Teacher support book. supplementary material. Teacher notes. Assessment sheets. Knowledge and skills grid. Activities. Answers

Transcription

1 Teacher support book supplementar material.. CONTENTS Teacher notes Assessment sheets Knowledge and skills grid Activities Answers 89

2 for New South Wales 5. Pathwa 0 Teacher notes TEACHER SUPPLEMENTARY MATERIAL The supplementar material comprises assessment sheets, a knowledge and skills grid, activities and answers. Assessment sheets The teacher support book contains assessment sheets, one for each chapter. The questions are designed to assess the relevant knowledge and skills dot points linked to the Stage 5. outcomes for the New South Wales Mathematics Sllabus. (Some questions are linked to Stage 4 and Stage 5. outcomes.) Codes for each knowledge and skills dot point are written in bold tpe beneath each question for teachers to see which outcomes are being assessed. Knowledge and skills grid The knowledge and skills grid displas each knowledge and skills dot point and the codes used for each dot point for man of Stage 4 and all of the Stage 5. outcomes. Some Stage 5. outcomes are also included. It also shows where the questions for each dot point are located. Activities The si etra activities are worksheets for teachers to use at their discretion, or at times when it is difficult to organise lesson preparation. Answers The answers section in the teacher support book contains the answers for all questions in the student homework book, the assessment sheets and the etra activities. 90

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5 for New South Wales 5. Pathwa 0 Name:... Assessment sheet.6 Teacher feedback: Chapter Number skills pages 4 Class:... Due date:... Parent/Guardian signature:... Use mental strategies to evaluate the following four statements. + ( 5) NS4.. 9 Estimate an answer to b first rounding each number involved in the calculation to significant figure. NS5... ( 6) NS4.. ( 4) NS4.. 0 Use a calculator to complete the following: =.86 (to decimal place) NS ( ) NS4.. Simplif then evaluate the following two epressions. 5 ( 8 + ) + ( ) NS ( ) NS How man significant figures are in the number ? NS Round the number to 4 significant figures. NS Reduce to simplest form. NS4.. 9 Write as a mied numeral. NS4..5 Find the value of the following four epressions NS NS NS

6 for New South Wales 5. Pathwa NS Convert -- to a decimal.ns4.. 8 Convert 0.4 to a fraction in simplest form.ns4.. 9 Calculate , rounding our answer to decimal place. NS4..9, NS Epress $8 as a percentage of $45. NS4..9, NS4..6 Calculate 5% of $4.60. NS4..4 The ratio of copper : silver : gold in 8-carat ellow gold is :.5 : 7.5. Use this information to answer the following two questions. 6 How much copper is there in a.5-g ellow gold necklace? NS4.. 7 How much gold is in the necklace? NS4..4, NS Wh is it necessar to have scientific notation as a form of epressing numbers? NS Epress the number two hundred and eight-seven million in scientific notation. NS5... Convert 85% to a fraction in simplest form. NS4.. 4 Write 0.75, -- and 78% in descending order. NS Write the number as a basic numeral.ns5...4 Write the numbers 400, , and in ascending order. NS5..., NS Write the ratio cm to m as a fraction in simplest form. NS4..0, NS4.. 5 The ratio -- : is equivalent to the ratio :. Calculate the value of. NS4.. Use a calculator to evaluate the epression ( ) Give our answer correct to 4 significant figures. NS

7 for New South Wales 5. Pathwa 0 Name:... Assessment sheet.6 Teacher feedback: Chapter Investing pages 4 6 Class:... Due date:... Parent/Guardian signature:... Epress the following four time periods as a fraction of a ear. 6 months months a fortnight 4 0 months NS5...5 Calculate the simple interest earned on the following four investments. 5 $500 at 7.5% p.a. for ears 6 $5 000 at 6.95% p.a. for month 7 $4500 at 6.8% p.a. for 9 months 8 $5 000 at 6.5% p.a. for months NS5...5 Michelle borrows $8500 for 5 ears at 7.9% p.a. flat interest rate. 9 How much interest is Michelle charged? 0 What total amount must she repa? NS5...5 The interest on credit cards is calculated on a dail basis and added to the outstanding balance at the end of the month. Tob s outstanding balance on December is $ and he is charged a flat rate of interest of 5.95% p.a. Use this information to answer the following two questions, assuming Tob makes no further purchases during December. What will be the interest charges on Tob s account for that month? How much will he owe at the end of the month? NS5...5 Charles invests $5000 at a simple interest rate of 5.4 % p.a. How long would it take for his investment to earn $50? Give our answer to the nearest month. NS How much must Janice invest at 5.8% p.a. flat interest to earn a earl income of $800? Give our answer to the nearest dollar. NS5...6 Hoa borrows $5 000 to purchase a car. The terms of the loan are that interest is charged at 9.5% p.a., with the loan plus interest to be repaid in equal monthl instalments over 5 ears. Consider this information when answering the following three questions. 5 How much interest will Hoa be charged over the period of the loan? 95

8 for New South Wales 5. Pathwa0 6 What is the total he must repa? 7 How much will he repa each month? NS Find the amount of compound interest earned on $ invested at 7% p.a. over ears, with interest compounded annuall. NS If the interest in question 8 was compounded si-monthl instead of earl, what would the compound interest amount to?ns5...7 Noel has saved $ and wants to invest his mone for a ear. He has two options: Option A 6.% p.a. flat interest Option B 6% p.a. with interest compounded ever months What interest would he earn with option B? NS5...7 Which option earns Noel the most mone? How much more? NS5...7 Refer to the table at the bottom of the page for the following two questions. What compound interest would be earned on an investment of $800 at 7% p.a. over 0 ears? NS Find the interest paid on an investment of $5 000 at 8% p.a. over ears with interest compounded ever months. NS How much interest would Noel earn with option A? NS5...6 Interest rate per period Periods % % % 4% 5% 6% 7% 8% 9% 0%

9 for New South Wales 5. Pathwa Chapter Data representation and analsis pages Assessment sheet.6 Name:... Teacher feedback: Class:... Due date:... Parent/Guardian signature:... Questions to displa data in different representations. For each data set, find the mean, median and mode. 8,, 4, 5, 0,, 6, 7 DS f DS4..DS4.. Ke 8 = 8 Stem Leaf DS4.. 4 Five scores have a mean of 6.4. Four of those scores are 5, 7, 8 and 9. What is the fifth score? DS4.. Use the following table to answer questions 5 8. Class interval Class centre () 5 Complete the entries in the frequenc distribution table. DS Calculate the mean. DS Determine the modal class. DS5...8 Frequenc ( f ) Frequenc class centre ( f ) Σf = Σ( f ) = 8 Construct a combined histogram and frequenc polgon to displa the data. DS

10 for New South Wales 5. Pathwa0 9 Complete the following frequenc table b entering the correct values in the cumulative frequenc column. Score () DS5... Twent students are asked to roll a die once and note the number that turns up. The results are shown below., 6, 4, 5,,, 6,, 4,, 5, 6, 4,, 6,, 6,, 4, Use this information to answer the following three questions. 0 Displa the results in a frequenc table that includes a cumulative frequenc column. DS5... Construct a cumulative frequenc histogram and ogive. DS5... Frequenc (f) Cumulative frequenc (cf) Use our result from question to determine the number of students who rolled a 4 or higher. DS4..5 The percentages obtained b a group of students in their end-of-semester mathematics eam are as follows. 4,, 6, 4, 70, 8, 94, 54, 7, 74, 8, 85, 66, 5, 7, 64, 65, 49, 7, 9, 87, 69, 48, 79, 89, 50, 46, 9, 77, 8, 67, 7, 77, 95, 55, 4, 74, 88, 68, 5, 5, 76, 7, 84, 66, 59, 75, 90, 55, 4. Use these data to answer questions 5. In the space provided, sort the data into a grouped distribution table using intervals of 0 (starting from 0). Include a cumulative frequenc column. DS5...4, DS On the grid lines provided, construct a cumulative frequenc polgon. DS Use the graph from question 4 to find the median score. DS

11 for New South Wales 5. Pathwa 0 Name:... Assessment sheet 4.6 Teacher feedback: Chapter 4 Indices pages 0 6 Class:... Due date:... Parent/Guardian signature:... State the base and the power for 5. NS5... Write 4 in factor form, and then epress it as a basic numeral. NS5... Complete the missing values in the following table. Base 5 Power 4 Value NS Write 5 4 in factor form. NS5...5 Multiple choice questions 5 to. 5 The epression 4 is the same as: A B 8 C D 8 NS The epression (4 ) is the same as: A B 4 4 C 4 5 D 4 NS The epression 5 5 is the same as: A 5 0 B C 5 D all of these NS The epression ---- is the same as: A B C 4 D 4 NS The epression 9 is the same as: A -- C 9 D 7 NS The epression is the same as: A B + C D PAS5... The epression ---- is the same as: A 9 B 9 + C 9 D 9 PAS B

12 for New South Wales 5. Pathwa0 The epression ( ) 0 simplifies to: A B C D ( ) PAS5... The epression a is the same as: A a B a a a C ---- D a a a a PAS (a) PAS PAS5... (p) (p) PAS5... For questions 4 to 5, simplif each epression b using the appropriate inde law(s), giving the answer in inde form. Where possible, show our working to demonstrate how ou arrive at our answer NS p p 6 p 4 PAS PAS a b 4a 5 PAS a 8 a PAS5... (4g) g PAS (k) 0 (7k) PAS d 4 (d ) PAS Find the value of 8. NS Calculate the value of 64. NS Use an appropriate method to simplif a. PAS d d 8 PAS Use an appropriate method to 00k 4. PAS

13 for New South Wales 5. Pathwa 0 Name:... Assessment sheet 5.6 Teacher feedback: Chapter 5 Purchasing pages 7 48 Class:... Due date:... Parent/Guardian signature:... Soft drink is on special at the supermarket this week. A pack of 8 cans costs $8.99 while a -pack costs $5.88. Use this information to answer the following three questions. What is the cost per can in the 8-can pack? What is the cost per can in the -can pack? Which pack is the better bu? NS5...0 Juice Pops are sold in a pack of 6 50-mL bottles. The are advertised as packs for $ What is the cost per bottle? 5 What is the cost per litre? NS An arm-band MP plaer has a marked price of $5. A cash purchaser is allowed a 5% discount. What is the cash price? NS The Camera House has a sale. One particular camera is advertised as shown in the figure below. Camera SALE IKON 400 model pa onl $97 for Cash SAVE $60.90 that s 5% off TODAY ONLY House Is the advertising correct or misleading? Give a reason to support our answer. 6 Karl paid $.4 for 400 g of mince. What is the price of mince per kg? NS Yoghurt can be purchased as 00-g tubs for $.98 or a -kg tub for $4.95. Which is the better bu? NS A digital set top bo is discounted from $49 to $9 for a cash customer. What percentage discount is this? NS5...9 NS5...9 Melissa used her credit card to purchase an airline ticket costing $875. Interest on the credit card is charged at the rate of.5% p.a. How much interest would Melissa be charged after month? NS

14 for New South Wales 5. Pathwa0 A credit card compan charges interest at the rate of 6% p.a. The outstanding balance on Ronald s card at the end of Ma is $850. Use this information to answer questions to 4. Calculate the interest due for the month of Ma. NS5...5 The minimum pament due is 5% of the balance or $0, whichever is the greater. If Ronald pas the minimum, how much does he pa? NS What is the total interest charged? NS What is the annual rate of interest? NS5...6 The purchase price of a second-hand car is $7500. Ale pas 0% deposit and borrows the balance from a finance compan. He agrees to pa simple interest of 0.5% p.a., and repa the total owing over a period of 5 ears in equal monthl instalments. Use this information to answer the following five questions, showing our working in the space provided. 4 Ronald makes no further purchases during June. Calculate the interest due on his credit card for June. NS How much deposit does Ale pa? 9 How much does Ale borrow from the finance compan? A DVD recorder can be purchased using the options advertised in the following figure. DVD Recorder 0 Calculate the interest Ale pas over the period of the loan. What is the total amount Ale must repa to the finance compan? CASH PRICE $99 or $0 per month for months OFFER VALID TODAY ONLY Determine the repament Ale must make each month. NS How much would ou pa if ou bought the recorder on terms? NS

15 for New South Wales 5. Pathwa 0 Chapter 6 Algebra and linear equations pages Assessment sheet 6.6 Name:... Teacher feedback: Class:... Due date:... Parent/Guardian signature:... Simplif each of the following four epressions. a + 4b a 6b PAS4.. The formula used to calculate the surface area of a clinder is SA = pr(r + h), where r represents the radius of the clinder, h is the height of the clinder and SA is the surface area. g 4w PAS4.. r h 8z z PAS m n m PAS4.. 9 Using π =.4, calculate the surface area of a clinder with a radius of 6.5 cm and a height of cm. Give our answer to the nearest cm. PAS4..6 Evaluate the following four epressions if =, = and z = z PAS4..6 Epand the following four epressions and simplif where appropriate. 0 (k + ) PAS z PAS4..6 4a(a 5) PAS PAS4..6 6( ) PAS z PAS4..6 7g(g + 9) + 4(g 5) PAS4..5 Factorise each of the following epressions b taking out a common factor. 4 d 5 PAS4.. 0

16 for New South Wales 5. Pathwa0 5 0m + 5n PAS4.. k 7 = PAS PAS p 8p PAS4.. Simplif each of the following algebraic fractions. Show all working in the space provided PAS4..4 a 4 -- = -- 8 PAS f 5 = 7f + PAS4.4. Substitute the number in the grouping smbols into its associated equation to determine whether it is a solution to the equation. 6 = 5 ( ) PAS PAS m + 7 = () PAS PAS4..4 z PAS4..4 Solve the following four equations b undoing the operations that have been performed on the pronumerals. p + = 5 PAS z k + 9 = 4 ( -- ) PAS b 5 = 6b 8 () PAS I think of a number then multipl it b 5. If I add 4 then divide b 4, m answer is 6. Form an equation, letting represent the number I am thinking of. Then solve the equation to determine the number. PAS

17 for New South Wales 5. Pathwa 0 Name:... Assessment sheet 7.6 Teacher feedback: Chapter 7 Geometr pages 77 8 Class:... Due date:... Parent/Guardian signature:... Find the complement and supplement of 7. SGS º Find the value of the pronumeral in each of the following diagrams. In each case provide a reason for our answer. 9 8º 40º 5 0 SGS º 8º Fill in the gaps for each of the following. a 5 mm = cm 4 9º b 400 cm = km MS º Calculate the perimeter of the following figure. MS cm 6 50º 5º 6 cm 7 Calculate the area of the shape in question. 50º MS

18 for New South Wales 5. Pathwa0 Calculate the area of the following two shapes. Calculate the surface area and the volume for the following two figures. 4 8 m 6 cm 6 cm 8 cm 6 m m MS4.., MS cm 5 4 mm 4.9 cm. mm 8. cm mm MS4.., MS4.. 6 mm MS Calculate the perimeter and the area of the following sector. MS A water tank in the shape of a clinder has a base diameter of m and a height of m. How man litres (to the nearest litre) could the tank hold when full? MS4.., MS mm 7 Calculate the perimeter and the area of the following figure. MS cm 06

19 for New South Wales 5. Pathwa 0 Name:... Chapter 8 Coordinate geometr pages 9 66 Assessment sheet 8.6 Teacher feedback: Class:... Due date:... Parent/Guardian signature:... Consider the straight lines with the equations = -, =, = 0 and = 0 in answering questions and. Complete the tables of values and then use the coordinates to plot each line on the one set of aes using the grid lines provided. PAS5...7 a = b = 0 Complete the two table of values below and plot the graphs of = + and = + on the one set of aes using an appropriate scale on the grid lines provided. PAS5... a = + 0 b = c = 0 0 d = Identif the - and -intercepts of the straight lines = + and = +. PAS5...8 What do ou notice about the graphs of the straight lines = 0 and = 0? PAS5...9, PAS Describe the slopes of the two graphs drawn in question as positive or negative b following the line from left to right. PAS

20 for New South Wales 5. Pathwa0 6 The graph of = 4 is shown on the grid lines provided. Using the two points given, construct a right-angled triangle and use it to find the gradient of the line. PAS = In the space provided, sketch the graph of = using the gradient intercept method. PAS Find the gradient of the line joining the two points (, ) and (0, 6). PAS5...6 Determine the midpoint of the interval from the diagram given. PAS Find the gradient of the linear graph shown. PAS (, 4) 4 (4, ) 4 5 Plot the points A(, ) and B(, ) onto a set of aes on the grid lines provided. Join AB and draw a vertical line through A and a horizontal line through B. Let these lines intersect at C to form a right-angled triangle ABC. PAS For the graph given below, find: iii the gradient, m iii the -intercept, b iii the rule, using our values for m and b found above. PAS Use Pthagoras theorem to find the length of AB in question above. PAS

21 for New South Wales 5. Pathwa 0 Name:... Assessment sheet 9.6 Teacher feedback: Chapter 9 Probabilit pages Class:... Due date:... Parent/Guardian signature:... A four-sided die, numbered from to 4, is rolled and the outcomes noted. Use this information to answer questions to 5. Give the sample space for the eperiment. NS4.4. List the set of prime numbers possible. NS4.4. What is the chance that a will result? NS Epress the probabilit of rolling an even number as a fraction. NS A bag contains red, blue and orange balls. If the chance of drawing out a red ball is and the chance of drawing out a blue ball is --, what is the chance of drawing out an orange ball? NS A game consists of throwing two dice. The two numbers on the upper faces are multiplied. You win if this resulting number is odd and ou lose if it is even. Is this game fair? Justif our answer with mathematical evidence. NS What is the chance that a 6 will result? NS4.4.5 A card is chosen from a normal deck of plaing cards. Answer questions 6 to 8 for this eperiment. 6 If this card is a red picture card, list possible outcomes. NS Describe the elements in the complementar event. NS Calculate the probabilit of this complementar event. NS4.4.8 A biased coin has resulted in 4 heads from 60 tosses. What is the relative frequenc of obtaining a tail on the net toss? NS

22 for New South Wales 5. Pathwa0 A school has an enrolment of 50 students. The number of students visiting the canteen for lunch each da last week is shown in the following table. Da What is the probabilit that a student will visit the canteen net Monda? NS5... Number of students Monda 56 Tuesda 7 Wednesda 45 Thursda 5 Frida 6 5 Determine the eperimental probabilit of drawing a red card on the net trial. NS What is the eperimental probabilit that the net card will not be a diamond? NS5...4 Each letter of the words MATHS QUEST is written on a card and the cards are then shuffled. One card is chosen at random. 7 What is the probabilit that the card has an E on it?ns5...4 What is the probabilit a student will not visit the canteen net Frida? NS5... A card is drawn from a normal deck of plaing cards and its suit noted. The card is replaced before another card is drawn. The results of 00 draws gave the following results. Card Number Heart Diamond 4 Club 8 Spade 6 8 What is the probabilit that the card has a vowel written on it?ns What is the probabilit there is a consonant written on the card? NS What is the total of the probabilities in questions 8 and 9? NS Complete the following: P(Heart) = = 00 NS5... 0

23 Chapter 0 Right-angled trigonometr pages 95 4 for New South Wales 5. Pathwa 0 Name:... Assessment sheet0.6 Teacher feedback: Class:... Due date:... Parent/Guardian signature:... Use the following figure to answer questions and. a Which side is the hpotenuse? b Which side is adjacent to the angle θ? c Which side is opposite the angle θ? MS5... Write an epression for each of the following. a b c sin α tan θ cos α θ MS5...4, MS5...5 Use the following figure to answer questions to 5. α z P 6 The sides of a triangle are sometimes labelled with lower-case letters of the opposite angle. Use this technique to label the sides of the following triangle. MS Use a calculator to determine each of the following, correct to 4 decimal places. a cos b sin 9 c tan 8 MS5...6 For the figures provided in questions 8 to 0, calculate the value of the pronumeral correct to decimal place. 8 M T R A.5 cm W X Measure the lengths of the sides WN and PN. Use these measurements to calculate the value of tan W (correct to decimal places). N 9 b mm 4 Measure the lengths of the sides WX and AX. Use these measurements to calculate the value of tan W (correct to decimal places). 0 6 mm 5 Comment on our answers to questions and 4. MS5... 7º MS5...8

24 for New South Wales 5. Pathwa0 A stake is used to support a tree so that the tree grows verticall, as shown in the diagram. Use this information to answer questions and. Stake 50.5 m 6 Label the angle of elevation in the figure below. MS5...0 MS5...8 Calculate the length of the stake, to the nearest metre. How far from the base of the tree is the base of the stake on the ground? 7 From the top of a 0-m vertical cliff, Jim views a boat at sea at an angle of depression of º. What distance is the boat from the shore? 0 m º Find the size of the angle θ in each of the following, to the nearest degree. a tan θ = 4.47 b cos θ = c sin θ = Find the values of the unknown angles in the following two triangles to the nearest degree. MS5... A ladder leans against a brick wall, as shown in the diagram. Use the measurements provided to answer the following two questions. 4 m 4. cm.57 m 6. cm 8 What angle does the base of the ladder make with the ground, to the nearest degree? MS mm 9 How far up the wall does the ladder reach? MS mm MS5...9

25 Chapter Graphs pages 5 68 for New South Wales 5. Pathwa 0 Name:... Assessment sheet.6 Teacher feedback: Class:... Due date:... Parent/Guardian signature:... Consider the straight line graph of the equation + 6 = 9 when answering the following three questions. Determine the -intercept. PAS5...8 Find the -intercept. PAS5...8 In the space provided, sketch a graph of the equation. Consider the quadratic equation = 6 when answering the following four questions. 8 Complete this table of values. 0 4 PAS Plot these points on the following grid to show the graph of = 6. PAS What is the equation of the -ais? PAS Write the equation of the -ais. PAS Describe the graph of the line = 5. PAS Use substitution to determine whether the point (, ) lies on the line 6 = 4. Show our working in the space provided. PAS From our graph, determine the coordinates of the -intercepts. PAS5...8 State the coordinates of the - intercept. PAS5...8

26 for New South Wales 5. Pathwa0 The graph of = is a simple concave-up parabola. Describe the changes which would occur in moving from this curve to the following three parabolas. Provide a sketch of each parabola on a separate set of aes in the space provided (along with a sketch of = ). State the coordinates of the turning point for each parabola. 6 Plot the points on this grid. PAS5... = + 4 PAS What are the coordinates of the - intercept? PAS5...8 Consider the hperbola = -- when answering the following three questions. = PAS Complete this table of values PAS Plot the points on this grid. PAS = ( + ) PAS5... Consider the eponential function = in answering the following three questions. 5 Complete this table of values. 0 PAS Give the equations of the two asmptotes. PAS5...9, PAS