Oxford Insight Mathematics Standard Year 11 Pdf
Unformatted text preview: OXFORD INSIGHT MATHEMATICS STANDARD 2 12 UNCORRECTED PAGE PROOF JOHN LEY MICHAEL FULLER DANIEL MANSFIELD ADDITIONAL RESOURCE CONTRIBUTORS BARBARA MARINAKIS ANDREW HOLLAND CONTENTS 1 INVESTMENTS, DEPRECIATION AND LOANS 6 NETWORK CONCEPTS NETWORKS (MS-N2 Network Concepts) FINANCIAL MATHEMATICS (MS-F4 Investments and Loans) 7 ANNUITIES 2 FINANCIAL MATHEMATICS MEASUREMENT 8 NON-LINEAR RELATIONSHIPS AF (MS-M6 Non-right-angled Trigonometry) (MS-F5 Annuities) T NON-RIGHT-ANGLED TRIGONOMETRY ALGEBRA 3 RATES AND RATIOS MEASUREMENT SIMULTANEOUS LINEAR EQUATIONS D 4 R (MS-M7 Rates and ratios) ALGEBRA (MS-A4 Types of Relationships A4.1) (MS-A4 Types of Relationships A4.2) 9 THE NORMAL DISTRIBUTION STATISTICAL ANALYSIS (MS-S5 The Normal Distribution) 10 CRITICAL PATH ANALYSIS NETWORKS 5 BIVARIATE DATA ANALYSIS STATISTICAL ANALYSIS (MS-S4 Bivariate data analysis) (MS-N3 Critical Path Analysis) Answers Glossary Index Acknowledgements 1A 1A 3 Given that a = 3, b = 4 and c = 8, what is the value of abc? A 348 B 15 C 96 D 3.48 1A 4 Given that a = 2, b = 5 and c = 9, what is the value of a(b + c)? A 214 B 54 C 28 D 16 T 2 What is 9.5% expressed as a decimal? A 0.95 B 0.095 C 9.5 D 950 5 What is 20% of 970? A 19 400 B 194 C 1940 D 19.4 R AF D ▶ making compound interest calculations using the formula ▶ making compound interest calculations using a compounded value table ▶ comparing different investment strategies ▶ calculating the price of goods following inflation ▶ calculating new salaries after increases in line with inflation ▶ calculating the appreciated value of items ▶ the mathematics of shares ▶ calculating the salvage value of an item using the declining- balance method of depreciation ▶ calculating declining-balance loan repayments, including the use of tables ▶ calculating payments, charges and balances on credit cards. F IN AN C IAL MATH EMATIC S M S-F 4 IN VESTMEN TS AN D LOAN S 1A 1A Investments, depreciation and loans The main mathematical ideas investigated are: 1 What is the result of 2000 × 0.05 × 3? A 1200 B 30 000 C 2003.05 D 300 1A 6 What is 7.5% of $11 300? A $84 750 B $847.50 C $1506.67 D $1.51 1A 7 How much interest is earned if $1000 is put into a simple interest account paying 5% p.a. for one year? A $5000 B $50 C $500 D $1050 1A 8 $2000 is put into a simple interest account paying 7% p.a. How much is in the account after 1 year? A $2070 B $14 000 C $140 D $2140 1A 9 The options below show relationships between x and y where k and a are constants. Which options shows a general equation for a linear relationship? A y = kx B y = k x 2 C y = _ kx D y = k a x 1A 10 The options below show relationships between x and y where k and a are constants. Which options shows a general equation for an exponential relationship? A y = kx B y = k x 2 C y = _ kx D y = k a x 1B 11 How many days are there in 3 years (excluding leap years)? A 1095 B 36 C 1098 D 156 1B 12 Given that x = 150 and y = 1.1, what is the value of xy2? A 181.5 B 165 C 123.97 D 151.1 1D 13 What is the value of $35 × 1.053? A $36.75 B $36.86 C $110.25 D $40.52 1F 14 A washing machine purchased for $1800 is depreciated by $220 per year. What is the salvage value of the washing machine after 5 years? A $700 B $2900 C $1580 D $920 ARE YOU READY? 1 ARE YOU READY? If you had difficulty with any of these questions or would like further practice, complete one or more of the matching Support sheets available on your obook assess. Q1 Support sheet 1A.1 Multiplying and dividing decimal numbers Q2 Support sheet 1A.2 Converting percentages, fractions and decimals Q3–4 Support sheet 1A.3 Substituting for pronumerals Q5–6 Support sheet 1A.4 Percentage of a quantity Q7–8 Support sheet 1A.5 Understanding the simple interest formula Q9–10 Support sheet 1A.6 Linear and non-linear relationships Q11 Support sheet 1B.1 Converting units of time Q12 Support sheet 1B.2 Evaluating algebraic expressions involving powers Q13 Support sheet 1D.1 Finding cubes of numbers Q14 Support sheet 1F.1 Straight-line depreciation OXFORD UNIVERSITY PRESS Chapter 1 Investments, depreciation and loans 3 1A comparing simple and compound interest investments Exercise 1A Comparing simple and compound interest investments where I = amount of interest in dollars P = the principal, the amount invested (or borrowed) r = interest rate per time period n = number of time periods. Example 1A–1 Calculating simple interest on investments Calculate the simple interest earned on these investments. a $5000 at 6.7% p.a. over 4 years b $2300 at 1.56% per month for 19 months c $3000 at 15% p.a. over 17 months 4 Solve P = $5000, r = 0.067, n = 4 I = Prn = 5000 × 0.067 × 4 = $1340 b P = $2300, r = 0.0156, n = 19 I = Prn = 2300 × 0.0156 × 19 = $681.72 c P = $3000 r = 15 ÷ 100 ÷ 12 = 0.0125 n = 17 I = Prn = 3000 × 0.0125 × 17 = $637.50 Oxford Insight Mathematics Standard 2 Year 12 Think/Apply D a Convert the percentage interest rate to a decimal by dividing by 100. If needed, convert the interest rate to a rate for the specified time period. Substitute the values of P, r and n into the formula I = Prn. Dominic borrows $2200 to buy a guitar. The simple interest rate is 9.75% p.a. and he takes the loan over 2 years. a Find the interest on the loan. b Find the total amount to be repaid. c Find the monthly repayment. a Solve/Think I = Prn Apply The total amount to be repaid is the interest added to the principal. 9.75 100 × 2 = 2200 × _ total to be repaid Monthly repayment = _____________________ number of months of the loan = $429 b Total to be repaid = 2200 + 429 = $2629 c Monthly repayment = _ 24 = $109.54 2629 3 Calculate the total amount to be repaid on a simple interest loan of: a $4500 at 13% p.a. over 3 years b $5750 at 0.9% per month over 15 months c $7100 at 0.031% per day over 19 days d $5290 at 14% p.a. over 17 months. 4 Chad borrows $14 300 to buy a car. The simple interest rate is 12.5% p.a. and he takes the loan over 3 years. Complete the following to find the: □ a interest on the loan = 14 300 × _ 100 × □ = $ b total to be repaid = 14 300 + ____ = $ F INANCIA L MAT HEMAT ICS Simple interest formula I = Prn Example 1A–2 C alculating the monthly repayment for simple interest investments T Simple interest is a type of interest based on a fixed percentage of the original amount invested or borrowed, the principal. Simple interest can be calculated by using the following formula. 2 Calculate the simple interest on the following investments. a $5600 at 13% p.a. for 16 months b $2900 at 15% p.a. for 23 days c $7890 at 18.6% p.a. for 11 months d $3540 at 12.8% p.a. for 53 days R AF simple interest interest that is calculated on the original principal for the lifetime of the investment/ loan; also known as flat rate interest UNDERSTANDING FLUENCY AND COMMUNICATION These resources are available on your obook assess: • Spreadsheet 1A: Compare growth of simple interest and compound interest investments • Worksheet 1A: Simple interest • assess quiz 1A: Test your skills with an auto-correcting multiple-choice quiz 1 Calculate the simple interest earned on these investments. a $6000 at 5.8% p.a. over 3 years b $3200 at 1.1% per month for 13 months c $780 at 0.025% per day for 19 days □ c monthly repayment = _ □ = $ 5 Monica borrows $5800 to buy a bedroom suite. The simple interest rate is 8.6% p.a. and she takes the loan over 4 years. a Find the interest on the loan. b Find the total amount to be repaid. c Find the monthly repayment. OXFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS Chapter 1 Investments, depreciation and loans 5 7 Toby invested $6500 for 4 years at 6.5% p.a. interest compounded annually. a Using a table, find the value of Toby's investment after 4 years. b Find the amount of interest earned by Toby in the 4 years. For a compound interest investment, the interest earned at the end of each time period is added to the principal. This increases the principal that is used to calculate the interest for the next time period. Therefore, with compound interest you are earning interest on the interest you have previously earned. 8 a Complete the table to determine the final value of $980 invested at 3% p.a. compound interest for 4 years. Year Example 1A–3 C alculating the total value of an investment and compound interest earned $2000 is invested for 3 years at 7% p.a. interest compounded annually. a Find the amount the $2000 will grow to after 3 years. b Find the amount of interest earned. $2000 2 $2140 3 $2289.80 4 $2450.09 Balance at end of year 7 _ 100 × 2000 = $140 7 _ 100 × 2140 = $149.80 7 _ 100 × 2289.80 = $160.29 2000 + 140 = $2140 2140 + 2149.80 = $2289.80 2289.80 + 160.29 = $2450.09 The amount the $2000 will grow to after 3 years is $2450.09. a b The amount of interest earned = 2450.09 − 2000 = $450.09 Think Apply Use I = Prn with P = 2000, r = 0.07 and n = 1 to find the interest for the first year of $140. Add $140 to $2000 to get a new principal of $2140, then calculate the interest on $2140. Use I = Prn with n = 1 to calculate the interest each year. The principal each year is the previous principal plus the interest for that year. The interest earned is the total balance less the original principal. Subtract $2000 from the total balance. D b 6 a Complete the table to determine the final value of $2800 invested at 7% p.a. compound interest for 3 years. Year 1 Balance at start of year 2 3 4 Interest Oxford Insight Mathematics Standard 2 Year 12 2 3 4 $2800 $196 $2996 $209.72 9 Adele decided to invest her savings of $10 350 for 5 years at 7.7% p.a. compound interest. a Complete the table. Year Balance at start of year Interest 1 2 3 4 5 6 Balance at end of year b If Adele intends to buy a car that is expected to be valued at $14 495 when her investment matures, will she have enough to buy the car? Explain. c By how much is the investment over or under the value of the car? 10 June receives a gift of $5000 from her grandparents for her 21st birthday. She looks at different investments options, and wants to compare simple and compound interest investments at 5% p.a. a Complete the following table to determine the final values of the different investments after 5 years. Time Balance at end of year $2996 Simple interest at 5% p.a. Compound interest at 5% p.a. Start of first year $5000 $5000 Start of second year $5250 $5250 Start of third year Start of fourth year Start of fifth year Start of sixth year b Calculate the total interest earned. Interest = ____−2800 = $____ 6 F INANCIA L MAT HEMAT ICS Interest P R O B L E M S O LV I N G , R E A S O N I N G A N D J U S T I F I C AT I O N 1 Balance at start of year 1 Balance at end of year b Calculate the total interest earned. c Use digital technology to produce a graph of the value of the investment over 4 years. Solve Year Interest T a Balance at start of year 5 R AF UNDERSTANDING FLUENCY AND COMMUNICATION compound interest interest that is calculated on the current balance of an investment, including the interest from the previous time period b What is the difference in the value of the investments after the 5 years? OXFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS Chapter 1 Investments, depreciation and loans 7 Type the formula =a*B2 into cell C2, where a represents the interest rate per time period expressed as a decimal. Fill down to C5 and beyond. Type the formula =B2+C2 into cell D2 and fill down to D5 and beyond. Type the formula =D2 into cell B3 and fill down to B5 and beyond. A B C D 1 Year Balance at start of year ($) Interest ($) Balance at end of year ($) 2 1 3 2 4 3 5 … T Enter in the amount of the principal (in dollars) into cell B2. 14 An amount of $70 000 is to be invested for 9 years. a Use a spreadsheet to determine the total interest earned on the investment if the initial amount is invested at: i 9.2% p.a. simple interest ii 9.2% p.a. compound interest. b Explain why the final value is different for the two investment options. c On the one set of axes, draw graphs to show how the value of the investment changes for each option over the 9 years. d The graph for simple interest shows a linear relationship. Explain why. e The graph for compound interest shows a non-linear relationship. From the shape, what type of relationship can be seen? (Hint: consider whether it has the shape of a quadratic, cubic, exponential or reciprocal relationship.) Explain your choice. f The graph for a simple interest investment has the equation A = Prn + P where A is the final value of the investment, P is the principal, r is the interest rate and n is the number of time periods. How does this relate to the general equation of y = mx + c? g The graph for compound interest has the equation A = P(1 + r)n. How does this relate to the general equation of y = kax? Does this confirm your choice of non-linear relationship in part e? 15 An amount of $100 000 is to be invested for 10 years. a Use a spreadsheet to determine the final value of the investment if the initial amount is invested at: i 8.5% p.a. simple interest ii 8.5% p.a. compound interest. b Explain why the final value is different for the two investment options. c On the one set of axes, use digital technology to draw graphs that show how the value of the investment changes for each option over the 10 years. d What type of relationship does the graph for simple interest show? Explain. e What type of relationship does the graph for compound interest show? Explain. f Using the fact that simple interest follows a linear model and compound interest follows an exponential model, explain why investors prefer to invest their money using compound interest rather than simple interest. R AF SPREADSHEET APPLICATION We can use a spreadsheet to generate tables for compound interest investments. Open a new spreadsheet and type in the column headings from the example below into cells A1 to C1. Then follow these instructions. SPREADSHEET APPLICATION 11 Leo wants to compare the potential value of two different investment opportunities. Bank A offers a simple interest rate of 6.2% p.a. and bank B offers a compound interest rate of 6.0% p.a., with the interest compounded monthly. a If $10 000 is invested with each bank at the start of the year, which investment will have the higher balance at the end of the first year, and by how much? b To receive the offered interest rates the investments have to be made for a minimum of 2 years. Which investment will have the higher balance at the end of the second year, and by how much? c Explain why the answers to parts a and b are different. D 12 a $1000 is invested at 7% p.a. interest compounding annually. Use a spreadsheet to calculate the value of the investment at the end of each year for 10 years. b Use digital technology to produce a graph showing the value of the investment over a period of 10 years. c On the same set of axes for part b, draw a simple interest graph for the same time period, but with a rate of 9% p.a. d Use the graph drawn in part c to determine the number of years it takes for the two investments to be the same total amount. 8 Oxford Insight Mathematics Standard 2 Year 12 OXFORD UNIVERSITY PRESS F INANCIA L MAT HEMAT ICS 13 a $4000 is invested at 7.4% p.a. interest compounding annually. Use a spreadsheet to create a table showing the value of the investment at the end of each year for 10 years. b Use digital technology to produce a graph showing the value of the investment over a period of 10 years. c Find the time for the investment to be worth $6500. d On the same set of axes for part b, draw a straight line joining the point representing the initial value of the investment and the point representing the investment value after 10 years. e Calculate the gradient of the straight line drawn for part d to help you determine the equivalent simple interest rate. OXFORD UNIVERSITY PRESS Chapter 1 Investments, depreciation and loans 9 1B The compound interest formula Exercise 1B The compound interest formula Compound interest can be calculated by using the following formula. 2 a Use the compound interest formula to calculate the amount of a fixed-term investment of $4000 over 6 years at 7.5% p.a. interest compounding yearly. b Find the total interest earned. 3 a Use the compound interest formula to calculate the amount of a fixed-term investment of $6453 over 3 years at 4.95% p.a. interest compounding yearly. b Find the total interest earned. T In the financial world the principal, or initial amount, is known as the present value of the investment. The amount to which the principal grows is known as the future value of the investment. UNDERSTANDING FLUENCY AND COMMUNICATION These resources are available on your obook assess: • Video tutorial 1B: Watch and listen to an explanation of Example 1B–1 • Spreadsheet 1B.1: Calculate compound interest on an investment • Spreadsheet 1B.2: Calculate the future value of an investment • Spreadsheet 1B.3: The compound interest formula • Worksheet 1B: Compound interest • assess quiz 1B: Test your skills with an auto-correcting multiple-choice quiz 1 a Using the compound interest formula, complete the following to calculate the final amount when $6500 is invested for 7 years at 4.2% p.a. interest compounding annually. r = 4.2 ÷ = 0. n = PV = n FV = PV(1 + r) = (1 + )7 = 6500( )□ = b Complete the following to find the total interest earned. Interest = − $6500 = PV = the present value r = interest rate per compounding period n = number of compounding periods Example 1B–1 Finding the interest earned for a compound interest investment Use the compound interest formula to calculate the future value of a fixed-term investment of $3500 over 7 years at 6.2% p.a. interest compounding quarterly. Solve FV = PV(1 + r)n = 3500 × (1 + 0.0155)28 = 5000 × (1.0155)28 = $5384.01 5 years at 6.5% p.a. interest compounding yearly. b Find the total interest earned. a b 10 Solve Think FV = PV(1 + r)n = 5000 × (1 + 0.065)5 = 5000 × (1.065)5 = $6850.43 PV = $5000 r = 0.065, as the compounding period is annual, the interest rate is the annual rate. n = 5, as the compounding period is annual, the number of time periods is the same as the number of years. Interest = 6850.43 − 5000 = $1850.43 Subtract the present value of $5000 from the answer to part a. Oxford Insight Mathematics Standard 2 Year 12 D a Use the compound interest formula to calculate the amount of a fixed term investment of $5000 over Think Apply There are 4 quarters in a year, so n = 7 × 4 = 28 time periods. Quarterly interest rate is the annual rate divided by 4: r= 0.062 ÷ 4 = 0.0155 Present value is $3500. Calculate to find the number of time periods, then find the interest rate for the required time period. Substitute into the compound interest formula. Usually, the time period is multiplied and the interest rate divided by the same number. Apply The interest rate and the time period must correspond. Substitute into the formula. The interest is calculated by subtracting the original investment amount (the present value) from the future value. OXFORD UNIVERSITY PRESS 4 Using the compound interest formula, complete the following to calculate the amount of a fixed-term investment of $1200 over 5 years at 8.4% p.a. interest compounding quarterly. n = × 4 = r = 0.084 ÷ = PV = FV = PV(1 + r)n = 1200(1 + ) □ = 1200 × ( ) □ = F INANCIA L MAT HEMAT ICS where FV = the future value R AF Example 1B–2 Calculating the future value of a compound interest investment Compound interest formula FV = PV(1 + r)n 5 Use the compound interest formula to calculate the future value of a fixed-term investment of $950 over 3 years at 4.1% p.a. interest compounding quarterly. OXFORD UNIVERSITY PRESS Chapter 1 Investments, depreciation and loan...
View Full Document
Oxford Insight Mathematics Standard Year 11 Pdf
Source: https://www.coursehero.com/file/70887235/Oxford-Yr-12-Standard-2pdf/
Posted by: myersounfee.blogspot.com
0 Response to "Oxford Insight Mathematics Standard Year 11 Pdf"
Post a Comment