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This is the assignment i need completed.
i need the whole assignment checked for any errors. It has already been completed so there shouldn’t be any work needed i just need to make sure all the answers are correct. I do however need some working out shown for around 14 questions (these questions are highlighted in dark green, not light green). The working out needs to support the answer if it is right, and if the answer tha is already given is wrong, please change it so that the working out matches the answer.I NEED THE ASSIGNMENT REVIEWED, EDITED AND COMPELTED AND SENT BACK TO ME WITHIN 4 HOURS OF THIS POST.ALL ADJUSTMENTS MADE TO THE WORD DOCUMENT CAN BE MADE ON THE FILE THAT IS ATTACHED.THANKYOU.
WEEK
2
SEND:
Work for Submission
PROBLEM SOLVING
1
.
Comparing different types of interest
$2
0
00 is invested for a period of 8 years at an interest rate of 10%p.a. Investigate t
h
e differences between the values of the investment with simple interest, interest compounded annually and interest compounded twice annually.
Complete the table below:
· State the formula in terms of t
that can be used to find the value of investment if the deposit of $2 000 compounded annually and twice yearly. The formula for finding the value of investment with simple interest has been done for you.
· Use each of these formulas to find the value of the different types of investment.
Value of investment (A) at the end of each year (nearest dollar) with
Compounded annually
Compounded twice yearly
A
= 2000 +
´´
200010t
100
A
=
A =
1
$2200
$220
5
2
$ 2
4
00
$2
42
0
$24
3
1
3
2662
2680
4
292
8.
20
295
4.
91
30
00
322
1.
02
325
7.
79
3541.12
3591.71
3897.43
3959.86
4287.18
436
5.
75
(a)
Graph all three investments on the grid given below. Use a different colour for each
investment. [Recommendation: use TI-CAS calculator or E
x
cel Spreadsheet to draw
these graphs]
Study the pattern of the graphs and then answer the questions on the following page.
(b)
What pattern does each investment follow over time? Explain the reasons for each pattern.
In the graph the first year of investment and returns are the same. But as time changes the return on investment accumulate with the interest return and gets almost double in the next year. However, the returns in simple interest are always fixed and same over the period. That’s why the trend of the graph is increasing over the time.
(c)
What effect does compounding more often have on the value of the investment?
As it is mentioned above that simple interest always have fixed returns on the investment. But in compounding annually or semi-annually the return rolls over the time and an individual can get higher returns because of this. Most importantly compounding annually and semi-annually also have difference in returns because a person can get dual returns in a year though with a small difference. But with a passage of time difference become more visible comparative to compounded annually investment.
2.
Use a TI-Nspire CAS calculator(Calculator > Menu> Algebra > Solve) or if you are
using the graphics calculator TI-84+, use the Equation Solver.
(a)
Tom’s business will have to replace a machine in four years’ time at an estimated cost of $18 000. How much should be invested now at 7.8% p.a., compounded quarterly, to pay for the machine?
The formula of calculation . By putting values in the formula
18000= P (1.0195)16 => 18000/(1.0195)16= 13215.859
(b)
Sam invests $7300 at compound interest of 4% per period. After two years the investment is worth $9990.
(i) Find the total number of periods that interest is calculated over the two years.
Ans: if the interest return is 16% and the investment should be compounded quarterly over the period the investment will be equal 9990.55. in quarter compounding we divide the interest rate on quarter basis e.g 16/4=4% as it was required.
(ii) What is the annual rate of interest earned on the investment?
The total interest earned over the period is 9990-7300=2690
3.
Jack takes out a personal loan of $25 000 to help finance the building of his holiday house. The terms of his loan specify monthly repayments of $595 over five years, with 15% per annum interest calculated monthly. By calculating the amount still owing on the loan after each month find:
(a) the amount still owing after five months
The payment payable after each month =595
Amount payable after each year with interest=595*12+11
47
=8287
By putting values in monthly compounding= formula
2
500
0= 8287 (.15/12)12*5
25000=
17
462.21
7537.39 still owed by jack
(b)
The interest charged over the 5-year period
The interest charged during the 5 year period => 9175.21
MULTIPLE CHOICE
(Advice: You are encouraged to show the essential workingsso your teacher could explain your mistake if you happen to make the wrong choice.)
To the nearest dollar, $8000 invested for three years at 12% p.a. compound interest, compounding monthly will amount to
A $
10
880
B
$11 239
C
C
$11 446
D
D
$19 446
E
E $247 301
The value of $18 500 compounded annually for 5 years at 9.5 per cent per annum is closest to
A $20 000
B $26 600
C $27 300
D
D $29 100
E
E $31 900
If $1000 is placed in an investment account which pays 8% per annum compounding annually, then the balance in the account after n years is
A
A $80n
B
B $1080n
C
C $1000 × 0.08n
D
D $1000 × 1.08n
E
E ($1000 × 1.08)n
How many months will it take for an investment of $4000 to be worth $6000 if interest is paid at 10% per annum compounding monthly?
A
A 48
B
B 49
C
C 50
D
D 51
E
E 60
An investment account opens with $4500.Compound interest accrues at 8 per cent per annum, credited quarterly.The least number of quarters needed for this account to exceed $6000 is
A 4B 5 C 14 D 15 E 16
6.
I have $1000 to invest for three years. Which of the following would be my best prospect?
A 7.5% per annum simple interest
B
B 7% per annum compounding annually
C
C 6% per annum compounding monthly
D
D $
120
0 paid to me at the end of three years
E
E $31 paid to me at the end of each month for 3 years
Karen and Lee each invest the same amount of money and both receive the same total amount of interest after 10 years. Karen earned 8 per cent interest compounding annually. If Lee was paid simple interest on his investment, then the simple interest would have been closest to
A 6 per cent
B 8 per cent
C 10 per cent
D 12 per cent
E 14 per cent
Brett and Tara each invest $P for a period of two years. Brett will earn 10 per cent per annum simple interest, while Tara will earn 10 per cent per annum compound interest. After two years, the difference in the value of these two investments will be.
A Zero. They both earn the same amount of interest
B
B $P/10 with Tara earning the most interest.
C
C $P/10 with Brett earning the most interest.
D
D $P/100 with Tara earning the most interest.
E
E $P/100 with Brett earning the most interest.
9.
The graph below shows the value of an investment over a 5 year period.
Which of the following statements is true?
A
The investment of $2000 is accruing simple interest, paid every quarter
B
The investment is accruing simple interest, paid every year
C
The investment is accruing compound interest, paid every month
D
The investment is accruing compound interest, paid every quarter
E
The investment is accruing compound interest, paid every year
|
SEND: Work for Submission – Exam Practice |
In Further Mathematics there are two end-of-year examinations. Examination 1 is a set of multiple-choice questions covering the core and the three modules. Business related mathematics is one of the modules.
In Exam 1, there are a total of 40 questions to be completed in 90 minutes with nine of these questions covering the Business related mathematics module. Each question should take, on average, 2 minutes. One mark is given for each correct answer.
In order to obtain practice working under such conditions, we suggest you complete the five multiple-choice questions below.
Tear out this sheet and include it with the rest of your submission for this week.
Restrict your time to 10 minutes only.
It is not necessary to show your working as credit is given for correct answers only.
Circle the letter beside the correct answer.
The compound interest, to the nearest dollar, on $2300 over a period of three years at an interest rate of 5.5% per annum compounded annually is:
A
$2701
B
$380
C
$2680
D
$427
E
$401
2
The amount of money which should be invested at 6.5% per annum compound interest, compounding monthly, if you require $30 000 in four years time is closest to:
A
$23 320
B
$23 148
C
$23 180
D
$28 127
E
$38 881
An investment account opens with $5000. Compound interest accrues at 5.7% per annum, credited quarterly. The least number of quarters needed for the value of this account to exceed $6000 is:
A
3
B
C
12
D
13
E
16
4
Suppose that $215 000 is invested at 4.25% per annum compounding monthly. The amount of interest the investment earns in the fourth year is closest to:
A
$10 582
B
$29182
C
$39 764
D
$244 182
E
$254 764
Questions 5 relates to the following information
Interest
is charged on a loan of $4400 at the rate of 1 % per month on the outstanding balance. Each month, after the interest has been debited, a repayment of $500 is made. The following table summarises the situation after four payments have been made:
|
End of month |
Interest (dollars) |
Repayment (dollars) |
Balance of loan (dollars) |
|
1 2 3 4 |
44.00 39.44 34.83 30.18 |
500 500 |
3944 3483.44 3018.27 2518.27 |
5
The value of b in the table is closest to:
A
$2988.09
B
$2518.27
C
$3488.09
D
$2488.09
E- 2548
WEEK 3
|
SEND: Work for Submission |
MULTIPLE CHOICE
Show the essential workingsso your teacher could explain your mistake if you happen to make the wrong choice
.
Giorgio’s credit card company charge 0.9% monthly interest based on the maximum monthly debt. At the beginning of March, Giorgio owed $1425. During the month he bought $550 worth of purchases. At the end of the month his statement will tell him that he owes:
A $1425
B $1975
C $1979.95
D $1987.83
E $1992.78
2.
Interest payments on a bank account are added on 1 July annually at a rate of 8 per cent per annum on the minimum monthly balance. A sum of $1620 was used to open an account on 15 May 1995. Assuming there had been no deposits or withdrawals, the interest payable on 1 July 1995 was:
A $8.00
B $10.80
C $16.20
D $21.60
E $32.40
Interest on Jerry’s bank account is paid yearly on 30th June and is calculated on the minimum monthly balance. The interest rate is 6 per cent per annum. For the year 1993-94, the complete statement for Jerry’s account, before adding interest, is known.
Date
Credit
Debit
Balance
30 June 1993
Interest $37.00
$2137.00
13 April 1994
$
102
5.00
$1112.00
Assuming no other deposits or further withdrawals were made after 13 April 1994, the
total interest in dollars to be credited to this account on 30th June 1994 is given by the
expression.
0.005 ( (2137 ( 9 + 1112 ( 3)
0.005 ( (21137 ( 10 + 1112 ( 2)
0.005 ( (2000 + 22137 ( 8 + 1112 ( 3)
0.06 ( (2137 ( 9 + 1112 ( 3)
0.06 ( (2137 ( 10 + 1112 ( 2)
|
Interest on a savings account is calculated on the minimum monthly balance at a rate of 6 per cent per annum. The following statement lists all the transactions on an account for July-September 1997. |
|||||
|
Transaction detail |
|||||
| 01 July 1997 |
Balance brought forward |
2000.00 |
|||
| Interest |
185.45 |
2185.45 |
|||
| 18 July 1997 |
Withdrawal |
1520.00 |
665.45 |
||
| 02 Aug 1997 |
250.00 |
915.45 |
|||
| 21 Aug 1997 |
200.00 |
715.45 |
|||
| 10 Sept 1997 |
100.00 |
615.45 |
|||
|
The interest, in dollars, for the month of August is calculated by evaluating. |
|||||
|
A 615.45 ( 0.005
D 715.45 ( 0.005 |
|
A Hi-Fi system with a marked price of $800 is bought on terms of no deposit, a flat interest rate of 11.5% per annum and 24 monthly repayments. The monthly repayment is |
||||
|
A $82.00 |
B $41.00 |
C $37.17 |
D $33.33 |
E $7.67 |
|
A microwave oven is advertised at $300 cash, or 20% deposit and 18 monthly repayments at 16% per annum flat interest. The monthly repayment, to the nearest cent, will be |
||||
| A $3.20 |
B $15.47 |
C $16.53 |
D $19.33 |
E $20.67 |
|
Andrew and Sarah borrow $8500 at a simple interest rate of 16.5 per cent per annum. They will repay the loan, plus interest, in 48 months, the monthly instalment, to the nearest dollar, is |
||||
|
A $177 |
B $206 |
C $232 |
D $294 |
E $349 |
PROBLEM SOLVING: Show your working on A4 paper
1.
The statement below shows all the transactions recorded for a 3 month period
(from the beginning of August to the end of October). The interest rate is 2.9% per annum.
|
Transaction Date |
|||
|
1/8 |
72.80 |
||
|
4/8 |
42.75 |
115.55 |
|
|
30/8 |
110.00 |
5.55 |
|
|
3/9 |
2.65 |
2.90 |
|
|
25/9 |
156.00 |
158.90 |
|
|
13/10 |
42.20 |
116.70 |
Calculate the total interest received for these three months if interest is calculated on the:
(i)
C
D
A
B
10
cm
minimum monthly balance
(ii)
minimumdaily balance
(b)
Comment on the results.
2.
Determine the income tax payable on the gross salary of $128 950
ANS. $60606.50
3.
Michael is paid an hourly rate of $22.50 in his part-time job.
(a)
If he works 18 hours per week for 52 weeks one year, how much did he earns that year? Ans: 21060
How much tax did he pay in that year?
As tax rate under 21600 is 17% so taxable amount will be 21060*.17=3580
What net hourly rate was he paid that year?
Ans: 21060-3580= 17479.8/52= 336.15/18=18.675
4.
Wendy and Frank buy and sell a block of land within the same financial year, making a profit of $62 000.
Ans.
(a) If Wendy has other income of $132 000, and the profit is all hers, how much capital gains tax must be paid on the land?
Ans. 62000*.30=18600
(b)
If Frank has other income of $32 000, and the profit is all his, how much capital gains tax must be paid on the land?
Ans. 62000*.30=18600
5.
The telephone bill is $318.97 after GST is added.
(a)
What was the price before GST was added?
(b)
How much GST must be paid?
6.
Louise buys a home unit for $523 000. What is the value of the stamp duty payable on this home unit?
Ans. 523000*.06=31380+2560=33940
7.
Paul and Belinda bought a farm and paid $19 996 in stamp duty. What was the purchase price of the property?
Ans. 19996-2560=17436/.06= $290600
8.
Russell buys a computer complete with a laser printer on a time payment plan (hire purchase). The package would normally cost $2530. Russell paid $1200 deposit and is repaying $19 a week for 2 years.\
(a) What is the total cost that Russell pay for his computer?
ANS: 52*2=104*19=1976+1200= $3176
(b) What amount of interest does he pay?
ANS: 3176-2530= $646=4.91%
(c) What flat rate of interest is he paying?
3176/646=4.91%
(d) What effective rate of interest is he paying?
ANS: 5.03% as formula for r = [ (1+i/n)^n ] – 1
(e) Would Russell have been better off paying $38 a week for 1 year with the same deposit? Justify your answer by quoting the flat and effective rates of interest.
Ans: there is no difference in the calculation with weekly payment whether he pays $19/week for two year or he pays $38/week for one year. Just the payment period will be change. With $19/ week he has to pay 1976 for two years and in other case with $38/ week he also has to pay the same amount, so there is nothing better by choosing the other option.
SEND: Work for Submission – Exam Practice
In Further Mathematics there are two end-of-year examinations. Examination 1 is a set of multiple-choice questions covering the core and the three modules. Business related mathematics is one of the modules.
In Exam 1, there are a total of 40 questions to be completed in 90 minutes with nine of these questions covering the Business related mathematics module. Each question should take, on average, 2 minutes. One mark is given for each correct answer.
In order to obtain practice working under such conditions, we suggest you complete the five multiple-choice questions below.
Tear out this sheet and include it with the rest of your submission for this week.
Restrict your time to 10 minutes only.
It is not necessary to show your working as credit is given for correct answers only.
Circle the letter beside the correct answer.
1
Geoff’s telephone bill one month is $58.50, including GST, how much would the phone bill be without GST?
A
$64.35
B
$52.65
C
$65.00
D
$53.18
E
$50.87
2
John enters into an arrangement to purchase a car for $
7500
deposit and monthly repayments of $1200 for two years. If the purchase price of the car is $25 990, then the flat rate of interest per annum this represents is closest to:
A
8.9%
B
39.7%
C
19.8%
D
27.9%
E
55.8%
Questions 3 and 4 require the use of the following table
|
Tax subdivision ($) |
(%) Tax payable (marginal rate) |
|
0 – 6000 |
0 |
|
6 001 – 21 600 |
17 |
|
21 601 – 70 000 |
30 |
|
70 001 – 125 000 |
42 |
|
125 001 + |
47 |
3
Genevieve’s gross salary is $62 000 per year. Assuming that there are exactly 52 weeks per year, how much does she pay in income tax per week, correct to the nearest dollar?
A
$284
B
$358
C
$203
D
$304
E
$233
4
If Nathan makes a profit of $10 300 on his investments in one financial year, and his other income for that financial year is $72 500, how much capital gains tax will he pay on the profit he makes on his investments, correct to the nearest dollar?
A
$3090
B
$1751
C
$4841
D
$4326
E
$5150
Question 5 requires the use of the following table
|
Purchase price of property |
Stamp duty payable |
|
0 – 20 000 |
1.4% |
|
20 001 – 115 000 |
$280 plus 2.4% of the value in excess of $20 000 |
|
115 001 – 870 000 |
$2560 plus 6% of the value in excess of $115 000 |
|
More than 870 000 |
5.5% of the value |
5
The value of the stamp duty payable when a house is purchased for $665 500 is closest to:
A
$30 378
B
$33 030
C
$35 590
D
$13 212
E
$7707
WEEK 4
SEND: Work for Submission
|
Watch the powerpoint! Insert your DECV course CD into your computer and then click: 4 h A 6 cm 120 8 cm |
MULTIPLE CHOICE
Show the essential workingsso your teacher could explain your mistake if you happen to make the wrong choice
1.
A washing machine costing $520 depreciates at a constant rate of 15% of its original cost each year.After five years its book value is:
A $130 B $230.73 C $390 D $ 442 E $ 475
An accountancy firm depreciates the value of its computing equipment at a flat rate of 20% per annum.In 1997 a computer was purchased for $4500.After three years the value of the computer will be:
A $ 1800 B $2700 C $ 2800 D $3600 E $ 4440
A car bought for $20 000 depreciates at a reducing balance rate of 10% per year.The book value of this car after five years is closest to:
A $8200 B $10 000 C $ 11 800 D $12 200 E $13 100
A computer, originally worth $2000 depreciates at a rate of 16% per annum.The owner wishes to replace the computer when its value falls to $800.The resale time,
t
can be decided by solving:
A
t
84
.
0
= 0.4 B
6
.
0
16
.
1
=
t
C
800
84
.
0
1
=
+
t
D
800
100
16
2000
´
=
´
´
t
E
4
84
.
0
=
t
The Consumer Price Index in 1990 was 145.3 and in 1991 it was 152.5.The inflation rate for 1991 was:
A 1.0% B 1.1% C 4.7% D 5.0% E 105%
In 1985, the price of a particular book was $12.50.Using 1985 as a base year, a 1994 price index of 140 applies to this book.The 1994 price of this book is:
A $13.90 B $14.00 C $17.50 D $118 000 E $121 000
A $109 000 B $112 000 C $115 000 D $118 000 E $121 000
PROBLEM SOLVING
|
$50 000 is hidden in a box in a shed. What is the purchasing power of this money in seven years, if the average inflation rate is 4.35% per annum? Principal amount = $50,000 Inflation rate = 4.35% n =7 => 50,000 (1.0435)7 = 67362.34 The buying power of 50,000 will be $67362.34 today |
|
A machine originally costing $37 000 is expected to produce 100 000 units. The output of the machine in each of the first three years was 5234, 6286, and 3978 units respectively. Its anticipated scrap value is $5000. Principal amount = $37000 Expected unit produce = 100,000 Cost/unit = 100,000/37000 = $.37 Unit produced 1st year and depreciation =5234 unit Total depreciation cost = 5234* .37 = $1936.58 2nd year total cost and production = 6286*.37 = $2325.82 3rd year total cost and unit production = 3978* .37 = $1471.86 Total cost of three years depreciation = $5734.26 Book value after three year 37000- 5734.26 = 31265.74 Avg. Output/year = (5234+6286+3978)/3 = 5166 unit/year Expected life of the machine = 100,000/5166 = 19.35 year |
|
A construction machine worth $100 000 may be depreciated either at a flat rate of 7.5 per cent per annum or at a reducing balance rate of 10 per cent per annum. (a) Completethe table. Calculate the amount of depreciation and the book value of the machine at the end of nth year under each type of depreciation. Time (years) n Amount of Depreciation (using flat rate) in nth year Book Value (flat rate) at the end of nth year Amount of Depreciation (using reducing balance rate) in nth year Book Value (reducing balance rate) at the end of nth year 1 7500 100,000-7500=92500 10000 0*.1= 10,000 100000-10000=90000 2 7500 92500-7500=85000 10000 90000-10000=80000 3 7500 85000-7500=77500 10000 80000-10000=70000 4 7500 77500-7500=70000 10000 70000-10000=60000 5 7500 70000-7500=62500 10000 60000-10000=50000 (b) For each type of depreciation, write the general formulas in terms of (c) To the nearest dollar what is the difference in the two depreciated values after 5 years? After 5 years the value difference will 62500-50000= 12500 (d) Graph the book value against time for both methods of depreciation on the same set of axes. Choose a suitable scale. Use your calculator or Excel spreadsheet to draw the graphs. (e) Describe each of the graphs – is it linear or non linear, increasing or decreasing? Pattern of the graph is linear because it is decreasing down in the same pattern there is no such variability in the trend of the book value. However, the discount rate has more effect on the book value of the machine comparative to 7.5% depreciation rate. As we can see above in the calculation that there is $2500 difference b/w the values. |
|
| 5. |
What reducing balance rate would cause the value of a car to drop from $8000 to $6645 in three years? If we calculate the value with present value of 8000 on trial basis of balance rate. The rate becomes 8000= P (1+n)3 => 8000/(1+n)3 = if we suppose that balance rate is 7% it shows a very little difference to $6645. With trial method the balance rate comes up to 6.9% where value of the car will be $6652.325 in three years |
|
After depreciating at a reducing balance rate of 12.5% per annum, a yacht is now worth $56 100. What was the yacht worth when it was new six years ago? Round your answer to the nearest $100. Formula of future value with number of year equalling 6 Formula = present value * (1+i)n 56100*(1.125)6 $113730 |
|
The wholesale price of a company’s dining suite in 1995 is $650. In 1990 the wholesale price for the same suite was $495 |
|
Using 1990 as the base year, calculate to one decimal place, the price index for this dining suite in 1995. Formula = A = P(1 + rt) putting the values in the formula 650= 495 (1+r.5) 650/495 =1+5r 1.3131 = 1+5r 1.3131-1 = 5r .3131 =5r .3131/5 = r .0626 6.26% Ans. |
|
The maximum profit a retailer is allowed to make when selling this particular dining suite is 85 per cent of the wholesale price. Calculate the maximum retail price of the suite in 1995. Whole sale price in 1995 = $650 Selling price = 650*.85 =552.5 Maximum retail price of the suit = $552.5 |
|
This year the wholesale price of the dining suite is $650. Calculate the minimum annual percentage increase in the wholesale price that would lead to the wholesale price exceeding $1000 per suite in five years time. |
1000 = 650 (1+r.5)
· 1000/650 = 1+5r
· 1.538 = 1+5r
· R =.538/5 = 10.76% Ans.
SEND: Work for Submission – Exam Practice
In Further Mathematics there are two end-of-year examinations. Examination 1 is a set of multiple-choice questions covering the core and the three modules. Business related mathematics is one of the modules.
In Exam 1, there are a total of 40 questions to be completed in 90 minutes with nine of these questions covering the Business related mathematics module. Each question should take, on average, 2 minutes. One mark is given for each correct answer.
In order to obtain practice working under such conditions, we suggest you complete the five multiple-choice questions below.
Tear out this sheet and include it with the rest of your submission for this week.
Restrict your time to 10 minutes only.
It is not necessary to show your working as credit is given for correct answers only.
Circle the letter beside the correct answer.
1
Suppose that the price of a magazine is $4.40 today. What will be the price of the magazine in 5 years’ time if the average annual inflation rate is 10%?
A
$7.09
B
$6.60
C
$4.62
D
$4.90
E
$2.20
2
A construction company has a machine worth $329 000. If its value depreciates at the rate of 17.5% per annum reducing balance then its book value after five years is closest to:
A
$125 740
B
$287 900
C
$203 260
D
$41 100
E
$205 500
3 A taxi is bought for $31 000 and it depreciates by an average of 28.4 cents perkilometre driven. In one year the car is driven 15 614 km. At the end of its useful lifeits scrap value is $12 000. During its useful life as a taxi it has been driven:
A
44 344 km
B
109 155 km
C
66 901 km
D
42 254 km
E
82515 km
4 The inflation rate for the past 6 years has averaged 3.75% per annum. If the salary of ateacher 6 years ago was $38 000 then the teacher, to maintain the standard of earnings at the present time should be receiving close to:
A
$44 000
B
$45 000
C
$46 000
D
$47 000
E
$48 000
5 On the birth of his daughter in 2007, Bernie decides to put cash savings of $50 000into a safety deposit box in the bank so that he can give it to her on her 21st birthday.In 2028 the purchasing power of this birthday present if the average inflation rate overthis period is 4.1% is closest to:
A
$20 757
B
$43 050
C
$116 261
D
$21503
E
$50 000
WEEK 7
|
SEND: Work for Submission |
1. The magnitudes of angles a and b in the given diagram are
respectively:
A
B
C
102
0
38 cm
27 cm
c
A
125(, 125(
B
118(, 117(
C
117(, 125(
D
125(, 117(
E
117(, 118(
Ans. B
2. To the nearest metre, the length of cable that would connect the
Roofs of two buildings that are 40 metres and 80 metres high
Respectively and are 30 metres apart is:
3 cm
120
0
4 cm
A
B
C
A
40 metres
B
45 metres
C
50 metres
D
55 metres
E
none of the above
Ans. C
3.
In the figure shown, the length of OD in centimetres is
14 cm
x
0
9 cm
19 cm
A
2
B
2
3
C
3
D
2
E
4
Ans. D
3. Two guide wires are used to support a flagpole as shown below.
S
F
H
P
Swimming platform
Pier
River
House
780 m
325 m
155 m
The height of flagpole would be closest to:
A
3 m
B
8 m
C
12 m
D
21 m
E
62 m
Ans. B
5.
A right pyramid with a square base is as shown in the diagram. The height of the pyramid is 3 metres, and the square base has sides of length 8 metres. The length of a sloping edge side in metres in.
A
41
B
52
C
73
D
80
E
137
Ans. B
6.
A right pyramid with a square base is shown in the diagram. The square base has sides of length 10 metres. The length of each sloping edge is also 10 metres. The height of the pyramid, in metres, is
A
40
B
50
C
60
D
200
E
1000
Ans. D
7.
A vertical mast, AD, of height 20 m, is supported by two cables attached to the ground at C and B as shown in the diagram. (CAB is a right angle. Cable CD is of length 40 m and cable BD is of length 30 m. The distance CB, in metres, is
Ans.
A
1700
B
2500
C
3300
D
1300
2000
+
E
500
1200
+
Ans. E
8.
A regular polygon has been divided into triangles. By joining the vertices to the centre of the polygon. Part of this polygon is shown in the given diagram. If each of the angles at the centre is 20o find
(a) The number of sides of this regular polygon.
(b) The size of the other angles a and b in the triangle.
(c) The size of each interior angle of the polygon.
Ans. C
9. State the sum of the interior angles of:
(a) a 7-sided regular polygon
(b) a hexagon
(c) an octagon
Ans. A
10. The angle sum of a regular polygon is 1260o. How many sides does the polygon have?
Ans. 7 , because the formula is (n-2)180=900 , where n = 1260
11. Triangle ABC is isosceles.
Find the length of CB
Ans. 22.97
12. In a circle of centre O, a chord AB is of length 4 cm.
The radius of the circle is 14 cm.
Find the distance of the chord from O.
Ans. 20
13. The midpoints of a square of side length 2 cm are joined to form a new square.
Find the area of the new square.
Ans. 4
SEND: Work for Submission – Exam Practice
See details on the next page.
SEND: Work for Submission – Exam Practice
In Further Mathematics there are two end-of-year examinations. Examination 1 is a set of multiple-choice questions covering the core and the three modules. Geometry and Measurement is one of the modules.
In Exam 1, there are a total of 40 questions to be completed in 90 minutes with nine of these questions covering the Geometry and Measurement module. Each question should take, on average, 2 minutes. One mark is given for each correct answer.
In order to obtain practice working under such conditions, we suggest you complete the five multiple-choice questions below.
Tear out this sheet and include it with the rest of your submission for this week.
Restrict your time to 10 minutes only.
It is not necessary to show your working as credit is given for correct answers only.
Circle the letter beside the correct answer.
1
Angle QPS =
A
10o
B
30o
C
50o
D
110o
E
120o
Ans. C
2
Lines m and l are parallel and cut by a transversal q. The value of z is:
A
65
B
135
C
115
D
25
E
45
Ans. C
3. In the isosceles triangle PRS, PR = PS = 12.5 m.
Q is the midpoint of RS and RS = 6.0 m
The length of PQ in metres, correct to one decimal place is
A
9.5
B
12.1
C
12.412.9
D
12.9
E 15.5
Ans. B
4.
The diagonal of the square is 10 cm. The length of the sides in cm is:
A
5
B
5 eq \r(2)
C
10 eq \r(2)
D
20
E
100
Ans. B
5.
The diagram shows a rectangular prism (cuboids). The dimensions are as marked.
The length of the diagonal AB is closest to:
A
7.1 cm
B
14.1 cm
C
30.0 cm
D
33.2 cm
E
31.6 cm
Ans. 31.6
WEEK 8
SEND: Work for Submission
Show the relevant workings for all the questions including the multiple choice questions.
1.
The value of x in the following figure is
A. 20
B. 25
C. 33
D. 45
E. 55
Ans. E
[Hint: Separate out the similar triangles and match up the corresponding sides and angles]
2.
for triangle ABC
AD = 4 cm
DB = 2 cm
AE = 3 cm
BC = 12 cm
If (ADE = (ACB, then x equals
A
2
9
B
6
C
9
D
10
E
11
Ans. B
3. A model of a ship is made to a scale of 1:300.If the volume of the model is 70 cm3, the volume of the ship is ….. [Hint: Refer to Example 22, Chapter 12 ESSENTIAL textbook]
A
2.10 × 10–2 cm3
B
1.89 × 103 cm3
C
6.30 × 104 cm3
D
6.30 × 106 cm3
E
1.89 × 109 cm3
Ans. A
4. Ben is making a 1:100 model of a car with an engine capacity of 2.3 litres (2300cm3). If Ben wants to include a scale model of the engine, then the capacity of the model engine should be ….. [Hint: Refer to Example 21, Chapter 12 ESSENTIAL textbook]
A
0.0023 cm3
B
0.023 cm3
C
0.23 cm3
D
2.3 cm3
E
23 cm3
Ans. B
5. A helium filled weather balloon has a surface area of 25 m2 when fully inflated. As it is just about to be released, the radius is 75% of its value when the balloon is fully inflated. The surface area just before release is closest to
A6 m2B 11 m2C 14 m2D 19 m2E 33 m2
Ans. D
6. A balloon is leaking. Over a period of 9 hours its radius is reduced to one quarter of its original value. During that time its surface area is
A
reduced to one thirty second of its original value
B
reduced to one sixteenth of its original value
C
reduced to one eighth of its original value
D
reduced to one half of its original value
E
unchanged
Ans. A
7. Triangle ABC is similar to triangle AXY.
AX =
3
2
AB
If the area of (ABC = 108 cm2, the area of (AXY is
A 32 cm2B 48 cm2C 54 cm2D 72 cm2E 81 cm2
Ans. D
( ABC = 108 then AB = 108/c , from AX = 2/3 AB will be , AX=2/3*108/c, so AXC=72 is answer)
8.
A conical container with height,
h, is filled with water to the height
shown.
(a)
The ratio of the volume of
water to the volume of airspace is
A
16:1
B
27:1
C
55:1
D
63:1
E
64:1
Ans. A
(b)
The cone has a capacity of 1280 cm3
The volume of water in the cone is
A 1300 cm3B 960 cm3C 1260 cm3D 1024 cm3E 1300 cm3
Ans. C
9. The volumes of two similar
cuboids are in the ratio 8:125
(a)
What is the ratio of their side lengths?
(b) What is the ratio of their surface area?
Ans. 4:5 and 16:25
10. A water reservoir is shaped like a right circular cone, as shown. AB is the diameter of the circular surface of the cone, and O is the centre of this surface. The height of the cone is 8 metres
(a) A cross section of ABV is shown.
Find the length VB, correct to one decimal place.
(b)
If the reservoir is filled to a depth of 4 metres, find the radius of the circular surface of water.
(c)
If the depth of water is 5.6 metres,
calculate the surface area of the
water; that is, the area of the circle,
centre D (correct to two decimal places).
(d)
If the reservoir is 80 percent full of water, the
volume of water is 80 percent of capacity.
Calculate the depth of water (correct to two
decimal places).
Ans. a is 13.6 , b is 2.8 , c is 45.98, d is 34.01
11. A farmer has his house, H, 780 metres from the pier, P, and 325 metres from a swimming platform, S, as shown. There is also a water pump on the river at W.
(a) Find the distance, in metres, of the swimming platform from the pier.
(b) Through similarity
PS
PH
SH
WH
=
and PH : PS = 12 : 13
Use this result to show that the distance of the water pump from the house is 300 metres.
(c) Find the distance, in metres, from the water pump to the pier.
Ans. a 845 m , b is 0.92 or same ratio, c is 720m
12. A man whose eye is 1.7 metres from the ground when standing 3.5 m in front of a wall 3 m high can just see the top of a tower that is 100 m away from the wall. Find the height of the tower.
(Hint: Draw a labelled diagram using the information given above. Note that the wall in the question is between the man and the tower. Two similar triangles should form part of your diagram.)
Ans. 31.36
13. The solid shape opposite consists of a half cylinder on a rectangular prism.
Find, correct to two decimal places:
(a) The total surface area
(b) The volume
Ans. a is 700 , b is 1000
SEND: Work for Submission – Exam Practice
See details on the next page.
SEND: Work for Submission – Exam Practice
In Further Mathematics there are two end-of-year examinations. Examination 1 is a set of multiple-choice questions covering the core and the three modules. Geometry and Measurement is one of the modules.
In Exam 1, there are a total of 40 questions to be completed in 90 minutes with nine of these questions covering the Geometry and Measurement module. Each question should take, on average, 2 minutes. One mark is given for each correct answer.
In order to obtain practice working under such conditions, we suggest you complete the five multiple-choice questions below.
Tear out this sheet and include it with the rest of your submission for this week.
Restrict your time to 10 minutes only.
It is not necessary to show your working as credit is given for correct answers only.
Circle the letter beside the correct answer.
1
Triangles ABC and XYZ are similar isosceles triangles. The length of XY is:
A
3.3 cm
B
5 cm
C
7.5 cm
D
8 cm
E
9.5 cm
Ans. B
2 The volumes of two similar solids are in the ratio 8 : 27. The ratio of their surface areas is:
A
2 : 3
B
Error! Objects cannot be created from editing field codes.
C
Error! Objects cannot be created from editing field codes.
D
4 : 9
E
Error! Objects cannot be created from editing field codes.
Ans. ????
3
The value of x is:
A
10
B
12.5
C
13
D
15
E
20
Ans. C
4
In the given triangles the length of XZ is 50% greater than AC. The ratio of the areas is:
A
4 : 25
B
9 : 4
C
16 : 9
D
81 : 16
E
7 : 5
Ans. B
5
An inverted right circular cone of capacity 1000 cm3 is filled with water to half of its depth. The volume of water (in cm3) is:
A
125
B
500
C
250
D
300
E
400
Ans. C
Week 9
SEND: Work for Submission
Show the relevant workings for all the questions including the multiple choice questions.
1. Given XZ = 8, XY = 10, sin
a
=
3
2
, then Sin
b
equals
A
4
15
B
15
8
C
12
5
D
5
4
E
6
5
Ans. D
2. In ( ABC(A is
A
30º
B
60º
C
75º
D
90
E
150º
Ans. C
3. In the figure shown (not drawn to scale), ABCD is a rectangle. The angle ACD is
equal to
A
tan–1 0.1
B
tan–1 0.25
C
tan–1 0.5
D
tan–1 0.75
E
tan–1
3
4
Ans. B
4. A rectangle is 8 cm long and 6 cm wide. The acute angle
q
, correct to the nearest degree is
A
37º
B
41º
C
49º
D
74º
E
83º
Ans. C
5. Angle B is closest to
A
52°
B
20° 7(
C
20° 13(
D
65° 19(
E
65° 32(
Ans. D
6. In triangle ABC shown sin x =
7
3
The value of sin y is
A
7
1
B
28
9
C
2
1
D
7
4
E
4
3
Ans. D
Problem Solving Questions 7 to 14 (Copy out the diagram)
7. Children using the swing, shown below find that if they swing high enough,
they will see over the fence. The swing is 0.9 metres above the ground originally.
The swing makes an angle of 62º when it moves from position A to position C.
Find the vertical distance
x
above the ground after the swing moves through 62º?
Ans. ???
8. A five-metre ladder leans against a wall making an angle of 27º. It slides down making an angle of 39º. How far along the horizontal ground has it moved?
Ans. 19 degrees
9.
Trish is working out the height of a communications tower. From point A she takes a sighting of the top of the tower. She then moves 100 metres to point B and takes another sighting.
Use the information to calculate the height of the tower, to the nearest metre.
Ans. 55
10. Find angles B and C. Are there two possible triangles? (Hint: Refer to the ambiguity test for sine rule, page 14)
Ans. angle B is 70 degree and C is 65 degree
11. A vertical mast is secured from its top by straight cables 200 m long fixed at the ground. The cables make angles of 66º with the ground. What is the height of the mast?
(As part of your solution, draw a large labelled diagram and cross-reference it to your working.)
Ans. ??????
A pendulum swings from the vertical through
an angle of 15º on each side of the vertical.
If the pendulum is 90 cm long, what is the
Distance x cm between its highest and lowest points?
Copy out the diagram given and cross-reference
it to your working.
Ans. 6 cm
14. A and B are two points on a coastline. They are 1070 m apart; C is a point at sea.
The angles CAB and CBA have magnitudes of 74º and 69º, respectively.
Find the distance of C from A.
Draw a large labelled diagram and cross-reference it to your working.
Ans. ????
15. In the diagram shown, find the length of
(a) AX
(b) AY
Copy out the diagram given and cross-reference it to your working.
Ans. a is 135 , b is 35
WEEK 10
SEND: Work for Submission
To answer these questions, you’ll need to refer to the topics learnt in the last four weeks. Show the relevant working even for the multiple choice questions.
Part A : Multiple choice questions (Exam practice questions)
1. In ABC, the length AC in centimetres
is determined by evaluating
A
0
120
cos
96
100
+
B
0
120
cos
96
100
–
C
0
60
cos
96
100
–
D
96
36
64
–
+
E
)
120
cos
2
1
(
100
0
+
Ans. A
2. In the diagram shown, the value of c is:
A
13 cm
B
42 cm
C
44 cm
D
49 cm
E
51 cm
Ans. D
3. In the diagram shown, the value
of b is
A
13
B
5
C
37
D
13
E
37
Ans. B
4. The angle xº in the diagram
is closest to
A
12º
B
19º
C
27º
D
36º
E
78º
Ans. C
5. A yacht follows a triangle course MNP as shown. The largest angle between any two legs of the course is closest to
A
50º
B
70º
C
120º
D
130º
E
140º
Ans. A
6. The length BC in centimetres is equal to
A
o
100
sin
12
× sin 30º
B
144 2 12 cos 30
-´
o
C
o
50
cos
100
30
2
2
100
2
30
´
´
–
+
D
o
50
sin
12
× sin 50º
E
o
50
sin
12
× sin 100º
Ans. A
7. For the triangle ABC, (ABC = (, cos( equals
A
–
4
1
B
–
2
1
C
4
1
D
2
1
E
4
3
Ans. E
Questions 8 and 9 refer to the following diagram
8. The value of x is closest to
A
4.08 cm
B
5.82 cm
C
6.73 cm
D
8.60 cm
E
16.66 cm
Ans. A
9. The area of the triangle is closest to
A
A 10.04 cm2
B
B 14.34 cm2
C
C 17.50 cm2
D
D 20.08 cm2
E
E 28.67 cm2
Ans. E
10.
The points M, N and P form the vertices of a triangular course for a yacht race.
MN = MP = 4 km. The bearing of N from M is 070°. The bearing of P from M is 180°
Three people perform different calculations to determine the length of NP in kilometres.
Graeme
NP =
o
16 + 16 2 × 4 × 4 × cos 110
–
Shelley
NP = 2 × 4 × cos 35°
Tran
NP
=
o
o
4sin110
sin35
´
The correct length of NP would be found by
A.
Graeme only.
B.
Tran only.
C.
Graeme and Shelley only.
D.
Graeme and Tran only.
E.
Graeme, Shelley and Tran. [VCAA Exam 1, 2007]
Ans. D
Part B Written answer questions
All relevant workings must be shown clearly in your responses.
1. A farmer has his house built near a river.The house, H, is 780 metres from the pier, P, and 325 metres from the swimming platform, S, shown in the diagram below.Beside the river are two paddocks, PHS and FHS as shown.
(a) Find the area of each paddock
(b) Find the length, FH, in metres, correct to one decimal place.
Ans. a is 76050000 , b is ?? , c is 325
2. Find the areas of the following triangles, correct to two decimal places,
using the most appropriate method.
(a)
(b)
(c)
3. The area of a triangle ABC is 6 cm2. AB = 3 cm and AC = 5 cm.
(a) Find two possible values for the magnitude of angle BAC
(b) Find two possible lengths for BC.
Ans. a 15 and 18 , b is 15 , 20
4.
Find the total area of the figure on the right.
Clearly show all of your working.
Ans. 12m
� EMBED Excel.Chart.8 \s ��
1 2 3 4 5 6 7 8
Refer to page 14 for the important note.
A
D
B
C
Given: AC = 8.5 m
BD = 2 m
BC = 4 m
3 m
8 m
8 m
A
B
C
D
E
height
10 m
10 m
10 m
B
C
D
E
A
A
20 m
C
D
30 m
40 m
B
a
b
60o
70o
P
R
S
Q
l
m
65o
zo
q
S
P
R
12.5 m
12.5 m
6 m
Q
�B
10 cm
30 cm
10 cm
10 cm
A
B
25
22
10
x
4 cm
2 cm
3 cm
12 cm
A
B
C
E
D
x
A
Y
X
B
C
h
� EMBED Equation.3 ���
Volume = 125 m3
Volume = 8 m3
O
D
V
A
B
5.6 m
M
8.m
House
H
P
Swimming platform
Pier
River
Water pump
780 m
325 m
S
W
Always separate out the overlapping similar triangles and match up the corresponding sides and angles.
X
A
B
C
Z
12 cm
12 cm
8 cm
5 cm
Y
6
2
5
x
8
Y
Z
10
(
(
X
300
A
B
C
A
B
C
D
40 cm
30 cm
(
6 cm
8 cm
340
2.4 cm
B
C
A
3.9 cm
8 cm
B
C
A
6 cm
x
y
B
A
C
0.9 m
2.4 m
x
620
2.4 m
ground level
270
390
A
B
850
300
100 m
Height of tower
CTB
HCTB
B
A
C
450
b = 6
a = 5
�
�
c
b
�
b
�
M
N
P
5 km
6 km
10 km
30 0
A
B
C
12 cm
100 0
(
A
B
C
3
4
2
7 cm
35 0
5 cm
x
�
�
�
�
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Chart1
2200
2400
2600
2800
3000
3200
3400
3600
time (years)
Value of investment ($)
Types of Investment
Sheet1
1 2200 2200 2205
2 2400 2420 2431
3 2600 2662 2680
4 2800 2928 2955
5 3000 3221 3258
6 3200 3543 3592
7 3400 3897 3960
8 3600 4287 4366
Sheet1
time (years)
Value of investment ($)
Types of Investment
Sheet2
Sheet3
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