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SACE Stage 2 Essential Mathematics study materials
SACE Stage 2 Essential Mathematics study resources

SACE Stage 2 Essential Mathematics practice questions

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Question 1Essential Mathematics (content domains not enumerated in source)

A car travels 180 km in 2.5 hours. What is its average speed in km/h?

  1. 60 km/h
  2. 45 km/h
  3. 72 km/h Correct answer.
  4. 90 km/h

Explanation

Average speed equals total distance divided by total time, so 180 divided by 2.5 gives 72. Dividing by 2.5 is the same as multiplying by 0.4, which confirms the result.

Question 2Essential Mathematics (content domains not enumerated in source)

A recipe uses 3 cups of flour for every 2 cups of milk. If 9 cups of flour are used, how many cups of milk are needed?

  1. 8
  2. 4
  3. 6 Correct answer.
  4. 4.5

Explanation

The ratio of flour to milk is 3:2, and 9 cups of flour is three times the base amount. Multiplying the milk quantity by the same factor of three gives 6 cups.

Question 3Essential Mathematics (content domains not enumerated in source)

What is 15% of 240?

  1. 30
  2. 48
  3. 36 Correct answer.
  4. 24

Explanation

To find a percentage of a quantity, convert the percentage to a decimal and multiply. So 0.15 multiplied by 240 equals 36.

Question 4Essential Mathematics (content domains not enumerated in source)

A shirt originally priced at $80 is discounted by 25%. What is the sale price?

  1. $60 Correct answer.
  2. $65
  3. $20
  4. $55

Explanation

A 25% discount removes one quarter of the original price, which is $20. Subtracting $20 from $80 leaves a sale price of $60.

Question 5Essential Mathematics (content domains not enumerated in source)

Convert 4.5 kilograms to grams.

  1. 45000 g
  2. 450 g
  3. 45 g
  4. 4500 g Correct answer.

Explanation

One kilogram contains 1000 grams, so multiply the number of kilograms by 1000. Thus 4.5 times 1000 equals 4500 grams.

Question 6Essential Mathematics (content domains not enumerated in source)

A savings account earns simple interest at 4% per year. How much interest is earned on $2500 after 3 years?

  1. $120
  2. $300 Correct answer.
  3. $250
  4. $100

Explanation

Simple interest is calculated as principal times rate times time. Here 2500 times 0.04 times 3 equals $300.

Question 7Essential Mathematics (content domains not enumerated in source)

Which measure of central tendency is most affected by a single very large outlier in a data set?

  1. The median
  2. The range
  3. The mode
  4. The mean Correct answer.

Explanation

The mean uses the sum of all values, so one extreme value pulls it strongly. The median and mode depend on position or frequency and are far more resistant to outliers.

Question 8Essential Mathematics (content domains not enumerated in source)

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

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

Explanation

The outcomes greater than 4 are 5 and 6, giving two favourable outcomes out of six. Simplifying 2/6 gives 1/3.

Question 9Essential Mathematics (content domains not enumerated in source)

A rectangular garden is 12 m long and 7 m wide. What is its perimeter?

  1. 38 m Correct answer.
  2. 19 m
  3. 42 m
  4. 84 m

Explanation

Perimeter of a rectangle is twice the sum of length and width. Adding 12 and 7 gives 19, and doubling gives 38 m.

Question 10Essential Mathematics (content domains not enumerated in source)

A circular table has a radius of 1.5 m. Using pi = 3.14, what is its area to one decimal place?

  1. 9.4 m²
  2. 3.5 m²
  3. 7.1 m² Correct answer.
  4. 4.7 m²

Explanation

Area of a circle is pi times the radius squared. Squaring 1.5 gives 2.25, and multiplying by 3.14 gives about 7.065, which rounds to 7.1 m².

Question 11Essential Mathematics (content domains not enumerated in source)

A ladder 5 m long leans against a wall with its base 3 m from the wall. How high up the wall does the ladder reach?

  1. 4 m Correct answer.
  2. 5.8 m
  3. 2 m
  4. 3.5 m

Explanation

The ladder, wall and ground form a right triangle with the ladder as hypotenuse. Using Pythagoras, the height squared is 25 minus 9, giving 16, so the height is 4 m.

Question 12Essential Mathematics (content domains not enumerated in source)

A car depreciates by 12% of its value each year. If it is worth $20000 now, what is its value after one year?

  1. $2400
  2. $17600 Correct answer.
  3. $18800
  4. $22400

Explanation

Depreciation of 12% means the car retains 88% of its value. Multiplying 20000 by 0.88 gives $17600.

Question 13Essential Mathematics (content domains not enumerated in source)

A worker earns $28.50 per hour and works 38 hours in a week. What is the gross weekly pay?

  1. $1042.50
  2. $1083.00 Correct answer.
  3. $1083.50
  4. $1140.00

Explanation

Gross pay equals the hourly rate multiplied by the hours worked. Multiplying 28.50 by 38 gives $1083.00.

Question 14Essential Mathematics (content domains not enumerated in source)

A data set contains the values 4, 7, 7, 9, 13. What is the mean?

  1. 7.5
  2. 8 Correct answer.
  3. 9
  4. 7

Explanation

The mean is the sum of all values divided by how many there are. The sum is 40 and there are 5 values, so the mean is 8.

Question 15Essential Mathematics (content domains not enumerated in source)

Two events A and B are independent with P(A) = 0.4 and P(B) = 0.5. What is the probability that both occur?

  1. 0.1
  2. 0.45
  3. 0.2 Correct answer.
  4. 0.9

Explanation

For independent events, the probability that both occur is the product of their individual probabilities. Multiplying 0.4 by 0.5 gives 0.2.

Question 16Essential Mathematics (content domains not enumerated in source)

A map uses a scale of 1:50000. A distance of 6 cm on the map represents what actual distance in kilometres?

  1. 300 km
  2. 30 km
  3. 0.3 km
  4. 3 km Correct answer.

Explanation

Each centimetre on the map represents 50000 cm in reality, so 6 cm represents 300000 cm. Dividing by 100000 converts centimetres to kilometres, giving 3 km.

Question 17Essential Mathematics (content domains not enumerated in source)

A tank holds 240 L and is currently 35% full. How many more litres are needed to fill it completely?

  1. 84 L
  2. 156 L Correct answer.
  3. 120 L
  4. 60 L

Explanation

The tank currently holds 0.35 times 240, which is 84 L. The amount still needed is 240 minus 84, giving 156 L.

Question 18Essential Mathematics (content domains not enumerated in source)

A student's test scores are 62, 78, 85, 90 and 95. What is the median score?

  1. 90
  2. 82
  3. 85 Correct answer.
  4. 78

Explanation

The median is the middle value once the data are ordered. With five values in order, the third value is 85.

Question 19Essential Mathematics (content domains not enumerated in source)

A recipe for 4 people requires 300 g of pasta. How much pasta is needed to serve 10 people at the same rate?

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

Explanation

The amount per person is 300 divided by 4, which is 75 g. Multiplying by 10 people gives 750 g.

Question 20Essential Mathematics (content domains not enumerated in source)

A loan of $8000 is repaid with simple interest at 6% per year over 4 years. What is the total amount repaid?

  1. $8480
  2. $1920
  3. $9920 Correct answer.
  4. $10400

Explanation

Simple interest is 8000 times 0.06 times 4, which equals $1920. Adding this interest to the principal gives $9920 in total.

Question 21Essential Mathematics (content domains not enumerated in source)

A box contains 5 red, 3 blue and 2 green marbles. One marble is drawn at random. What is the probability it is blue?

  1. 3/10 Correct answer.
  2. 1/3
  3. 2/10
  4. 5/10

Explanation

There are 3 blue marbles out of a total of 10 marbles. The probability is therefore 3/10, which cannot be simplified further.

Question 22Essential Mathematics (content domains not enumerated in source)

A cone has a base radius of 3 cm and a height of 10 cm. Using pi = 3.14, what is its volume to one decimal place?

  1. 282.6 cm³
  2. 31.4 cm³
  3. 188.4 cm³
  4. 94.2 cm³ Correct answer.

Explanation

Cone volume is one third of pi times radius squared times height. Squaring 3 gives 9, and 9 times 10 times 3.14 divided by 3 equals 94.2 cm³.

Question 23Essential Mathematics (content domains not enumerated in source)

A car uses 8 L of fuel per 100 km. Fuel costs $1.85 per litre. What is the fuel cost for a 450 km trip, to the nearest cent?

  1. $66.60 Correct answer.
  2. $59.20
  3. $83.25
  4. $74.00

Explanation

Fuel used is 8 times 4.5, which equals 36 L for 450 km. Multiplying 36 L by $1.85 per litre gives $66.60.

Question 24Essential Mathematics (content domains not enumerated in source)

A worker earns $32 per hour for the first 38 hours and 1.5 times the normal rate for overtime. If the worker works 44 hours, what is the total pay?

  1. $1504 Correct answer.
  2. $1536
  3. $1408
  4. $1600

Explanation

Normal pay is 38 times 32, which is $1216. Overtime is 6 hours at $48 per hour, giving $288, and adding these totals gives $1504.

Question 25Essential Mathematics (content domains not enumerated in source)

A population grows at 5% per year, compounded annually. If it is 4000 now, what will it be after 2 years, to the nearest whole number?

  1. 4400
  2. 4410 Correct answer.
  3. 4200
  4. 4420

Explanation

Compound growth multiplies the amount by 1.05 each year. Applying the factor twice gives 4000 times 1.1025, which equals 4410.

Question 26Essential Mathematics (content domains not enumerated in source)

A quarterly electricity bill is $186.40 before a 5% GST surcharge is added. What is the total amount payable, to the nearest cent?

  1. $195.27
  2. $186.45
  3. $195.72 Correct answer.
  4. $191.60

Explanation

The surcharge equals 5% of $186.40, which is $9.32, and adding this to the original bill gives the total payable. Rounding to the nearest cent keeps two decimal places, so the answer is $195.72.

Question 27Essential Mathematics (content domains not enumerated in source)

A rectangular room measures 4.2 m by 3.5 m. Carpet costs $46 per square metre. What is the cost to carpet the room?

  1. $1,352.40
  2. $676.20 Correct answer.
  3. $338.10
  4. $354.20

Explanation

The floor area is found by multiplying length by width, giving 4.2 x 3.5 = 14.7 square metres. Multiplying the area by the unit price of $46 per square metre gives $676.20.

Question 28Essential Mathematics (content domains not enumerated in source)

Which of these units is most appropriate for reporting the capacity of a household water tank?

  1. Kilometres
  2. Litres Correct answer.
  3. Milligrams
  4. Hectares

Explanation

Capacity measures how much liquid a container holds, and litres are the standard metric unit for liquid volume at household scale. The other units measure mass, length and land area respectively, so they cannot describe volume.

Question 29Essential Mathematics (content domains not enumerated in source)

A train travels 315 km in 3.5 hours. What is its average speed in kilometres per hour?

  1. 85
  2. 110.25
  3. 90 Correct answer.
  4. 105

Explanation

Average speed equals total distance divided by total time, so 315 divided by 3.5 gives 90 kilometres per hour. Checking by multiplying 90 by 3.5 returns 315 km, confirming the result.

Question 30Essential Mathematics (content domains not enumerated in source)

A data set records the number of pets owned by 20 students. Which display is best for showing how many students own each possible number of pets?

  1. A line graph of cumulative totals
  2. A pie chart of the students' ages
  3. A frequency table or column graph of counts Correct answer.
  4. A scatterplot of pets against age

Explanation

The variable counts pets per student, and the question asks how many students fall into each count, so tallies grouped by value are needed. A frequency table or column graph displays exactly those counts for each category.

Question 31Essential Mathematics (content domains not enumerated in source)

A jacket priced at $180 is reduced by 30%. What is the sale price?

  1. $126 Correct answer.
  2. $150
  3. $54
  4. $234

Explanation

The discount is 30% of $180, which is $54, and subtracting this from the original price gives $126. Equivalently, the sale price is 70% of $180, which also equals $126.

Question 32Essential Mathematics (content domains not enumerated in source)

A bag contains 4 red, 6 yellow and 10 black counters. One counter is drawn at random. What is the probability that it is yellow?

  1. 0.3 Correct answer.
  2. 0.5
  3. 0.6
  4. 0.2

Explanation

There are 20 counters in total, and 6 of them are yellow, so the probability is 6 out of 20. Simplifying 6/20 gives 3/10, which equals 0.3.

Question 33Essential Mathematics (content domains not enumerated in source)

A recipe uses 3 cups of flour to make 12 muffins. How many cups of flour are needed to make 30 muffins at the same rate?

  1. 5
  2. 6
  3. 9
  4. 7.5 Correct answer.

Explanation

Each muffin requires 3 divided by 12, which is 0.25 cups of flour. Multiplying 0.25 by 30 muffins gives 7.5 cups.

Question 34Essential Mathematics (content domains not enumerated in source)

A loan of $12,000 is charged simple interest at 7.5% per year for 2 years. What is the total interest charged?

  1. $1,800 Correct answer.
  2. $2,700
  3. $1,125
  4. $900

Explanation

Simple interest equals principal multiplied by rate multiplied by time, so 12000 x 0.075 x 2 = $1,800. The rate applies to the original principal each year, with no compounding.

Question 35Essential Mathematics (content domains not enumerated in source)

A company's revenue rises from $48,000 to $60,000 in one year. What is the percentage increase?

  1. 12%
  2. 20%
  3. 25% Correct answer.
  4. 80%

Explanation

The increase is $12,000, and percentage change is found by dividing the increase by the original value. So 12000 divided by 48000 equals 0.25, which is a 25% increase.

Question 36Essential Mathematics (content domains not enumerated in source)

The masses of five parcels in kilograms are 2.4, 3.1, 2.8, 7.6 and 3.3. Which statement about these data is true?

  1. The mean and median are both 3.1
  2. The median is 2.8 and the mean is 3.84
  3. The median is 3.1 and the mean is greater than the median Correct answer.
  4. The mode is 7.6 and the mean is 3.84

Explanation

Ordering the values gives 2.4, 2.8, 3.1, 3.3, 7.6, so the middle value and median is 3.1. The mean is 19.2 divided by 5, which is 3.84, and the high parcel of 7.6 pulls the mean above the median.

Question 37Essential Mathematics (content domains not enumerated in source)

A cylinder has a radius of 5 cm and a height of 12 cm. Using pi = 3.14, what is its volume to the nearest whole number?

  1. 314 cm^3
  2. 942 cm^3 Correct answer.
  3. 377 cm^3
  4. 1884 cm^3

Explanation

The volume of a cylinder is pi times the radius squared times the height. Here 3.14 x 25 x 12 = 942 cubic centimetres.

Question 38Essential Mathematics (content domains not enumerated in source)

A right-angled triangle has a hypotenuse of 13 cm and one shorter side of 5 cm. What is the length of the other shorter side?

  1. 18 cm
  2. 8 cm
  3. 11.5 cm
  4. 12 cm Correct answer.

Explanation

Pythagoras' theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides. So the unknown side squared is 169 minus 25, which is 144, and its square root is 12 cm.

Question 39Essential Mathematics (content domains not enumerated in source)

A population of 5,000 bacteria doubles every 3 hours. Assuming unlimited growth, what is the population after 12 hours?

  1. 80,000 Correct answer.
  2. 40,000
  3. 20,000
  4. 60,000

Explanation

Twelve hours contains four doubling periods of 3 hours each. Applying four doublings to 5,000 gives 5000 x 2^4 = 5000 x 16 = 80,000.

Question 40Essential Mathematics (content domains not enumerated in source)

A car is purchased for $34,000 and depreciates at 15% per year using reducing balance. What is its value after 2 years, to the nearest dollar?

  1. $24,565 Correct answer.
  2. $23,800
  3. $28,900
  4. $24,650

Explanation

Reducing balance applies the multiplier 0.85 each year, so the value is 34000 x 0.85^2. Since 0.85 squared is 0.7225, the value is $24,565.

Question 41Essential Mathematics (content domains not enumerated in source)

Two events A and B are mutually exclusive with P(A) = 0.35 and P(B) = 0.40. What is the probability that neither A nor B occurs?

  1. 0.65
  2. 0.14
  3. 0.75
  4. 0.25 Correct answer.

Explanation

For mutually exclusive events, the probability of either occurring is the sum, 0.35 + 0.40 = 0.75. The probability that neither occurs is the complement, 1 minus 0.75, which equals 0.25.

Question 42Essential Mathematics (content domains not enumerated in source)

A plan uses a scale of 1:250. A wall measures 8 cm on the plan. What is the actual length of the wall in metres?

  1. 20 m Correct answer.
  2. 200 m
  3. 2 m
  4. 31.25 m

Explanation

A scale of 1:250 means each centimetre on the plan represents 250 cm in reality. Multiplying 8 by 250 gives 2000 cm, and dividing by 100 converts this to 20 metres.

Question 43Essential Mathematics (content domains not enumerated in source)

A worker is paid $24.60 per hour for a standard 35-hour week, with time-and-a-half for any additional hours. If the worker works 41 hours, what is the gross pay?

  1. $1,107.00
  2. $1,008.60
  3. $861.00
  4. $1,082.40 Correct answer.

Explanation

The first 35 hours earn 35 x $24.60 = $861.00. The 6 overtime hours are paid at $36.90 each, giving $221.40, and adding the two amounts gives $1,082.40.

Question 44Essential Mathematics (content domains not enumerated in source)

An investment of $6,000 earns 4.2% per year compounded annually. What is the value after 3 years, to the nearest dollar?

  1. $6,756
  2. $7,560
  3. $6,252
  4. $6,788 Correct answer.

Explanation

Compound interest uses the multiplier 1.042 raised to the power of the number of years. So 6000 x 1.042^3 gives approximately $6,788.

Question 45Essential Mathematics (content domains not enumerated in source)

A survey records the daily rainfall in millimetres for 30 days. Which measure best summarises the typical daily rainfall when one day has an unusually high reading?

  1. The range, because it spans all readings
  2. The maximum, because it captures the heaviest fall
  3. The median, because it is resistant to extreme values Correct answer.
  4. The mean, because it uses every reading

Explanation

The median depends on position in the ordered data, so a single extreme value shifts it very little. The mean uses every value and is pulled towards the outlier, making the median a more representative summary here.

Question 46Essential Mathematics (content domains not enumerated in source)

A swimming pool is a rectangular prism 25 m long, 12 m wide and 1.8 m deep. How many litres of water are needed to fill it completely?

  1. 1,080,000 L
  2. 54,000 L
  3. 5,400 L
  4. 540,000 L Correct answer.

Explanation

The volume in cubic metres is 25 x 12 x 1.8 = 540 cubic metres. Since one cubic metre holds 1000 litres, the pool requires 540,000 litres.

Question 47Essential Mathematics (content domains not enumerated in source)

A courier charges a fixed $8.50 plus $1.20 per kilometre. A delivery costs $32.50. How far was the delivery in kilometres?

  1. 27 km
  2. 35 km
  3. 20 km Correct answer.
  4. 24 km

Explanation

Subtracting the fixed charge from the total gives $24.00, which is the distance charge. Dividing $24.00 by $1.20 per kilometre gives 20 kilometres.

Question 48Essential Mathematics (content domains not enumerated in source)

A student needs an average of at least 75 across five tests. The first four scores are 68, 82, 79 and 71. What minimum score is needed on the fifth test?

  1. 79
  2. 71
  3. 75 Correct answer.
  4. 80

Explanation

A total of 5 x 75 = 375 marks is needed for the average. The first four scores sum to 300, so the fifth test must supply 375 minus 300, which is 75 marks.

Question 49Essential Mathematics (content domains not enumerated in source)

A loan of $15,000 is repaid monthly over 4 years with simple interest at 9% per year, with interest calculated on the original amount for the whole term. What is the monthly repayment, to the nearest cent?

  1. $431.25
  2. $312.50
  3. $387.50
  4. $425.00 Correct answer.

Explanation

The simple interest is 15000 x 0.09 x 4 = $5,400, so the total repayment is $20,400. Dividing by 48 monthly payments gives $425.00 per month.

Question 50Essential Mathematics (content domains not enumerated in source)

A data set of 40 values has a mean of 62. When one value is removed, the mean of the remaining 39 values becomes 61.5. What was the removed value?

  1. 61.5
  2. 81.5 Correct answer.
  3. 80
  4. 62

Explanation

The original total is 40 x 62 = 2480, and the new total is 39 x 61.5 = 2398.5. The difference between these totals is the removed value, 2480 minus 2398.5 = 81.5.