Math Quiz 4 Remedial

Math Quiz 4
Lesson and Remedial

Ratio and Proportion
Indices and Standard Form
Money and Finances
Time

For direct proportion, as one value increases, so does the other value and conversely, as one value decreases, so does the other value. For example, more workers on a job would increase the amount of task done in a certain time.

​​Direct Proportion

Inverse proportion occurs when one value increases and the other decreases. For example, more workers on a job would reduce the time to complete a certain amount of task.

​​Inverse Proportion

Solving Problems Involving Direct Proportion

The Unitary Method

The Ratio Method

​Example: A machine prints four books in 10 minutes. How many will it print in 2 hours?
Important! You need to make sure you are using the same units in your proportion.

Multiple Choice

A machine used to paint white lines on a road uses 250 litres of paint for each 8 km of road marked. Calculate how many litres of paint would be needed for 200 km of road.

• 5000 litres
• 7500 litres
• 4000 litres
• 6250 litres

Multiple Choice

A fruit juice is made by mixing the juices of oranges and mangoes in the ratio of 9 : 2.

If 189 litres of orange juice are used, calculate the number of litres of mango juice needed.

• 60 litres
• 36 litres
• 54 litres
• 42 litres

Divide a quantity to a given ratio

Multiple Choice

A small company makes a profit of $8000. This is divided between the directors in the ratio of their initial investments, and the ratio is 4 : 7 : 5. Calculate the amount of the profit they will each receive.

• Director 1: $3000, Director 2: $4000, Director 3: $1000
• Director 1: $2500, Director 2: $2500, Director 3: $3000
• Director 1: $1500, Director 2: $4500, Director 3: $2000
• Director 1: $2000, Director 2: $3500, Director 3: $2500

Inverse Proportion

Multiple Choice

Chairs in a hall are arranged in 35 rows of 18. How many rows would there be with 21 chairs to a row?

• 32
• 30
• 28
• 25

Multiple Choice

From the previous question: Chairs in a hall are arranged in 35 rows of 18.

How many chairs would there be in each row if there were 15 rows?

• 42
• 45
• 36
• 30

Increase and Decrease by a Given Ratio

Multiple Choice

A photograph measuring 8 cm by 6 cm is enlarged by a ratio 11 : 4. What are the dimensions of the new print?

• 20 cm by 15 cm
• 24 cm by 18 cm
• 18 cm by 13.5 cm
• 22 cm by 16.5 cm

Multiple Choice

A map measuring 60 cm by 25 cm is reduced in the ratio 3 : 5. Calculate the new dimensions of the map.

• 22.5 cm by 9.375 cm
• 25 cm by 10 cm
• 18 cm by 7.5 cm
• 30 cm by 12.5 cm

Laws of Indices

Zero Index

Negative Index

Exponential Equation

Multiple Choice

Without using calculator, evaluate 6³ x 6^-3

• 36
• 6
• 1
• 0

Multiple Choice

Without using calculator, evaluate $$\frac{3^4\times3^2}{3^5}$$

• 12
• 3
• 9
• 6

Multiple Choice

Without using calculator, evaluate 4³ + 25⁰

• 50
• 70
• 64

• 65

Multiple Choice

Find the value of z.

3^{(z + 2)} = 27

• 1
• 3
• 2
• 0

Standard Form

Multiple Choice

Write 784 000 000 000 in standard form.

• 7.84 x 10¹¹

• 784 x 10⁹

• 78.4 x 10¹⁰

• 7.84 x 10¹⁰

Multiple Choice

Write 0.000 000 088 in standard form

• 8.8 x 10⁸

• 0.88 x 10^-7

• 88 x 10^-10

• 8.8 x 10^-8

Multiple Choice

Multiply the following and write your answer in standard form:

500 x 600 million

• 3 x 10¹¹

• 3 x 10¹⁰

• 3 x 10¹²

• 3 x 10⁹

Multiple Choice

Write as ordinary number:

4.2 x 10^-4

• 0.042
• 0.42
• 0.00042
• 0.0042

Fractional Indices

Multiple Choice

Without using calculator, evaluate:

$$81^{\frac{3}{4}}$$

• 27
• 81
• 36
• 64

Multiple Choice

Without using calculator, evaluate:

$$\frac{4^{\frac{5}{2}}}{4^2}$$

• 4
• 8
• 16
• 2

Percentage Profit and Loss

Profit or Loss = Earning - Cost

If the result is positive, then it's profit
If the result is negative, then it's loss

Profit and Loss

Money and Finance

Multiple Choice

At an auction a company sells 150 television sets for an average $65 each. The production cost was $10 000. How much loss did the company make?

• 250
• 1000
• 500
• 150

Multiple Choice

An electrician bought five broken washing machines for $550. He repaired them and sold them for $143 each. What was his percentage profit?

• 20%
• 30%
• 40%
• 50%

Multiple Choice

Students in a school organise a disco. The disco company charges $350 hire charge. The students sell 280 tickets at $2.25. What is the percentage profit?

• 60%
• 100%
• 50%
• 80%

Multiple Choice

$1500 is invested for 6 years at 3.5% simple interest per year. What is the interest earned?

• $315
• $450
• $210
• $600

Multiple Choice

A shipping company borrows $70 million at 5% p.a. compound interest to build a new cruise ship. If it repays the debt after 3 years, how much interest will the company pay?

• $10,500,000

• $11,033,750

• $12,000,000

• $9,500,000

Time: Duration and
12 or 24 hour format

Multiple Choice

A journey to work takes a woman three quarters of an hour. If she catches the bus at 07:55, when does she arrive?

• 08:40
• 09:00
• 08:50
• 08:30

Multiple Choice

The same woman catches a bus home each evening. The journey takes 55 minutes. If she catches the bus at 17:50, when does she arrive?

• 18:45
• 18:30
• 19:00
• 18:15

Multiple Choice

A journey to school takes a boy 22 minutes. What is the latest time he can leave home if he must be at school at 08:40?

• 08:20
• 08:30
• 08:10
• 08:18