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Question 1 (12 marks)
a. Express the following numbers in scientific notation
i. 0.0678
ii. 678 × 104
iii. 678 × 10−5
iv. 678 000 000 (1 mark each)
b. Round off the answer to two decimal places
(2.35+5.43)×√17
3.22×1.244−2.89
(1 mark)
c. Simplifying the following
i. (𝑎𝑏)
3
(𝑐𝑎)
−2
(𝑏𝑧)
4
(1 mark)
ii. 2𝑥 − 5 = 7 + 3𝑥 (1 mark)
iii. (𝑥
2
)
2 + 𝑥
2 + 2𝑥 × 3𝑥
...
Question Preview:
Question 1 (12 marks)
a. Express the following numbers in scientific notation
i. 0.0678
ii. 678 × 104
iii. 678 × 10−5
iv. 678 000 000 (1 mark each)
b. Round off the answer to two decimal places
(2.35+5.43)×√17
3.22×1.244−2.89
(1 mark)
c. Simplifying the following
i. (𝑎𝑏)
3
(𝑐𝑎)
−2
(𝑏𝑧)
4
(1 mark)
ii. 2𝑥 − 5 = 7 + 3𝑥 (1 mark)
iii. (𝑥
2
)
2 + 𝑥
2 + 2𝑥 × 3𝑥
3
(1 mark)
d. 𝑝
𝑞
=
𝑟
𝑚
i. Make 𝑚 the subject of this equation. (1 mark)
ii. Make 𝑟 the subject of this equation. (1 mark)
e. Find the value of 𝑥 in the following equation
5𝑥−2
4
=
2𝑥+5
6
(1 mark)
f. 𝑐
𝑏
= 𝑎
𝑦
, make 𝑦 the subject following the equation. (1 mark)
4
Question 2 (10 marks)
a. 60 students took QBM120. The percentages of the students who got HD and
DI are 15% and 20%.
I. How many students received HD?
(1 mark)
II. How many students received the other grades except HD and DI?
(2 marks)
b. 36 students took MTH328. If 32 students passed the subject, what percent do
not pass?
(1 mark)
c. A taxi charges a flat rate of $5.00 for the first 5 kilometres and then $0.60 per
kilometre. If Susan cannot spend more than $10, what is the longest distance
in kilometres she can travel in the taxi?
(3 marks)
d. Ruth has had an investment that pays 5% annual interest and charges $10
processing fee. If her interest for the year comes to $100, how much money
does she have invested?
(3 marks)
Question 3 (10 marks)
a. The Reliable Chair Company manufactures solid wood tables. The following
are the monthly costs:
Building rent $10,000
General Maintenance $500
Telephone $600
Depreciation $8,000
Utilities $200
Insurance $700
Advertising $3,000
General Office Salaries $7,000
5
The following are the cost for manufacturing 400 chairs per month:
Materials (wood, paints, etc.) $28,000
Direct labour $10,500
Billing $1,500
I. What is the fixed cost per month?
(1 mark)
II. What is the variable cost?
(1 mark)
III. Find the break-even point if the company sets one chair price at $250.
(2 marks)
IV. What was the profit last month if the company sold 600 chairs?
(1 mark)
b. The relation between demand and price for a publisher's line of a statistics book
is given by 𝑝 = 50 −
𝑥
4
where 𝑝 is the price in dollars of one book when 𝑥 books
are demanded.
I. What is the revenue function 𝑅(𝑥)?
(1 mark)
II. Find the number of the book which makes the maximum revenue.
(2 marks)
III. Plot the graph around the 𝑥 value found at II.
(2 marks)
Question 4 (20 marks)
a. You take out a loan of $800 from a bank.
I. If the bank charges you 15% simple interest per year and you don't pay
off any of the loan in 5 years, how much would you owe the bank?
(2 marks)
II. If the bank charges you 15% compound interest per year and you don't
pay off any of the loan in 5 years, how much would you owe the bank?
(2 marks)
6
III. If the bank charges you 15% simple interest per year and you pay off
$140 every half years in 5 years, what is the effective rate of interest
p.a.?
(2 marks)
IV. If the bank charges you 15% compound interest per year, compounded
half yearly and you don't pay off any of the loan in 5 years, what is the
effective annual rate of interest?
(2 marks)
b. A man wants to save $100,000 to pay for his son’s education. An education
fund requires the investors to deposit equal instalments annually at the end of
each year.
I. If interest rate of 8% is paid and the man wants to meet the target in 10
years’ time, how much does the man need to save each year?
(3 marks)
II. If interest rate of 8% is paid and the man wants to deposit $4,651.16
each year, how long does the man need to meet the target?
(4 marks)
c. The following table shows the income tax rate for 2016/2017 financial year for
individuals who are Australian residents for tax purposes.
Income Marginal tax rate Tax payable
$0-$18,200 0% Nil
$18,201- $37,000 19% 19 cents for each $1 over
$18,200
$37,001-$87,000 32.5% $3,572 plus 32.5 cents for
each dollar over $37,000
$87,001-$180,000 37% $19,822 plus 37 cents for
each dollar over $87,000
$180,001 and above 47% $54,232 plus 47 cents for
each dollar over $180,000
John is working at a university and his taxable income is $190,500 in 2016/2017
financial year. Calculate his total tax payable.
(2 marks)
7
d. Trevor and Helen plan to build a new house. The total cost for the house is
$500,000 and the couple have $150,000. They decide to take out a 25 year
fixed home load from a bank for the rest of cost. The current fixed rate is 5.2%
per year. The loan is to be repaid equally at the end of each month over the 25
years. How much is their monthly repayment and how much extra they pay over
the term of the loan?
(3 marks)
Solution in attached
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