I85PREP
⌘ K
HSC Minimum Standard Numeracy study materials
HSC Minimum Standard Numeracy study resources

HSC Minimum Standard Numeracy practice questions

One question at a time. Build your HSC Minimum Standard Numeracy understanding.

First 50 of 195 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Numeracy

A recipe uses 250 g of flour for 10 biscuits. How much flour is needed to make 30 biscuits at the same rate?

  1. 500 g
  2. 1000 g
  3. 2500 g
  4. 750 g Correct answer.

Explanation

The number of biscuits triples from 10 to 30, so the flour must also triple. Multiplying 250 g by 3 gives 750 g. Keeping the same ratio for every biscuit is the key idea.

Question 2Numeracy

A shirt costs $48. It is reduced by 25% in a sale. What is the sale price?

  1. $23
  2. $36 Correct answer.
  3. $12
  4. $44

Explanation

A 25% reduction means one quarter of the price is taken off. One quarter of $48 is $12, so the sale price is $48 minus $12, which is $36.

Question 3Numeracy

A bag holds 4 red, 6 blue and 10 green counters. One counter is drawn at random. What is the probability that it is blue?

  1. 3/10 Correct answer.
  2. 6/16
  3. 1/3
  4. 6/10

Explanation

There are 4 + 6 + 10 = 20 counters in total, and 6 are blue. The probability is 6 out of 20, which simplifies to 3/10. Always divide the favourable outcomes by the total outcomes.

Question 4Numeracy

What is 3.6 + 0.75?

  1. 4.11
  2. 4.35 Correct answer.
  3. 3.135
  4. 1.11

Explanation

Line up the decimal points and add: 3.60 + 0.75 = 4.35. Writing 3.6 as 3.60 helps keep the place values aligned.

Question 5Numeracy

A rectangle has a length of 12 cm and a width of 5 cm. What is its perimeter?

  1. 30 cm
  2. 34 cm Correct answer.
  3. 60 cm
  4. 17 cm

Explanation

The perimeter is the distance around the rectangle: 12 + 5 + 12 + 5. This equals 34 cm. Adding the length and width once each gives only half the perimeter.

Question 6Numeracy

A train leaves at 9:45 am and arrives at 11:20 am. How long is the journey?

  1. 1 hour 25 minutes
  2. 2 hours 25 minutes
  3. 1 hour 45 minutes
  4. 1 hour 35 minutes Correct answer.

Explanation

From 9:45 to 10:45 is one hour, and from 10:45 to 11:20 is another 35 minutes. Adding these gives 1 hour 35 minutes.

Question 7Numeracy

Which number is largest?

  1. 0.077
  2. 0.007
  3. 0.7 Correct answer.
  4. 0.07

Explanation

Compare the place values after the decimal point. 0.7 has seven tenths, which is greater than any number with only hundredths or thousandths. The more digits a decimal has does not make it larger.

Question 8Numeracy

A worker earns $22 per hour. She works 7.5 hours in a day. What is her pay for that day?

  1. $154
  2. $165 Correct answer.
  3. $176
  4. $150

Explanation

Multiply the hourly rate by the hours worked: 22 × 7.5. This equals 22 × 7 plus 22 × 0.5, which is 154 + 11 = $165.

Question 9Numeracy

A car travels 180 km in 3 hours. What is its average speed?

  1. 60 km/h Correct answer.
  2. 540 km/h
  3. 45 km/h
  4. 90 km/h

Explanation

Average speed is distance divided by time. Dividing 180 km by 3 hours gives 60 km/h. This is the constant speed that would cover the same distance in the same time.

Question 10Numeracy

A jacket originally costs $80. It is discounted by 15%, then a further 10% is taken off the reduced price. What is the final price?

  1. $68.00
  2. $60.00
  3. $72.00
  4. $61.20 Correct answer.

Explanation

After 15% off, the price is 85% of $80, which is $68. Then 10% off $68 leaves 90% of $68, which is $61.20. The discounts are applied one after the other, not added together.

Question 11Numeracy

A recipe for 4 people needs 300 g of rice. How much rice is needed for 10 people?

  1. 750 g Correct answer.
  2. 600 g
  3. 1200 g
  4. 700 g

Explanation

The amount per person is 300 ÷ 4 = 75 g. For 10 people this is 75 × 10 = 750 g. Scaling by the unit rate keeps the proportion correct.

Question 12Numeracy

A rectangular garden is 9 m long and 6 m wide. A path runs around its outer edge. What is the area of the garden itself?

  1. 45 m²
  2. 30 m²
  3. 54 m² Correct answer.
  4. 15 m²

Explanation

The area of a rectangle is length multiplied by width. Here 9 × 6 = 54 square metres. The perimeter would add the sides rather than multiply them.

Question 13Numeracy

A bag contains 5 red and 7 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?

  1. 10/12
  2. 5/33 Correct answer.
  3. 25/144
  4. 5/22

Explanation

The first red has probability 5/12. After removing one red, 4 red remain out of 11, so the second is 4/11. Multiplying gives 20/132, which simplifies to 5/33.

Question 14Numeracy

A phone plan charges $30 per month plus $0.10 per megabyte over 5 GB. If a user uses 7 GB in a month, what is the bill?

  1. $204.80
  2. $250.00
  3. $230.00
  4. $234.80 Correct answer.

Explanation

The user exceeds the limit by 2 GB, which is 2048 MB. At $0.10 per MB that is $204.80, plus the $30 base fee, giving $234.80.

Question 15Numeracy

A worker is paid $18 per hour for the first 38 hours and $27 per hour for overtime. In one week she works 46 hours. What is her total pay?

  1. $828
  2. $900 Correct answer.
  3. $1242
  4. $864

Explanation

Regular pay is 38 × $18 = $684. Overtime is 8 hours × $27 = $216. Adding gives $900.

Question 16Numeracy

A circular garden has a diameter of 10 m. Using π ≈ 3.14, what is its area?

  1. 15.7 m²
  2. 78.5 m² Correct answer.
  3. 314 m²
  4. 31.4 m²

Explanation

The radius is half the diameter, so r = 5 m. Area = πr² = 3.14 × 25 = 78.5 m². Using the diameter instead of the radius gives the wrong result.

Question 17Numeracy

A recipe uses 2 parts flour to 3 parts sugar by mass. If 450 g of sugar is used, how much flour is needed?

  1. 675 g
  2. 225 g
  3. 300 g Correct answer.
  4. 900 g

Explanation

The ratio of flour to sugar is 2:3. Each part is 450 ÷ 3 = 150 g. Flour is 2 parts, so 2 × 150 = 300 g.

Question 18Numeracy

A tank holds 240 litres. It is 3/8 full. How many more litres are needed to fill it?

  1. 90 L
  2. 180 L
  3. 150 L Correct answer.
  4. 60 L

Explanation

3/8 of 240 is 90 litres already in the tank. The remaining capacity is 240 − 90 = 150 litres.

Question 19Numeracy

A temperature rises from −6 °C to 9 °C. By how many degrees did it rise?

  1. 9 degrees
  2. −15 degrees
  3. 3 degrees
  4. 15 degrees Correct answer.

Explanation

The change is the final temperature minus the starting temperature: 9 − (−6) = 15. Subtracting a negative is the same as adding.

Question 20Numeracy

A shop sells pens at 3 for $2.40. What is the cost of 8 pens?

  1. $6.40 Correct answer.
  2. $7.20
  3. $19.20
  4. $4.80

Explanation

Each pen costs $2.40 ÷ 3 = $0.80. Eight pens cost 8 × $0.80 = $6.40. Finding the unit price makes the scaling straightforward.

Question 21Numeracy

A rectangular room is 5 m by 4 m. Tiles are 50 cm by 50 cm. How many tiles are needed to cover the floor?

  1. 100
  2. 40
  3. 20
  4. 80 Correct answer.

Explanation

The floor area is 5 × 4 = 20 m². Each tile is 0.5 × 0.5 = 0.25 m². Dividing 20 by 0.25 gives 80 tiles.

Question 22Numeracy

A data set shows daily sales of 12, 15, 15, 18 and 40. Which measure best represents the typical daily sale?

  1. The maximum, 40
  2. The median, 15 Correct answer.
  3. The range, 28
  4. The mean, 20

Explanation

The value 40 is much larger than the others and pulls the mean upward. The median of 15 is not affected by this outlier and better represents a typical day.

Question 23Numeracy

A savings account earns 4% simple interest per year. If $500 is deposited, how much interest is earned in 3 years?

  1. $60 Correct answer.
  2. $120
  3. $62.43
  4. $20

Explanation

Simple interest is principal × rate × time. Here 500 × 0.04 × 3 = $60. Simple interest is calculated only on the original amount.

Question 24Numeracy

A map has a scale of 1:50 000. A distance of 4 cm on the map represents what real distance?

  1. 2 km Correct answer.
  2. 500 m
  3. 200 m
  4. 20 km

Explanation

Each centimetre on the map represents 50 000 cm in reality. Four centimetres is 200 000 cm, and dividing by 100 000 converts to 2 km.

Question 25Numeracy

A student scores 18 out of 24 on a test. What is this as a percentage?

  1. 66%
  2. 75% Correct answer.
  3. 80%
  4. 72%

Explanation

Divide the score by the total and multiply by 100: 18 ÷ 24 = 0.75, which is 75%. Converting to a decimal first makes the percentage clear.

Question 26Numeracy

A supermarket sells a 1.5 kg bag of potatoes for $4.50. What is the price per kilogram?

  1. $6.75
  2. $4.50
  3. $3.00 Correct answer.
  4. $2.25

Explanation

Price per kilogram is found by dividing the total cost by the mass in kilograms: 4.50 ÷ 1.5 = 3.00. Checking by multiplication, 1.5 kg × $3.00/kg gives $4.50, which matches the price on the bag.

Question 27Numeracy

A jug contains 2.4 litres of juice. How many 200 mL cups can be filled completely from the jug?

  1. 14
  2. 48
  3. 12 Correct answer.
  4. 10

Explanation

Convert litres to millilitres first: 2.4 L = 2400 mL. Then divide by the cup size: 2400 ÷ 200 = 12 cups.

Question 28Numeracy

A shape is made of a rectangle 8 cm by 3 cm with a square of side 3 cm attached to one short end. What is the total area of the shape?

  1. 30 cm²
  2. 33 cm² Correct answer.
  3. 24 cm²
  4. 39 cm²

Explanation

Split the shape into two parts: the rectangle has area 8 × 3 = 24 cm² and the square has area 3 × 3 = 9 cm². Adding the two parts gives 24 + 9 = 33 cm².

Question 29Numeracy

A bus timetable shows departures every 25 minutes starting at 7:10 am. What is the fourth departure after 7:10 am?

  1. 8:50 am Correct answer.
  2. 8:35 am
  3. 9:00 am
  4. 8:25 am

Explanation

Add 25 minutes repeatedly: 7:35, 8:00, 8:25, 8:50. The fourth departure after 7:10 am is therefore 8:50 am.

Question 30Numeracy

A survey of 40 students found that 25% walk to school. How many students walk to school?

  1. 10 Correct answer.
  2. 25
  3. 4
  4. 16

Explanation

To find 25% of 40, divide 40 by 4 (since 25% is one quarter), giving 10 students. Equivalently, 0.25 × 40 = 10.

Question 31Numeracy

A rectangular sign is 1.2 m wide and 0.8 m high. What is its perimeter?

  1. 4.0 m Correct answer.
  2. 0.96 m
  3. 1.92 m
  4. 2.0 m

Explanation

Perimeter of a rectangle is 2 × (length + width) = 2 × (1.2 + 0.8) = 2 × 2.0 = 4.0 m.

Question 32Numeracy

A number line shows a point halfway between −4 and 6. What number is at that point?

  1. 0
  2. −1
  3. 1 Correct answer.
  4. 2

Explanation

The midpoint is the average of the two end values: (−4 + 6) ÷ 2 = 2 ÷ 2 = 1. Counting 5 units right from −4 also lands on 1.

Question 33Numeracy

A spinner has 8 equal sections numbered 1 to 8. What is the probability of spinning a number greater than 5?

  1. 3/5
  2. 3/8 Correct answer.
  3. 1/2
  4. 5/8

Explanation

The numbers greater than 5 are 6, 7 and 8, which is 3 favourable outcomes out of 8 equally likely sections. The probability is therefore 3/8.

Question 34Numeracy

A cyclist rides 45 km on Saturday and 38 km on Sunday. What is the total distance ridden over the weekend?

  1. 73 km
  2. 93 km
  3. 7 km
  4. 83 km Correct answer.

Explanation

Total distance is the sum of the two daily distances: 45 + 38 = 83 km. Adding the tens (40 + 30 = 70) and ones (5 + 8 = 13) confirms 83.

Question 35Numeracy

A laptop is advertised at $960. A customer pays a 20% deposit. How much deposit is paid?

  1. $240
  2. $192 Correct answer.
  3. $96
  4. $768

Explanation

A 20% deposit means paying 0.20 × 960. Since 10% of 960 is 96, doubling it gives 192, so the deposit is $192.

Question 36Numeracy

A recipe needs 3/4 cup of milk for 6 muffins. How much milk is needed for 10 muffins at the same rate?

  1. 1 1/4 cups Correct answer.
  2. 1 cup
  3. 1 1/2 cups
  4. 1 3/4 cups

Explanation

Find the amount per muffin: 3/4 ÷ 6 = 1/8 cup. For 10 muffins, multiply 1/8 × 10 = 10/8 = 1 1/4 cups.

Question 37Numeracy

A rectangular tank is 2 m long, 1.5 m wide and 1 m deep. How many litres of water will it hold when full?

  1. 3000 L Correct answer.
  2. 30 000 L
  3. 3000 mL
  4. 300 L

Explanation

Volume = 2 × 1.5 × 1 = 3 cubic metres. Since 1 cubic metre holds 1000 litres, the tank holds 3 × 1000 = 3000 litres.

Question 38Numeracy

A bank charges a monthly account fee of $6.50. What is the total fee charged over one year?

  1. $78.00 Correct answer.
  2. $91.00
  3. $65.00
  4. $72.00

Explanation

There are 12 months in a year, so multiply 6.50 × 12 = 78.00. Checking with 6 × 12 = 72 and 0.50 × 12 = 6 gives 78.

Question 39Numeracy

A student's test marks are 62, 75, 75, 88 and 90. What is the mean mark?

  1. 80
  2. 77
  3. 78 Correct answer.
  4. 75

Explanation

Add the marks: 62 + 75 + 75 + 88 + 90 = 390. Divide by the number of marks: 390 ÷ 5 = 78.

Question 40Numeracy

A rectangular floor is 6 m by 4.5 m. Carpet costs $28 per square metre. What is the cost to carpet the whole floor?

  1. $840
  2. $756 Correct answer.
  3. $504
  4. $588

Explanation

First find the area: 6 × 4.5 = 27 square metres. Then multiply by the rate: 27 × 28 = 756, so the cost is $756.

Question 41Numeracy

A shirt costs $45. It is reduced by 30%. What is the sale price?

  1. $31.50 Correct answer.
  2. $13.50
  3. $30.00
  4. $58.50

Explanation

The discount is 30% of $45, which is 0.30 × 45 = $13.50. Subtract the discount from the original price: 45 − 13.50 = $31.50. Alternatively, 70% of 45 = 31.50.

Question 42Numeracy

A car uses 8 litres of fuel to travel 100 km. How much fuel will it use for a 350 km trip at the same rate?

  1. 28 L Correct answer.
  2. 24 L
  3. 2.8 L
  4. 32 L

Explanation

Find the fuel per kilometre: 8 ÷ 100 = 0.08 L/km. Multiply by 350: 0.08 × 350 = 28 litres.

Question 43Numeracy

A savings balance grows from $1500 to $1620. What is the percentage increase?

  1. 6%
  2. 8% Correct answer.
  3. 12%
  4. 7.5%

Explanation

The increase is 1620 − 1500 = 120. Divide the increase by the original amount: 120 ÷ 1500 = 0.08, which is 8%.

Question 44Numeracy

A rectangular picture is 18 cm by 12 cm. It is enlarged so both dimensions double. By what factor does the area increase?

  1. 2
  2. 3
  3. 4 Correct answer.
  4. 8

Explanation

Original area = 18 × 12 = 216 cm². New area = 36 × 24 = 864 cm². The ratio 864 ÷ 216 = 4, so the area increases by a factor of 4.

Question 45Numeracy

A worker's pay is $840 for a 35-hour week. What is the hourly rate?

  1. $24.00 Correct answer.
  2. $22.00
  3. $26.00
  4. $28.00

Explanation

Hourly rate = total pay ÷ hours worked = 840 ÷ 35. Since 35 × 24 = 840, the rate is $24.00 per hour.

Question 46Numeracy

A container of 5 kg of rice is split into bags of 250 g each. How many bags are filled?

  1. 20 Correct answer.
  2. 15
  3. 25
  4. 50

Explanation

Convert kilograms to grams: 5 kg = 5000 g. Divide by 250: 5000 ÷ 250 = 20 bags.

Question 47Numeracy

A train travels 240 km in 2 hours 30 minutes. What is its average speed in km/h?

  1. 120 km/h
  2. 96 km/h Correct answer.
  3. 100 km/h
  4. 80 km/h

Explanation

Convert the time to hours: 2 hours 30 minutes = 2.5 hours. Speed = distance ÷ time = 240 ÷ 2.5 = 96 km/h.

Question 48Numeracy

A shop offers a 25% discount on a $120 item, then adds 10% GST to the discounted price. What is the final price?

  1. $102.00
  2. $99.00 Correct answer.
  3. $90.00
  4. $108.00

Explanation

After the 25% discount the price is 0.75 × 120 = $90. Adding 10% GST gives 1.10 × 90 = $99.00.

Question 49Numeracy

A data set of weekly sales is 20, 22, 22, 24 and 62. Which statement best describes the effect of the value 62 on the mean and median?

  1. The median is raised more than the mean.
  2. Both are raised by exactly the same amount.
  3. The mean is raised more than the median. Correct answer.
  4. Both the mean and median are unchanged.

Explanation

The median is 22, the middle value, and is unaffected by how large the top value becomes. The mean is 30 and is pulled upward by the outlier 62, so the mean is affected more.

Question 50Numeracy

A rectangular pool is 25 m long and 10 m wide. A tiled border 1 m wide runs around the outside. What is the area of the border?

  1. 50 m²
  2. 24 m²
  3. 100 m²
  4. 74 m² Correct answer.

Explanation

The outer rectangle measures 27 m by 12 m, with area 324 m². The pool area is 25 × 10 = 250 m². The border area is 324 − 250 = 74 m².