Write Your Answers in the Space Provided. Show All Necessary Working Out

Assessment tasks

Assessment 1

Write your answers in the space provided. Show all necessary working out.

eq1

(b) What fraction of $3 is 50 cents?

2 Write these fractions as decimals:

(a) / eq2
(b) / eq3
(c) / eq4
(d) / eq5

3 Use your calculator to find the value of the following, giving your answer to two decimal places:

(a) / 18.2 ´ 6.94
(b) / 0.212
(c) / eq6

4 Austin spends eq7 of his $630 weekly wage on rent and eq8 on repaying the loan for his car. How much money does he have left for other expenses?

5 What number is halfway between:

(i) 0.7 and 1.5

(ii) – 9 and – 3

6 Find the answer to each of the following:

(a) / 3 ´ – 4
(b) / – 8.2 – 2.4
(c) / eq9
(d) / – 8 ´ (– 3 + 5)
(e) / 50 ¸ – 5 ´ 2

7 (a) Write each of the following as a percentage by multiplying by 100:

(i) / eq10
(ii) / eq11
(iii) / 0.08

(b) Random breath tests are used to determine whether a driver has drunk too much alcohol to drive safely. On New Year’s Eve, 2500 drivers were tested and 75 were found to be above the legal limit and charged.

What percentage of those tested was charged?

8 Following the screening of a new movie 120 people were surveyed.
35% said that it was ‘the best movie that they had seen all year’.

How many people made this claim?

9 Shonky Real Estate charge a commission of 5% on the first $30 000 of a sale and 2% on the balance. If they sell a villa for $195 000 find the:

(a) commission earned on the first $30 000.

(b) commission earned on the remainder.

10 Harry Norman Discounts are having a ‘15% off’ sale on all items. How much will you pay for a DVD player priced at $680?

11 Zoran invested $9000 in an account earning 4% per annum simple interest.
How much interest would he have received after:

(a) 1 year

(b) 5 years

12 (a) Find the selling price of a $24 hat after a 10% G.S.T. is added.

(b) Find the original cost of a soccer ball with a GST included price of $39.60 if the rate of GST is 10%.

13 Find the meaning of each of the following from Section 1 of your module notes.

term / meaning
(a) numerator
(b) integer
(c) principal
(d) GST

Assessment 2

Write your answers in the space provided. Remember to show all your working.

1 If a=2, b= –3 and c=4, evaluate each of these algebraic expressions. Show all your working. You may use a calculator if you wish.

(a) / 3ab / (b) / ac – b2 / (c) / eq12

2 (a) Use the formula A = eq13 bh to find A if b = 9 and h = 6

(b) The formula eq14 can be used to convert temperature in degrees Fahrenheit (°F) to Celsius degrees (°C).
What would a temperature of 77°F be equivalent to in Celsius degrees?

3 Simplify the following algebraic expressions.

(a) 3a ´ 4ab

(b) 7pq – 8pq + 3p – 2pq

4 Expand and simplify where possible

(a) / 5(2m – 3)
(b) / t(u –5) + 3(t + 7)

5 Solve the following equations:

(a) / m + 16 = 38
(b) / eq15
(c) / 5a + 7 = 2
(d) / 4(y–2) = 35
(e) / eq16

6 I am thinking of a number. If I divide the number by 4 and then add 6 the result is 10. What is the number? Re-write this number puzzle as an equation and solve it to find the number.

7 (a) Name each type of angle drawn below.

______uf01

(b) Name each type of triangle drawn below.

______uf02

(i) a radius
(ii) a minor segment
(iii) an arc / uf03

(d) (i) What is the supplement of 85°?

(ii) What is the complement of 38°?

8 Find the value of the pronumerals in each of the following diagrams. (The diagrams are not drawn to scale and the values cannot be found by measuring).

uf04

9 (a) Calculate x in this triangle

uf05

(b) What is the length of a diagonal of a square of side 6 m?
Give your answer to one decimal place.
[Hint: Draw a diagram first.]

(c) A flagpole is held steady by a wire connected to the pole 8 m above the ground. The wire is also attached to the ground 3 m from the base of the pole. Find the length of the wire correct to 2 decimal places.

uf06

10 Two words have been listed in the following glossary table. Find the meaning of these words from Section 2 of your module notes. For each of the last three parts, write a word (or words) to match the meaning given.

Word / Meaning
(a) / coefficient
(b) / hypotenuse
(c) / An instrument used to measure angles.
(d) / The distance around the outside of a circle.
(e) / An angle that is greater than 90° but less than 180°

Assessment 3

Write your answers in the space provided. Remember to show all your working.

1 A fertilizer mixture contains 18 kg of nitrogen, 18 kg of potash, and 27 kg of phosphate. What is the ratio of nitrogen: potash: phosphate? Give your answer in its simplest form.

2 Write the following ratios in their simplest form. You may start by changing the numbers to the same units.

(a) / eq17
(b) / 50 cents to $2.40

3 The manager of Café O’ conducted a survey. He found that the ratio of bread rolls to sandwiches sold was 3:2 and the ratio of sandwiches to pies sold was 4:1.

(a) If 15 pies were sold on Friday, how many sandwiches were sold?

(b) Using your answer to (a) find how many bread rolls were sold on the same day?

4 Terry and Huon divide their payment for a cleaning job in the ratio 4:3.

(a) What fraction of the total does Terry get?

(b) If the payment is $2779, how much does Terry get?

5 Find the lengths of the sides marked with pronumerals given the ratio of the corresponding sides.

uf07

Answers: / (a) / x = / (b) / m =
y = / n =
z = / p =

6 A girl 1.5 m tall casts a shadow 2.0 m long. At the same time of the day, a man 1.8mtall casts a shadow x cm long.

On the diagram below mark in the given information.

uf08

The ratio (proportion) of the height to the shadow can be written as

eq18

eq19 ______

(b) Find the length of the man’s shadow. ______

______

7 The following table is taken from a Water Board account for Tran’s household.

Meter read from / Period included / Last meter reading / This meter reading / Water used / Average daily use for this period
7 March to 5June / 90 days / 3041kL / 3070kL / 29kL / 0.322kL

During this period, there are two people in the household.
What is the average daily water usage by each person?
Write your answer in litres.

8 An octagonal sign is made by cutting four identical triangles from a rectangle.

uf09

(a) Calculate the area of one of the discarded triangles.

(b) What is the area of the octagonal sign (that is the shaded area)?

9 The McDougall family has bought a new home. Below is a site plan showing the house, pool and garage.

uf10

(a) Find the area of the house.

(b) The pool is in the shape of a rectangle and a semicircle. Find the area of the pool correct to the nearest m2.

(d) Find the amount of water in the pool, in litres.

(e) Pool fences are marked on the diagram. Calculate the total length of the pool fence.

(f) (i) What are the dimensions (length and width) of the block of land?

(ii) Find the area of this block in m2.

(iii) How many blocks of land of this size would fit into 1 hectare?

10 The wheels of this bicycle have a diameter of 64 cm.

(a) / What distance is covered by one revolution of the wheels?
(Answer to the nearest cm) / uf11

(b) How many revolutions are needed for the bicycle to travel a distance of one kilometre?

11 Answer the following questions.

(a) / uf12 / (i) / Name this solid ______
(ii) / Find the area of the square base
______
______
(iii) / Find the volume of this solid
______
______
______
(b) / uf13 / (i) / Find the area of the circular base of this cone to the nearest cm2
______
______
(ii) / Find the volume to the nearest cm3
______
______
(c) / uf14 / (i) / Name this solid
______
(ii) / Calculate the area of the cross-section of this solid
______
______
(iii) / What is the height of this solid
______
(iv) / Find its volume
______
(d) / A kidney shaped medallion is shown below:
uf15 / (i) / What is the height of this medallion in cm?
______
(ii) / Find the volume in cm3
______
______

12 In the space below write three formulas you have learnt in Section 3 of your module notes. For each formula describe how you could apply it in a real life situation. Read the example below first.

Example

Formula: / eq20
Application: / A square based pyramid is designed to hold grain. A farmer can use this volume of a pyramid formula to find how much grain the container holds when full.

(a) Formula

Application

(b) Formula

Application

4930CF: Assessment guide XXX

Ó OTEN, 2005/008/012/06/2006 P0025997