 2 p27-36 10 ticks level 7-8 pack 5 p7-10 4. Review 114- 115 Test 11,12 TIME SCALE: End of term. 5 lessons End of Half Term Page 9 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 13 WORKING WITH DATA 1. The Mean (a) to calculate the mean of a small set of data 116- Teacher File C3 Chapter 13 (b) to calculate the mean of a large set of data from a 117 Calculating the Mean Worksheet frequency table Calculating the median worksheet Calculating the median worksheet 2. Median Mode (a) to find the median of a small set of data 118- Calculating the mode worksheet And Range (b) when the median may be more appropriate than the mean 119 Calculating the mode worksheet (c) to find the mode of a set of data averages and range interactive (d) to find the range of a set of data. averages and range worksheet averages and range worksheet 3. Stem & Leaf (a) to display data in a stem-and-leaf diagram 120- Averages worksheet Diagrams (b) to use a stem-and-leaf diagram to find the median 121 Which average? Worksheet (c) to use a stem-and-leaf diagram to find the modal Finding the range worksheet class of a set of data. 10 Ticks Level 5 pack 6 upto p6 Mean From A Frequency Table Worksheet 4. Estimating the (a) to estimate the mean of a set of grouped data by 122- Mean From A Frequency Table Presentation mean of Grouped using mid-interval values. 123 Mean Of Grouped Data Worksheet Data Mean Of Grouped Data Presentation 10 ticks level 7-8 pack 6 p33-34 5. Estimating the (a) to construct a cumulative frequency table from a 124- Spread of set of grouped data 125 Grouped Data (b) to draw a cumulative frequency graph (c) to use a cumulative frequency graph to estimate the median of a set of grouped data. 6. Estimaing (a) to estimate the range of a set of grouped data 126- Spread (b) to use a cumulative frequency graph to estimate the 127 interquartile range of a set of grouped data (c) to use the interquartile range to compare the spread of two sets of data. 7. Review 128- 129 TIME SCALE: End of term. 7 lessons Page 10 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 14 INDICES & STANDARD 1. Using (a) to multiply and divide using indices 132- Teacher File C3 Chapter 14 FORM Indices (b) to understand zero and negative numbers as indices 133 Standard Form Worksheet Standard Form Worksheet Answers 2. Writing Large (a) to write large and small numbers in standard form 134- Standard Form Presentation and Small (b) to order numbers written in standard form. 135 10 Ticks Level 5 pack 1 p33-36 Numbers 10 Ticks Level 6 pack 4 p23 10 Ticks Level 7-8 pack 2 p32-40 3. Standard (a) to enter a number in standard form on their calculator 136- Form on the (b) to interpret the display when a calculator shows a 137 Calculator number in standard form. 4. Review 138- 139 TEST 13,14 TIME SCALE: End of term. 5 lessons 15 FORMULAE 1. Formulae (a) to construct a formula from given information 140- Teacher File C3 Chapter 15 (b) to substitute values into a formula. 141 Substitution Exam Questions Worksheet Substitution Worksheet 2. Rearranging (a) to rearrange a formula. 142- 10 Ticks level 4 pack 5 p42 onwards Formulae 143 10 Ticks level 5 pack 5 p33-34 10 Ticks Level 7-8 pack 3 p21-26 3. Review 144- 145 mental test TIME SCALE: End of term. 3 lessons End of Term Page 11 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 16 ACCURACY 1. Accuracy (a) to understand significant figures 146- Teacher File C3 Chapter 16 (b) to round to a given number of significant figures 147 Rounding to decimal places Interactive Estimation Presentation 2. Range of (a) that a measurement to a given degree of accuracy is 148- Rounding to decimal places Presentation Values really a range of values 149 Using Rounding in Calculations Worksheet (b) that calculations with measured values produce an Rounding To Significant Figures Presentation even wider range of values 10 Ticks Level 4 pack 3 p7-8 10 Ticks Level 5 pack 2 p27 3. Estimating (a) to estimate answers to problems that are difficult to 150- 10 Ticks Level 6 pack 4 p21-25 Answers calculate exactly 151 (b) to round the numbers in a calculation to 1 significant figure to provide an estimate of the answer (c) to estimate square and cube roots. 4. Review 152- 153 test 15,16 TIME SCALE: End of term. 5 lessons 17 THREE DIMENSIONS 1. Viewing (a) to view 3-D solids using the plan, side elevation and 154- Teacher File C3 Chapter 17 Solids front elevation. 155 Plans and Elevations Presentation Isometric Drawing Worksheet 2. Planes of (a) how to recognise planes of symmetry. 156- Isometric Drawing Rotation Worksheet Symmetry 157 Isometric Drawing Rotation Worksheet Answers Isometric Drawing Interactive 3. Cylinders (a) to find the volume and surface area of a cylinder 158- Chapter Review Worksheet 159 10 ticks level 6 pack 2 p37 onwards 4. Review 160- 10 ticks level 6 pack 5 p23-26 161 10 ticks level 5 pack 4 p41 onwards 10 ticks level 5 pack 6 p35 onwards Composite Volumes Worksheet TIME SCALE: End of term. 4 lessons Page 12 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 18 REAL LIFE GRAPHS 1. Shapes Of (a) to interpret a range of linear and non-linear 162- Teacher File C3 Chapter 18 Graphs graphs arising from real situations 163 10 Ticks Level 5 Pack 6 p19-29 (b) to draw and sketch graphs to illustrate real 10 Ticks Level 6 Pack 5 p3-4, 15-20 situations (c) to obtain information from graphs of real situations. 2. Working with (a) to plot graphs to illustrate real situations 164- Equations of (b) to obtain information from equations of 165 Graphs graphs of real situations 3. Review 166- 167 TEST 17,18 TIME SCALE: End of term. 4 lessons End of Half Term 19 TRANS- FORMATIONS 1. Trans- (a) that a transformation is a movement of shape 168- Teacher File C3 Chapter 19 formations (b) of the nature of translations, reflections and 169 Enlargement Worksheet rotations and how to specify them and combinations of them Enlargement Worksheet Answers (c) that in translations, reflections and rotations the Reflection Worksheet object and image are congruent. Reflection Worksheet 2 Reflection Worksheet 3 2. Enlargement (a) of the nature of an enlargement and how to draw one 170- Rotation Presentation 1 and similar (b) of the meaning of scale factor 171 Rotation Presentation 2 figures (c) how to find the centre of enlargement Rotation Interactive (d) of the relationship between scale factor and Translation Worksheet corresponding object and image lengths. 10 Ticks level 4 pack 7 p29-38 10 Ticks level 5 pack 4 p31-35 3. Fractional (a) be reminded that under an enlargement the object and the 172- 10 Ticks level 6 pack 2 p3-22 Enlargements image are similar 173 10 Ticks level 7-8 pack 4 p31 onwards (b) extend their knowledge of enlargements from positive integer scale factors to fractional scale factors. 4. Review 174- 175 Test 19, mental test TIME SCALE: End of term. 5 lessons Page 13 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 20 INEQUALITIES 1. Inequality (a) to recognise and use inequalities signs 176- Teacher File C3 Chapter 20 Signs (b) to write information as inequalities 177 10 Ticks Level 6 Pack 6 p7,8 (c) that inequalities can be read in both directions 10 Ticks Level 7-8 Pack 4 p13-16 2. Inequality (a) to show inequalities on a number line 178- Number Lines (b) to use number lines to solve simultaneous 179 inequalities. 3. Solving (a) to solve inequalities 180- Inequalities (b) to describe regions using inequalities 181 4. Review 182- 183 TIME SCALE: End of term. 4 lessons 21 PROBABILITY 1. Calculating (a) the meaning of the term mutually exclusive 184- Teacher File C3 Chapter 21 Probabilities (b) that the probabilities of all the mutually exclusive 185 Probability Interactive outcomes of an experiment add up to 1. Probability Scales Worksheet Probability Spinners Worksheet 2. Combined (a) to find all the possible outcomes of 186- Relative Frequency Interactive Outcomes two or more events, using a list or a table 187 One Dice experiment interactive (b) to use a list or table to find probabilities 10 Ticks Level 4 pack 6 p27-39 10 Ticks Level 5 pack 1 p39-43 3. Estimating (a) to use relative frequency as an estimate of probability 188- 10 Ticks Level 6 pack 6 p22-42 Probabilities (b) that the more trials that are carried out, the more 189 10 Ticks Level 7-8 pack 1 p1-18 reliable the results. 4. Review 190- 191 Test 20,21 TIME SCALE: End of term. 5 lessons Page 14 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls LLANTWIT MAJOR SCHOOL YEAR 9 SET 1 SCHEME OF WORK KEY STAGE 3 22 TRIGONOMETRY 1. Right Angled (a) the meaning of hypotenuse, opposite and adjacent 192- Teacher File C3 Chapter 22 Triangles (b) the ratios of pairs of sides. 193 2. Trig ratios (a) the definitions of the three trigonometrical ratios: 194- sinx, cosx and tanx 195 (b) how to calculate each ratio using measurements or a calculator. 3. Finding (a) how to find lengths given one side and one angle of 196- Lengths a right-angled triangle. 197 4. Finding (a) to calculate inverse trigonometrical values using a 198- Angles calculator 199 (b) how to calculate angles given two sides of a rightangled triangle. 5. Review 200- 201 Test 22, mental test TIME SCALE: End of term. 6 lessons End of Term Page 15 ec2cc0f8-b42a-4ee0-b9fd-863a5a28cca3.xls