CTJan27 Online Year 9 - NAPLAN Practice Test 27022026

1
A jacket is priced at $250. It's first discounted by 20\%, and then an additional 15\% is taken off the discounted price. A customer incorrectly assumes this is equivalent to a single 35\% discount. What is the difference in dollars between the actual final price and the price calculated with the incorrect single 35\% discount?

$7.50

$10.00

$12.50

$0
2
The pie chart shows a family's monthly budget of $4500. To save for a vacation, they decide to decrease their 'Entertainment' budget by 25\%. What will be the new annual budget for Entertainment?

$4050

$337.50

$5400

$4250
3
A company is creating a circular logo. The cost of the special material is $50$ per square meter. The logo's design requires a radius of exactly $r = \frac{\sqrt{7}}{\sqrt{\pi}}$ meters. What is the exact cost of the material for one logo? (Area of a circle $A = \pi r^2$)

$350

$50\pi

$$50\sqrt{7}$

$\frac{350}{\pi}$
4
A company produces gadgets. The total cost function is $C(x) = 15x + 2000$ and the revenue function is $R(x) = 40x$, where $x$ is the number of gadgets sold. The graph shows both functions. The break-even point occurs where cost equals revenue. Which statement is best supported by functions?

The company starts making a profit after selling 80 units.

The company breaks even when revenue reaches $2000.

The company makes a profit of $25 on every unit sold.

The break-even point is at 40 units sold.
5
A traveler exchanges $1500$ USD to EUR. The exchange rate is $1$ USD = $0.92$ EUR. The bank charges a fixed fee of $5$ EUR *plus* a $1.5\%$ commission on the initial EUR amount *before* fees. How many EUR does the traveler receive, rounded to two decimal places?

$1354.30

$1359.30

$1375.00

$1349.53
6
An investor puts $5000 into four different funds (A, B, C, D) at the start of the year. The bar chart shows the final value of the investment in each fund after one year. What is the absolute difference in the percentage return on investment (ROI) between the best and worst-performing funds?

$14%$

$6%$

$10%$

$700
7
A country's national debt is approximately $\\$2.5 \times 10^{13}$, and its population is $5 \times 10^8$ people. If the debt were divided equally among the population, what would the debt per person be?

$$\$50,000$$

$$\$5,000$$

$$\$500,000$$

$$\$20,000$$
8
A smartphone is advertised for $882, a price that already includes a 5\% sales tax. A store offers a special deal where they 'pay the tax,' meaning the customer pays the pre-tax price. What is the price of the phone during this special deal?

$840.00

$837.90

$877.00

$850.00
9
The line chart shows the purchasing power of 100 dollars over a 5-year period due to a constant annual inflation rate. If a specific basket of goods cost 100 dollars in Year 0, what would be the approximate cost of the *same* basket of goods in Year 4?

$112.55

$88.53

$111.47

$112.00
10
A store sells two sizes of olive oil: - Brand A: 750 mL for $10.80. - Brand B: 1.5 L for $20.40. A coupon for Brand B gives a 20\% discount off its price. After applying the coupon, what is the difference in the price per 100 mL between the two brands, rounded to the nearest cent?

$0.35

$0.08

$0.27

$1.09
11
A shopkeeper buys 150 pens at a rate of 120 dollars per 100 pens. He sells $\frac{2}{3}$ of them at a 25\% profit and the remaining $\frac{1}{3}$ at a 15\% loss. What is his net profit percentage on the entire transaction, rounded to one decimal place?

11.7% profit

10.0% profit

5.0% profit

1.7% loss
12
An investment of 5000 dollars grows to 5832 dollars in 2 years with interest compounded annually. What is the annual interest rate?

$8.0%$

$8.3%$

$9.0%$

$4.0%$
13
Let $x$ be the recurring decimal $0.5\overline{18} = 0.5181818...$. When $x$ is expressed as a fraction $\frac{p}{q}$ in its simplest form, what is the value of $p+q$?

$167$

$1502$

$1367$

$215$
14
A country has the following annual income tax brackets: - Up to 15,000: 10% - 15,001 to 60,000: 20% - Above 60,000: 35% An individual earns an annual income of 75,000. What is their *effective tax rate* (total tax divided by total income), rounded to the nearest tenth of a percent?

$21.0%$

$35.0%$

$20.0%$

$21.7%$
15
Sarah invests $2000 in an account with a nominal annual interest rate of 12\%. How much *more* interest will she earn over 2 years if the interest is compounded monthly versus compounded annually? Round your final answer to the nearest cent.

$30.67

$24.00

$539.47

$508.80
16
A company's profit of $\\$1,180,000$ is to be allocated to three departments: Research (R), Marketing (M), and Sales (S). The allocation is done such that for every 3 dollars given to R, M gets 4 dollars . For every 5 dollars given to M, S gets 6 dollars . What is the amount allocated to the Sales department?

$$\$480,000$$

$$\$400,000$$

$$\$300,000$$

$$\$566,400$$
17
An employee receives a 5\% raise in a year where the rate of inflation is 7\%. What is the approximate change in the employee's *real* income (their purchasing power)?

A decrease of about 2%

An increase of 5%

A decrease of 7%

An increase of 2%
18
The pie chart shows the monthly budget for the Kumar family, whose total monthly income is $4,500. Due to an unexpected expense, they had to use half of their 'Savings' allocation for a car repair. How much money was spent on the car repair?

$337.50

$675.00

$450.00

$1,350.00
19
A jacket with a marked price of $250 is offered with two successive discounts. The first discount is 20\% and the second is 15\%. What is the final selling price of the jacket?

$170

$162.50

$175

$215
20
Which of the following numbers is an irrational number?

$\sqrt{121}$

$5.1\overline{8}$

$\frac{\pi}{2}$

$\frac{22}{7}$
21
A television costs $950 before tax. If a Goods and Services Tax (GST) of 18\% is added, what is the total amount a customer has to pay?

$171

$1121

$1021

$968
22
An investment of $10,000 is made for 5 years at an annual interest rate of 6\%. The chart compares the final amount based on different compounding frequencies. Which conclusion is correct?

Compounding annually yields the highest return.

The more frequently the interest is compounded, the higher the final amount.

The compounding frequency has no effect on the final amount.

Compounding semi-annually is worse than compounding annually.
23
A laptop has a cash price of 1,500 dollars. A store offers a hire-purchase plan with a down payment of 300 dollars followed by 12 monthly installments of 110 dollars. How much more does the laptop cost on the hire-purchase plan compared to the cash price?

$110

$120

$1320

$1620
24
A retailer buys a watch for $80. He marks up the price by 60\% to set the selling price. What is his profit if he sells the watch at the marked price?

$128

$48

$80

$60
25
In how many years will a principal of 2,000 dollars amount to 2,480 dollars at a simple interest rate of 8\% per annum?

2.5 years

3 years

3.5 years

4 years
26
The chart below shows Maya's monthly income and expenses for the first four months of the year. In which month did she have the highest net savings (Income - Expenses)?

January

February

March

April
27
Evaluate the expression $(\sqrt[3]{27})^2 \times 3^{-3}$.

1

3

$\frac{1}{3}$

$\frac{1}{9}$
28
An electrician's charges are represented by the linear function $C = 60 + 45h$, where $C$ is the total cost in dollars and $h$ is the number of hours worked. The relationship is shown on the graph. What is the total cost for a job that takes 2.5 hours?

$112.50

$162.50

$172.50

$105.00
29
The final price of a laptop after a 12\% sales tax was added is $1,400. What was the price of the laptop *before* the tax was added? (Round to the nearest dollar).

$1232

$1250

$1568

$1288
30
The population of a small town was 12,000 in 2020. If it increases at a rate of 5\% per year, what will be the approximate population at the end of 2022 (after 2 years)?

13,200

12,600

13,230

13,000
31
Arrange the following numbers from smallest to largest: $0.85$, $\frac{4}{5}$, $82\%$, $\frac{7}{8}$.

$\frac{4}{5}, 82%, 0.85, \frac{7}{8}$

$82%, \frac{4}{5}, 0.85, \frac{7}{8}$

$\frac{4}{5}, 0.85, 82%, \frac{7}{8}$

$\frac{7}{8}, 0.85, 82%, \frac{4}{5}$
32
A 400g can of beans costs 1.80. A larger 650g can of the same beans costs $2.86. Which option represents the better value for money?

The 400g can is better value.

The 650g can is better value.

Both cans offer the same value.

It is impossible to determine the better value.
33
Calculate the value of $(4.2 \times 10^5) \div (2 \times 10^{-2})$ and express the answer in proper scientific notation.

$2.1 \times 10^3$

$21 \times 10^6$

$2.1 \times 10^7$

$2.1 \times 10^{-7}$
34
What is the equation of the line shown in the graph?

$y = -2x + 3$

$y = 2x + 3$

$y = -2x - 3$

$y = -\frac{1}{2}x + 3$
35
Which equation represents the vertical line shown in the graph?

$x = -2$

$y = -2$

$x = 2$

$y + x = -2$
36
The graph of a linear equation is shown below. Which of the following points does *NOT* lie on this line?

$(5, 4)$

$(0, -1)$

$(2, 2)$

$(4, 5)$
37
A bag contains 4 red marbles and 6 blue marbles. A marble is drawn at random, its color is noted, and then it is **replaced**. A second marble is then drawn. What is the probability that *both* marbles drawn are red?

$4/25$

$2/5$

$4/5$

$2/15$
38
From a standard deck of 52 playing cards, two cards are drawn one after another *without replacement*. What is the probability that the first card is a King and the second card is a Queen?

$4/663$

$1/169$

$2/13$

$1/221$
39
The probability that a student passes a math test is $0.6$. The probability that they pass a science test is $0.7$. Assuming the two events are independent, what is the probability that the student fails *both* tests?

$0.12$

$0.42$

$0.70$

$0.58$
40
A box contains 3 green pens and 5 yellow pens. A pen is chosen at random and **not replaced**. Then a second pen is chosen. What is the probability that the two pens are of *different* colors?

$15/28$

$15/56$

$15/32$

$13/28$