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Tasmania TCE Everyday Adult Standard - Mathematics study materials
Tasmania TCE Everyday Adult Standard - Mathematics study resources

Tasmania TCE Everyday Adult Standard - Mathematics practice questions

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Question 1Number and quantity in everyday contexts

A recipe uses 250 g of flour to make 10 biscuits. How much flour is needed to make 25 biscuits at the same rate?

  1. 600 g
  2. 500 g
  3. 750 g
  4. 625 g Correct answer.

Explanation

Each biscuit needs 250 ÷ 10 = 25 g of flour, so 25 biscuits need 25 × 25 = 625 g. Setting up the proportion 250/10 = x/25 gives the same result.

Question 2Number and quantity in everyday contexts

Which number is largest?

  1. 0.7
  2. 0.705
  3. 0.075
  4. 0.75 Correct answer.

Explanation

Compare digits place by place: 0.75 has 7 tenths and 5 hundredths, which exceeds 0.7 (only 7 tenths), 0.705, and 0.075. Writing each to three decimals (0.750, 0.700, 0.705, 0.075) makes the ordering clear.

Question 3Number and quantity in everyday contexts

A jacket priced at $80 is discounted by 15%. What is the sale price?

  1. $12
  2. $72
  3. $68 Correct answer.
  4. $65

Explanation

The discount is 15% of $80, which is 0.15 × 80 = $12. Subtracting from the original price gives $80 − $12 = $68.

Question 4Number and quantity in everyday contexts

Which of these is equal to 3/8?

  1. 0.3
  2. 0.38
  3. 0.83
  4. 0.375 Correct answer.

Explanation

Dividing 3 by 8 gives 0.375 exactly, since 8 × 0.375 = 3. The decimal terminates after three places.

Question 5Number and quantity in everyday contexts

A bank account earns simple interest at 4% per year. How much interest is earned on $1500 after 3 years?

  1. $120
  2. $180 Correct answer.
  3. $540
  4. $60

Explanation

Simple interest is principal × rate × time, so 1500 × 0.04 × 3 = $180. The interest accrues only on the original $1500.

Question 6Number and quantity in everyday contexts

A car travels 180 km in 2 hours. What is its average speed in kilometres per hour?

  1. 45 km/h
  2. 360 km/h
  3. 60 km/h
  4. 90 km/h Correct answer.

Explanation

Average speed equals distance divided by time, so 180 ÷ 2 = 90 km/h. The units are already kilometres and hours, so no conversion is needed.

Question 7Number and quantity in everyday contexts

Which value is the same as 2.5 kilograms?

  1. 2500 grams Correct answer.
  2. 250 grams
  3. 25000 grams
  4. 0.25 grams

Explanation

One kilogram equals 1000 grams, so 2.5 kg = 2.5 × 1000 = 2500 g. Moving the decimal three places to the right performs the conversion.

Question 8Number and quantity in everyday contexts

A worker earns $22.50 per hour. What is the pay for 8 hours of work?

  1. $176.00
  2. $160.00
  3. $202.50
  4. $180.00 Correct answer.

Explanation

Multiply the hourly rate by the number of hours: 22.50 × 8 = 180.00. Checking with 22 × 8 = 176 plus 0.50 × 8 = 4 confirms $180.

Question 9Number and quantity in everyday contexts

A shirt costs $45. GST of 10% is added at the checkout. What is the total price?

  1. $55.00
  2. $49.50 Correct answer.
  3. $40.50
  4. $45.10

Explanation

GST is 10% of $45, which equals $4.50. Adding this to the base price gives $45 + $4.50 = $49.50.

Question 10Number and quantity in everyday contexts

A recipe for 4 people needs 300 g of rice. How much rice is needed for 10 people at the same serving size?

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

Explanation

The rice per person is 300 ÷ 4 = 75 g. For 10 people, 75 × 10 = 750 g. Equivalently, the scale factor is 10/4 = 2.5, and 300 × 2.5 = 750.

Question 11Number and quantity in everyday contexts

A store offers 20% off, and the reduced price is then taxed at 10%. What single percentage change does this produce on the original price?

  1. A 30% decrease
  2. A 12% decrease Correct answer.
  3. A 10% decrease
  4. A 2% increase

Explanation

After the discount the price is 0.80 of the original; the tax multiplies this by 1.10, giving 0.88. So the net effect is a 12% decrease from the original price.

Question 12Number and quantity in everyday contexts

A car uses 8 litres of fuel per 100 km. How much fuel is needed for a 350 km trip?

  1. 24 litres
  2. 35 litres
  3. 32 litres
  4. 28 litres Correct answer.

Explanation

Fuel per kilometre is 8 ÷ 100 = 0.08 L. For 350 km, 0.08 × 350 = 28 L. Alternatively, 350 km is 3.5 hundreds, and 3.5 × 8 = 28.

Question 13Number and quantity in everyday contexts

A sum of $2000 is invested at 5% per year compound interest. What is the value after 2 years, to the nearest dollar?

  1. $2205 Correct answer.
  2. $2100
  3. $2200
  4. $2420

Explanation

Compound growth multiplies by 1.05 each year: 2000 × 1.05² = 2000 × 1.1025 = 2205. The second year's interest is earned on the increased balance, adding $5 beyond simple interest.

Question 14Number and quantity in everyday contexts

A map has a scale of 1:50000. A distance of 6 cm on the map represents what real distance?

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

Explanation

Each centimetre represents 50000 cm, so 6 cm represents 300000 cm. Converting to metres gives 3000 m, which is 3 km.

Question 15Number and quantity in everyday contexts

Three friends share a lottery prize in the ratio 2:3:5. If the total prize is $4000, how much does the person with the largest share receive?

  1. $1600
  2. $2000 Correct answer.
  3. $1200
  4. $800

Explanation

The ratio has 2 + 3 + 5 = 10 parts, so each part is 4000 ÷ 10 = $400. The largest share is 5 parts, giving 5 × 400 = $2000.

Question 16Number and quantity in everyday contexts

A worker's hourly rate rises from $20 to $23. What is the percentage increase?

  1. 13%
  2. 15% Correct answer.
  3. 30%
  4. 3%

Explanation

The increase is $3 on an original rate of $20, so the percentage increase is 3 ÷ 20 × 100 = 15%. The original value is always the denominator.

Question 17Number and quantity in everyday contexts

A rectangular garden is 12 m long and 8 m wide. A path runs around the outside edge. What is the perimeter of the garden?

  1. 40 m Correct answer.
  2. 32 m
  3. 96 m
  4. 20 m

Explanation

Perimeter of a rectangle is 2 × (length + width) = 2 × (12 + 8) = 40 m. Perimeter measures the distance around the boundary.

Question 18Number and quantity in everyday contexts

A phone plan charges $30 per month plus $0.10 per megabyte over a 5 GB allowance. If a user consumes 6 GB in a month, what is the bill? (1 GB = 1000 MB)

  1. $60
  2. $40
  3. $100
  4. $130 Correct answer.

Explanation

Usage over the allowance is 6 − 5 = 1 GB, which is 1000 MB. Excess charges are 1000 × $0.10 = $100, plus the $30 base fee, giving $130.

Question 19Number and quantity in everyday contexts

A quantity is increased by 25% and then decreased by 20%. What is the overall change from the original?

  1. No change Correct answer.
  2. A 45% increase
  3. A 5% increase
  4. A 5% decrease

Explanation

Multiplying by 1.25 and then 0.80 gives 1.25 × 0.80 = 1.00, which returns exactly to the original value. The percentages act on different bases, so they cancel.

Question 20Number and quantity in everyday contexts

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

  1. 90 litres
  2. 120 litres
  3. 150 litres Correct answer.
  4. 180 litres

Explanation

The tank currently holds 3/8 × 240 = 90 litres. The remaining capacity is 240 − 90 = 150 litres, or 5/8 × 240 = 150.

Question 21Number and quantity in everyday contexts

A currency exchange charges a 2% commission on the amount exchanged. If a traveller hands over $1500, how much is actually converted?

  1. $30
  2. $1440
  3. $1530
  4. $1470 Correct answer.

Explanation

The commission is 2% of $1500, which is $30. The amount converted is $1500 − $30 = $1470.

Question 22Number and quantity in everyday contexts

A worker is paid $18 per hour for the first 38 hours each week and $27 per hour for overtime. If she works 44 hours in a week, what is her total pay?

  1. $792
  2. $1188
  3. $846 Correct answer.
  4. $810

Explanation

Base pay is 38 × $18 = $684. Overtime is 6 hours at $27 = $162. The total is $684 + $162 = $846.

Question 23Number and quantity in everyday contexts

A loan of $5000 is repaid with simple interest at 6% per year over 4 years. What is the total amount repaid?

  1. $6200 Correct answer.
  2. $5300
  3. $6800
  4. $1200

Explanation

Simple interest is 5000 × 0.06 × 4 = $1200. The total repaid is the principal plus interest, $5000 + $1200 = $6200.

Question 24Number and quantity in everyday contexts

A store marks a product up by 40% and later discounts the marked price by 30%. Compared with the original cost price, what is the final price?

  1. 10% above the original
  2. 10% below the original
  3. 2% below the original Correct answer.
  4. 2% above the original

Explanation

Multiplying the cost by 1.40 and then 0.70 gives 1.40 × 0.70 = 0.98, which is 98% of the original. The final price is therefore 2% below the original cost.

Question 25Number and quantity in everyday contexts

Two workers together can complete a job in 6 hours. One worker alone takes 10 hours. How long would the second worker take alone?

  1. 4 hours
  2. 16 hours
  3. 15 hours Correct answer.
  4. 12 hours

Explanation

Combined rate is 1/6 of the job per hour, and the first worker's rate is 1/10. The second's rate is 1/6 − 1/10 = 5/30 − 3/30 = 2/30 = 1/15, so it takes 15 hours alone.

Question 26Number and quantity in everyday contexts

A bulk order of 3.6 tonnes of gravel is packed into 15 kg bags. How many bags are filled?

  1. 240 Correct answer.
  2. 54
  3. 540
  4. 24

Explanation

One tonne equals 1000 kilograms, so 3.6 tonnes is 3600 kilograms. Dividing 3600 by 15 gives 240 bags, since 15 times 240 equals 3600.

Question 27Number and quantity in everyday contexts

Which fraction is equivalent to 0.375?

  1. 3/8 Correct answer.
  2. 7/20
  3. 3/7
  4. 4/11

Explanation

The decimal 0.375 means 375 thousandths, which simplifies by dividing top and bottom by 125 to give 3/8. Checking, 3 divided by 8 equals 0.375 exactly.

Question 28Number and quantity in everyday contexts

A supermarket sells pasta at $2.40 for a 500 g pack and $4.20 for a 1 kg pack. Which pack is better value and by how much per kilogram?

  1. The 1 kg pack, cheaper by $0.60 per kg Correct answer.
  2. The 500 g pack, cheaper by $0.60 per kg
  3. Both packs cost the same per kilogram
  4. The 1 kg pack, cheaper by $0.30 per kg

Explanation

Two 500 g packs would cost $4.80 per kilogram, while the 1 kg pack costs $4.20. The difference is $0.60 per kilogram, so the larger pack is better value.

Question 29Number and quantity in everyday contexts

A bank statement shows a balance of -$45. A deposit of $120 is then made. What is the new balance?

  1. $75 Correct answer.
  2. -$165
  3. -$75
  4. $165

Explanation

Adding a deposit to a negative balance means calculating -45 + 120, which equals 75. The account ends with a positive balance of $75.

Question 30Number and quantity in everyday contexts

A worker's weekly pay of $840 is split so that 15% goes to tax. How much tax is paid?

  1. $714
  2. $84
  3. $126 Correct answer.
  4. $12.60

Explanation

Fifteen percent means 15 per hundred, so multiply 840 by 0.15. The calculation 840 times 0.15 equals 126, meaning $126 of tax.

Question 31Number and quantity in everyday contexts

A jug contains 1.5 litres of juice. It is poured equally into 6 glasses. How many millilitres are in each glass?

  1. 250 mL Correct answer.
  2. 90 mL
  3. 25 mL
  4. 150 mL

Explanation

One litre is 1000 millilitres, so 1.5 litres is 1500 millilitres. Dividing 1500 by 6 gives 250 millilitres per glass.

Question 32Number and quantity in everyday contexts

Which of these is a rational number?

  1. Pi
  2. The square root of 9 Correct answer.
  3. The square root of 7
  4. The square root of 2

Explanation

A rational number can be written as a fraction of two integers. The square root of 9 equals 3, which is the fraction 3/1, so it is rational.

Question 33Number and quantity in everyday contexts

A plumber charges a $60 call-out fee plus $45 per hour. A job takes 3.5 hours. What is the total bill?

  1. $202.50
  2. $247.50
  3. $157.50
  4. $217.50 Correct answer.

Explanation

The hourly charge is 45 times 3.5, which equals 157.50. Adding the call-out fee of $60 gives a total of $217.50.

Question 34Number and quantity in everyday contexts

A savings account earns simple interest at 4% per year. How much interest is earned on $750 over 9 months?

  1. $2.50
  2. $30.00
  3. $270.00
  4. $22.50 Correct answer.

Explanation

Simple interest is principal times rate times time in years. Nine months is 0.75 years, so 750 times 0.04 times 0.75 equals 22.50.

Question 35Number and quantity in everyday contexts

A recipe uses flour and sugar in the ratio 5:2. If 350 g of flour is used, how much sugar is needed?

  1. 875 g
  2. 100 g
  3. 140 g Correct answer.
  4. 70 g

Explanation

Each part of the ratio equals 350 divided by 5, which is 70 grams. Sugar is 2 parts, so 2 times 70 equals 140 grams.

Question 36Number and quantity in everyday contexts

A jacket is reduced by 30% in a sale and now costs $84. What was the original price?

  1. $120 Correct answer.
  2. $114
  3. $280
  4. $109.20

Explanation

After a 30% reduction the customer pays 70% of the original price. Dividing 84 by 0.7 gives 120, so the original price was $120.

Question 37Number and quantity in everyday contexts

A car travels 250 km using 20 litres of fuel. What is its fuel consumption in litres per 100 km?

  1. 12.5 L
  2. 2.5 L
  3. 8 L Correct answer.
  4. 5 L

Explanation

Set up a proportion: 20 litres for 250 km means 20 divided by 250 litres per kilometre. Multiplying by 100 gives 8 litres per 100 km.

Question 38Number and quantity in everyday contexts

A worker's superannuation contribution is 12% of gross pay. If gross pay is $950 per week, how much is contributed over 4 weeks?

  1. $4,560
  2. $456 Correct answer.
  3. $1,368
  4. $114

Explanation

The weekly contribution is 12% of 950, which is 114. Over four weeks this is 114 times 4, giving $456.

Question 39Number and quantity in everyday contexts

Which expression gives the total cost of n items at $3.50 each plus a fixed delivery fee of $8?

  1. 8n - 3.50
  2. 3.50n + 8 Correct answer.
  3. 3.50 + 8n
  4. (3.50 + 8)n

Explanation

Each item contributes $3.50, so n items cost 3.50n. The delivery fee is added once, giving the expression 3.50n + 8.

Question 40Number and quantity in everyday contexts

A phone is priced at $640 including 10% GST. What is the price before GST, to the nearest cent?

  1. $704.00
  2. $581.82 Correct answer.
  3. $630.00
  4. $576.00

Explanation

If the GST-inclusive price is 110% of the pre-GST price, divide 640 by 1.1. This gives about 581.82, so the pre-GST price is $581.82.

Question 41Number and quantity in everyday contexts

A town's population rises from 12,500 to 14,000. What is the percentage increase?

  1. 12% Correct answer.
  2. 150%
  3. 10.7%
  4. 1.5%

Explanation

The increase is 1500 people, and the original population is 12,500. Dividing 1500 by 12,500 gives 0.12, which is a 12% increase.

Question 42Number and quantity in everyday contexts

A 2.4 kg bag of dog food lasts 30 days. How many grams are fed each day?

  1. 72 g
  2. 800 g
  3. 8 g
  4. 80 g Correct answer.

Explanation

Two point four kilograms is 2400 grams. Dividing 2400 by 30 gives 80 grams per day.

Question 43Number and quantity in everyday contexts

A loan of $1200 is repaid in equal monthly instalments over 18 months with a total interest charge of $216. What is the monthly repayment?

  1. $90.00
  2. $78.67 Correct answer.
  3. $86.00
  4. $66.67

Explanation

The total to repay is 1200 plus 216, which equals 1416. Dividing 1416 by 18 gives about 78.67, so each instalment is $78.67.

Question 44Number and quantity in everyday contexts

A quantity is multiplied by 0.85. Which single percentage change does this represent?

  1. A decrease of 15% Correct answer.
  2. An increase of 85%
  3. A decrease of 85%
  4. An increase of 15%

Explanation

Multiplying by 1 would leave the quantity unchanged, so a multiplier of 0.85 is 0.15 below 1. This corresponds to a 15% decrease.

Question 45Number and quantity in everyday contexts

A store sells 3 items for $7.50. At the same rate, what is the cost of 8 items?

  1. $60.00
  2. $22.50
  3. $18.00
  4. $20.00 Correct answer.

Explanation

The unit price is 7.50 divided by 3, which is $2.50 per item. Multiplying by 8 gives $20.00.

Question 46Number and quantity in everyday contexts

A worker's taxable income is $58,000. Tax is 19% on the first $40,000 and 32.5% on the remainder. What is the total tax, to the nearest dollar?

  1. $11,020
  2. $14,500
  3. $13,450 Correct answer.
  4. $18,850

Explanation

Tax on the first $40,000 is 0.19 times 40,000, which equals 7,600. Tax on the remaining $18,000 is 0.325 times 18,000, which equals 5,850, giving a total of $13,450.

Question 47Number and quantity in everyday contexts

A sum of money is invested at 6% per year compounded annually. After 2 years the investment is worth $5,618. What was the original amount?

  1. $5,000 Correct answer.
  2. $5,020
  3. $4,980
  4. $5,300

Explanation

Compound growth multiplies the principal by 1.06 each year, so after two years the multiplier is 1.06 squared, which equals 1.1236. Dividing 5,618 by 1.1236 gives $5,000.

Question 48Number and quantity in everyday contexts

Two investments are compared. Investment A grows by 8% each year. Investment B grows by 0.6% each month, compounded monthly. Which grows faster over one year?

  1. They grow at exactly the same rate
  2. Investment A, by about 0.2 percentage points
  3. Investment B, by about 0.2 percentage points Correct answer.
  4. Investment A, by about 4 percentage points

Explanation

Investment A grows by a factor of 1.08. Investment B grows by 1.006 to the power 12, which is about 1.0744, so B is slightly ahead by roughly 0.2 percentage points.

Question 49Number and quantity in everyday contexts

A tank is filled by two pipes. Pipe A alone fills it in 12 hours, and pipe B alone fills it in 18 hours. Working together, how long will they take?

  1. 6 hours
  2. 9 hours
  3. 15 hours
  4. 7.2 hours Correct answer.

Explanation

In one hour pipe A fills 1/12 of the tank and pipe B fills 1/18. Together they fill 5/36 per hour, so the time is 36/5, which is 7.2 hours.

Question 50Number and quantity in everyday contexts

A currency exchange offers a rate of 1 AUD = 0.62 USD and charges a 3% commission on the amount converted. A traveller converts $2,000 AUD. How many US dollars are received, to the nearest dollar?

  1. $1,180
  2. $1,240
  3. $1,203 Correct answer.
  4. $1,264

Explanation

After a 3% commission, 97% of the money is converted, which is $1,940 AUD. Multiplying by 0.62 gives about 1,202.80, which rounds to $1,203.