Download Mid-year Exam Revision

SACE STAGE 1 MATHEMATICS
MID YEAR EXAM
Revision
Earning & Spending, Mensuration, Interest
Name: _______________________
Mathematics Teacher___________________
Time: 1.5 hours plus 10 minutes reading time should be enough to complete this work.
Students should use their own calculators and Phone Calculators are not to be used.
Students may use two sheets of paper containing hand written notes to assist in answering the questions.
Students should answer all questions on their question sheets in the spaces supplied.
Students should show all working when answering questions, and marks may be deducted if working is not shown.
There are only a few questions involving interest because it is the most recent work we have covered.
Approximately 1/3 of the marks in the exam will be from interest calculations.
SECTION A
Mensuration
1.2
Area
1.
Calculate the area of each of the following figures.
(a)
Rectangle
[2]
15 m
25 m
(b)
Triangle
[2]
14 cm
18 cm
10 cm
22cm
(c)
Circle
[2]
12 cm
(d)
Composite
[3]
12 cm
18 cm
2.
Find x in each of the following figures given they have an area of 36 cm2
(a)
Rectangle
[2]
x cm
9 cm
(b)
Triangle
[2]
10 cm
12 cm
6 cm
x cm
(c)
Circle
[2]
x cm
3.
Find the volume of each of the following. Express the answer in cubic units e.g. cm3 and in Liters.
(a)
Rectangular Prism
[2]
3 cm
12 cm
4 cm
(b)
Triangular Prism
[3]
6 cm
20 cm
(c)
8 cm
Circular Prism
[3]
5 cm
8 cm
(d)
Rectangular Pyramid
[2]
Height
3 cm
4 cm
5 cm
(e)
Triangular Pyramid
[2]
Height = 6cm
Area of base = 6 cm2
(f) Composite
[3]
20 cm
12 cm
30 cm
12 cm
12 cm
1.4
Problem Solving
4.
(a)
Pebble – pave costs $36 per square metre. How much would be charged to lay pebble – pave one
metre wide around a rectangular swimming pool 19 metres long and 7 metres wide?
[3]
(b)
A rectangular concrete drive is to be laid. If the drive is 3 metres wide and 12 metres long, and the
concrete has to be 6 cm thick, how many cubic metres of concrete must be ordered?
[3]
SECTION B
1
5.
Earning & Spending
Earnings & Income Tax
John has an annual salary of $49500. Calculate his
(a)
Weekly salary
[1]
(b)
Fortnightly salary
[1]
(c)
Monthly salary
[1]
6.
Mary is paid $16.40 per hour. Her normal working day is 8 hours for Monday to Friday. She is paid time
and half overtime on time worked more than 8 hours for Monday to Friday and all time worked on
Saturday. She worked the following hours last week. Calculate her pay.
[3]
Mon
Tues
Wed
Thurs
Fri
Sat
8
12
7
10
8
4
7.
Ben receives $1.50 for each clock he assembled in a standard 8 hour day, or a day rate of $4.20 per hour,
which ever is greater. If he assembled 23 clocks on Monday, what was his pay?
[3]
8.
Steven is paid 60 cents for each toy he makes plus a bonus of 15 cents for each toy produced above a
minimum of 80 per day. Last week he made the following number of toys. Calculate his pay.
Mon
Tues
Wed
Thurs
Fri
90
85
80
100
80
[3]
9.
Karen works as a machinist in a clothing factory where she attaches hip pockets to jeans. The standard time
to attach one hip pocket is 0.022 hours. She works a standard 8 hour day and is paid at $12.50 per hour. On
Tuesday she attached 400 hip pockets. Calculate her pay for Tuesday.
[3]
10.
Calculate the commission paid if a sales person sells a vacuum cleaner for $580 and the commission rate is
5%.
[2]
11.
Use the table below to calculate the commission on sales of $2450.
Sales Value
Commission Rate
Up to $1000
No commission Paid
$1000 to $2000
Nil plus 3% of sales above $1000
$2000 to $3000
$300 plus 2,5% of sales above $2000
Over $3000
$550 plus 2% of sales above $3000
12.
James is paid a retainer of $200 per week plus a commission of 15% on sales above $500 per week. Last
week he sold goods worth $1800, what was his pay?
[3]
[3]
2.
Sales Tax & Discounts
13.
An electrical store offers 4.5% discount on goods if they are paid for with cash. If I pay cash for a television
set marked at $850, how much discount do I receive?
[2]
14.
Complete the following invoice and calculate:
(a)
The net price.
(b)
The price if the account is paid after 10 days.
Date
Order Number
Item No
1762
1978
2763
Description
TV/Clock Radio
Calculator 100V
Keyboard
[10]
Delivered to
Quantity
20
40
15
Price
$210
$27
$250
Trade Discount 7.5% =
_______________________
Net Price =
_____________________
Total Price
Terms:2.5% discount 30 days
15.
Calculate the amount of trade discount and hence the net price of each of the following. Complete the
details in the table below:
Item
Desk
Chair
Lamp
16.
Price
$400
$250
$90
Trade Discount Rate
18%
15%
10%
Trade Discount
[6]
Net Price
A lounge suit is marked in a shop at $1500. James receives a discount of $250.
(a)
Calculate discount as a percentage of the marked price.
[3]
(b)
Calculate discount as a percentage of the selling price.
[3]
17.
18.
Susan was given $4 discount on a dress she purchased. If the discount was 5% of the marked price,
calculate the marked price.
[2]
Calculate the sales tax on a CD player priced at $340 given that the tax rate is 35%.
[2]
Interest
19.
(a)
Calculate how much simple interest I would earn on an investment of $10,000 placed in an
account that paid 10% if I left the money there for 20 years.
(b)
How much would I earn if the account paid compound interest of only 7% for the 20 years?
(c)
Explain the difference in answers to a and b above.
20.
How long would it take me to save $2,000 for a holiday if I was able to invest $20,000 in an account that
paid 8% interest compounded quarterly?
21.
Determine the flat interest rate on an account that paid me $400 interest after I had deposited $10,000 and
left it for 2 years.