Year 9 Reviewing number and financial mathematics: free practice test with answers

Sample reviewing number and financial mathematics questions with answers

Try each one before you open the answer.

1. Integer operations

   Evaluate without a calculator:

   (a) $-8 + 15 - (-6)$

   (b) $-4 \times (-7) \div 2$

   (c) $(-3)^3$

   Show the answer

   Key idea: Subtracting a negative is the same as adding its opposite. A product or quotient of two negatives is positive; an odd number of negative factors gives a negative result.

   1. (a) $-8 + 15 = 7$, then $7 - (-6) = 7 + 6 = 13$
   2. (b) $-4 \times (-7) = 28$, then $28 \div 2 = 14$
   3. (c) $(-3)^3 = (-3) \times (-3) \times (-3) = 9 \times (-3) = -27$

   Answer: (a) $13$ (b) $14$ (c) $-27$

2. Decimal places and significant figures

   Round $7.3846$ to:

   (a) $2$ decimal places

   (b) $1$ decimal place

   (c) the nearest whole number

   Show the answer

   Key idea: Look at the digit after the last digit you keep. If it is $5$ or more, round up; otherwise leave the kept digit as it is.

   1. (a) Keep $7.38$; the next digit is $4$, so it stays $7.38$
   2. (b) Keep $7.3$; the next digit is $8$, so round up to $7.4$
   3. (c) Keep $7$; the next digit is $3$, so it stays $7$

   Answer: (a) $7.38$ (b) $7.4$ (c) $7$

3. Operations with fractions

   Evaluate, giving each answer as a mixed number:

   (a) $2\frac{1}{3} + 1\frac{3}{4}$

   (b) $3\frac{1}{5} - 1\frac{2}{3}$

   Show the answer

   Key idea: Change mixed numbers to improper fractions, then use a common denominator to add or subtract.

   1. (a) $\frac{7}{3} + \frac{7}{4} = \frac{28}{12} + \frac{21}{12} = \frac{49}{12} = 4\frac{1}{12}$
   2. (b) $\frac{16}{5} - \frac{5}{3} = \frac{48}{15} - \frac{25}{15} = \frac{23}{15} = 1\frac{8}{15}$

   Answer: (a) $4\frac{1}{12}$ (b) $1\frac{8}{15}$

4. Ratios, rates and best buys

   Runner A completes 10 km in 48 minutes. Runner B runs at 13.5 km/h. Which runner is faster, and by how much (in km/h)?

   Show the answer

   Key idea: Convert both speeds to the same units before comparing.

   1. Convert Runner A's time to hours: $48 \text{ min} = \frac{48}{60} \text{ h} = 0.8 \text{ h}$
   2. Find Runner A's speed: $\text{Speed} = \frac{10}{0.8} = 12.5 \text{ km/h}$
   3. Compare: Runner B runs at 13.5 km/h and Runner A at 12.5 km/h, so Runner B is faster.
   4. Find the difference: $13.5 - 12.5 = 1 \text{ km/h}$

   Answer: Runner B is faster by 1 km/h.

5. Percentage increase and decrease

   (a) Increase $80 by $15\%$.

   (b) Decrease $250 by $8\%$.

   Show the answer

   Key idea: To increase by $r\%$, multiply by $(100 + r)\%$. To decrease by $r\%$, multiply by $(100 - r)\%$.

   1. (a) $80 \times 1.15 = 92$
   2. (b) $250 \times 0.92 = 230$

   Answer: (a) $92 (b) $230

6. Income

   Sophie earns $28.50 per hour. How much does she earn in a week when she works $38$ hours?

   Show the answer

   Key idea: Wage $=$ hourly rate $\times$ number of hours.

   1. $28.50 \times 38 = 28.5 \times 40 - 28.5 \times 2 = 1140 - 57 = 1083$

   Answer: $1083

7. The PAYG income tax system

   Use this tax table for resident taxpayers.

   Taxable income	Tax on this income
   $0 to $\text{\textdollar}18\,200$	Nil
   $\text{\textdollar}18\,201$ to $\text{\textdollar}45\,000$	$16$c for each $1 over $\text{\textdollar}18\,200$
   $\text{\textdollar}45\,001$ to $\text{\textdollar}135\,000$	$4288 plus $30$c for each $1 over $\text{\textdollar}45\,000$
   $\text{\textdollar}135\,001$ to $\text{\textdollar}190\,000$	$\text{\textdollar}31\,288$ plus $37$c for each $1 over $\text{\textdollar}135\,000$
   $\text{\textdollar}190\,001$ and over	$\text{\textdollar}51\,638$ plus $45$c for each $1 over $\text{\textdollar}190\,000$

   Kim's taxable income is $\text{\textdollar}38\,000$. Find the tax payable on this income.

   Show the answer

   Key idea: Find the row of the table that contains the income, then apply that row's rule.

   1. $\text{\textdollar}38\,000$ is in the row $\text{\textdollar}18\,201$ to $\text{\textdollar}45\,000$
   2. Amount over $\text{\textdollar}18\,200$: $38\,000 - 18\,200 = 19\,800$
   3. Tax: $0.16 \times 19\,800 = 3168$

   Answer: $3168

8. Compound interest and depreciation

   $2000 is invested at $5\%$ per annum, compounded annually. Find the balance at the end of each of the first two years, and the total interest earned.

   Show the answer

   Key idea: With compound interest, each year's interest is calculated on the balance at the start of that year.

   1. Year 1: interest $= 0.05 \times 2000 = 100$, balance $= 2100$
   2. Year 2: interest $= 0.05 \times 2100 = 105$, balance $= 2205$
   3. Total interest: $2205 - 2000 = 205$

   Answer: $2100, then $2205; interest $205

Free worksheets for this chapter

Worked examples and a free PDF with answers for each topic.

• Year 9 pythagoras (applied) worksheet
• Year 9 direct proportion, rates and scale worksheet
• Year 9 simple interest worksheet