Sace Stage 1 General Mathematics

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

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

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

8 cm (c) 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

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 Earning & Spending 1 Earnings & Income Tax 5. John has an annual salary of $49500. Calculate his (a) Weekly salary [1]

(b) Fortnightly 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. [3] Mon Tues Wed Thurs Fri 90 85 80 100 80

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. [3] 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] 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: [10] (a) The net price. (b) The price if the account is paid after 10 days.

Date Order Number Delivered to

Item No Description Quantity Price Total Price 1762 TV/Clock Radio 20 $210 1978 Calculator 100V 40 $27 2763 Keyboard 15 $250 Trade Discount 7.5% = ______

Net 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: [6] Item Price Trade Discount Rate Trade Discount Net Price Desk $400 18% Chair $250 15% Lamp $90 10%

16. 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. Susan was given $4 discount on a dress she purchased. If the discount was 5% of the marked price, calculate the marked price. [2]

18. 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?

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.