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Question 1Mathematical Literacy - Number, Algebra and Computation

Evaluate 18 − 3 × (4 + 2) ÷ 3.

  1. 12 Correct answer.
  2. 6
  3. 30
  4. 0

Explanation

Work inside the parentheses first: 4 + 2 = 6. Multiplication and division are then done from left to right, so 3 × 6 ÷ 3 = 6, and finally 18 − 6 = 12. Addition and subtraction come after multiplication and division in the standard order of operations.

Question 2Mathematical Literacy - Number, Algebra and Computation

A paint mix uses blue and yellow paint in the ratio 3 : 5. If 24 litres of blue paint are used, how many litres of yellow paint are needed?

  1. 8 litres
  2. 40 litres Correct answer.
  3. 14.4 litres
  4. 15 litres

Explanation

The ratio 3 : 5 means every 3 parts of blue require 5 parts of yellow. Since 24 litres of blue is 8 litres per part, the yellow amount is 5 × 8 = 40 litres.

Question 3Mathematical Literacy - Number, Algebra and Computation

A student scores 45 out of 60 on a test. What is this score as a percentage?

  1. 72%
  2. 80%
  3. 70%
  4. 75% Correct answer.

Explanation

A percentage compares the score with 100, so divide 45 by 60 and multiply by 100. This gives 45 ÷ 60 × 100 = 75%.

Question 4Mathematical Literacy - Number, Algebra and Computation

Solve the equation 5(x − 2) = 3x + 8.

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

Explanation

Expand the left side to get 5x − 10 = 3x + 8. Subtracting 3x from both sides gives 2x − 10 = 8, and adding 10 gives 2x = 18, so x = 9.

Question 5Mathematical Literacy - Number, Algebra and Computation

A cyclist covers 45 km in 2 hours 30 minutes. What is the average speed in kilometres per hour?

  1. 18 km/h Correct answer.
  2. 22.5 km/h
  3. 15 km/h
  4. 20 km/h

Explanation

Convert 2 hours 30 minutes to 2.5 hours, because 30 minutes is half an hour. Average speed is distance divided by time, so 45 ÷ 2.5 = 18 km/h.

Question 6Mathematical Literacy - Number, Algebra and Computation

Expand and simplify (2x − 3)(x + 5).

  1. 2x² + 7x + 15
  2. 2x² + 13x − 15
  3. 2x² − 7x − 15
  4. 2x² + 7x − 15 Correct answer.

Explanation

Multiply each term in the first bracket by each term in the second: 2x(x + 5) − 3(x + 5) = 2x² + 10x − 3x − 15. Combining 10x and −3x gives 2x² + 7x − 15.

Question 7Mathematical Literacy - Number, Algebra and Computation

A price is increased by 20% and then the new price is decreased by 20%. What is the overall percentage change from the original price?

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

Explanation

After a 20% increase the price is 1.20 times the original. The 20% decrease applies to that new amount, so multiply by 0.80: 1.20 × 0.80 = 0.96. The final price is 96% of the original, which is a 4% decrease.

Question 8Mathematical Literacy - Number, Algebra and Computation

Solve the simultaneous equations 2x + 3y = 12 and x − y = 1.

  1. x = 2, y = 3
  2. x = 1, y = 2
  3. x = 4, y = 1
  4. x = 3, y = 2 Correct answer.

Explanation

Rearrange x − y = 1 to get x = y + 1. Substitute into 2x + 3y = 12: 2(y + 1) + 3y = 12, so 5y + 2 = 12 and y = 2. Then x = 2 + 1 = 3.

Question 9Mathematical Literacy - Number, Algebra and Computation

$2,000 is invested at 5% per year compound interest. What is the value after 3 years, to the nearest cent?

  1. $2,310.00
  2. $2,300.00
  3. $2,315.25 Correct answer.
  4. $2,157.63

Explanation

Compound interest multiplies the balance by 1.05 each year, so the value is 2000 × 1.05³. Since 1.05³ = 1.157625, the amount is 2000 × 1.157625 = $2,315.25.

Question 10Mathematical Literacy - Number, Algebra and Computation

Pipe A fills a tank in 6 hours, pipe B fills it in 9 hours, and drain C empties the full tank in 18 hours. If all three are open at the same time, how long will the tank take to fill?

  1. 4.5 hours Correct answer.
  2. 6.0 hours
  3. 3.6 hours
  4. 5.0 hours

Explanation

Add the rates: pipe A fills 1/6 of the tank per hour, pipe B fills 1/9, and drain C removes 1/18. The combined rate is 3/18 + 2/18 − 1/18 = 4/18 = 2/9 of the tank per hour, so the time is 9/2 = 4.5 hours.

Question 11Mathematical Literacy - Number, Algebra and Computation

Evaluate (−4)^2 − 3 × (−5).

  1. −1
  2. 31 Correct answer.
  3. 1
  4. 11

Explanation

Evaluate the power before the multiplication: (−4)^2 = 16. Then 3 × (−5) = −15, so the expression is 16 − (−15), which equals 16 + 15 = 31. Subtracting a negative number is the same as adding its positive value.

Question 12Mathematical Literacy - Number, Algebra and Computation

Round 0.005286 to 2 significant figures.

  1. 0.0053 Correct answer.
  2. 0.005
  3. 0.00529
  4. 0.0052

Explanation

The first significant figure is 5 and the second is 2. The next digit is 8, so the second significant figure rounds up from 2 to 3, giving 0.0053. Leading zeros are not significant.

Question 13Mathematical Literacy - Number, Algebra and Computation

Find the highest common factor (HCF) of 84 and 120.

  1. 6
  2. 840
  3. 12 Correct answer.
  4. 24

Explanation

Write both numbers as products of primes: 84 = 2² × 3 × 7 and 120 = 2³ × 3 × 5. The HCF uses the lowest power of each shared prime: 2² × 3 = 12.

Question 14Mathematical Literacy - Number, Algebra and Computation

Calculate (4.2 × 10^5) ÷ (7 × 10^−2), giving your answer in standard form.

  1. 6 × 10^5
  2. 6 × 10^8
  3. 0.6 × 10^7
  4. 6 × 10^6 Correct answer.

Explanation

Divide the coefficients: 4.2 ÷ 7 = 0.6. Subtract the indices: 10^(5 − (−2)) = 10^7. Then 0.6 × 10^7 = 6 × 10^6 in standard form.

Question 15Mathematical Literacy - Number, Algebra and Computation

Make x the subject of the formula y = (3x − 5)/4.

  1. x = (y + 5)/12
  2. x = 4y/3 + 5
  3. x = (4y − 5)/3
  4. x = (4y + 5)/3 Correct answer.

Explanation

Multiply both sides by 4: 4y = 3x − 5. Add 5: 4y + 5 = 3x. Divide by 3: x = (4y + 5)/3.

Question 16Mathematical Literacy - Number, Algebra and Computation

Simplify (2a^3b^−2)^3 × (a^−1b^4).

  1. 6a^8/b^2
  2. 8a^9/b^2
  3. 8a^8b^2
  4. 8a^8/b^2 Correct answer.

Explanation

Apply the power to each factor: (2a^3b^−2)^3 = 8a^9b^−6. Multiply by a^−1b^4 by adding indices: a^(9−1)b^(−6+4) = a^8b^−2. This equals 8a^8/b^2.

Question 17Mathematical Literacy - Number, Algebra and Computation

The time t taken to fill a tank is inversely proportional to the flow rate r. When r = 15 litres/min, t = 40 minutes. Find t when r = 25 litres/min.

  1. 66.7 minutes
  2. 24 minutes Correct answer.
  3. 15 minutes
  4. 40 minutes

Explanation

Inverse proportion means t = k/r. Using r = 15 and t = 40 gives k = 15 × 40 = 600. When r = 25, t = 600 ÷ 25 = 24 minutes.

Question 18Mathematical Literacy - Number, Algebra and Computation

A linear sequence begins 7, 11, 15, 19, ... Find the 20th term of the sequence.

  1. 80
  2. 79
  3. 83 Correct answer.
  4. 87

Explanation

The common difference is 4 and the first term is 7, so the nth term is 4n + 3. Substituting n = 20 gives 4(20) + 3 = 83.

Question 19Mathematical Literacy - Number, Algebra and Computation

Simplify (x^2 − 9)/(x^2 + x − 12).

  1. (x + 3)/(x + 4) Correct answer.
  2. (x − 3)/(x + 4)
  3. (x − 3)/(x − 4)
  4. (x + 3)/(x − 4)

Explanation

Factorise the numerator as (x − 3)(x + 3) and the denominator as (x + 4)(x − 3). Cancel the common factor (x − 3), leaving (x + 3)/(x + 4), provided x ≠ 3.

Question 20Mathematical Literacy - Number, Algebra and Computation

A rectangle has length 12.4 cm and width 7.8 cm, each measured to 1 decimal place. What is the upper bound for the area?

  1. 96.72 cm²
  2. 97.7325 cm² Correct answer.
  3. 97.8 cm²
  4. 97.68 cm²

Explanation

Each measurement to 1 decimal place has a half-unit error of 0.05 cm, so the upper bounds are 12.45 cm and 7.85 cm. The upper bound for area is 12.45 × 7.85 = 97.7325 cm².

Question 21Mathematical Literacy - Number, Algebra and Computation

Express 0.375 as a fraction in its simplest form.

  1. 15/40
  2. 3/8 Correct answer.
  3. 37.5/100
  4. 3/7

Explanation

The decimal 0.375 means 375 thousandths, so it can be written as 375/1000. Dividing the numerator and denominator by their highest common factor, 125, gives 3/8.

Question 22Mathematical Literacy - Number, Algebra and Computation

Calculate 2/3 of 45.

  1. 15
  2. 30 Correct answer.
  3. 60
  4. 27

Explanation

One third of 45 is 15, so two thirds is 2 × 15 = 30. Equivalently, multiply 45 by 2/3.

Question 23Mathematical Literacy - Number, Algebra and Computation

Simplify 3x + 5x − 2x.

  1. 6x^2
  2. 4x
  3. 6x Correct answer.
  4. 10x

Explanation

Add and subtract the coefficients of the like terms: 3 + 5 − 2 = 6. The variable x remains, so the expression simplifies to 6x.

Question 24Mathematical Literacy - Number, Algebra and Computation

Solve the inequality 4x − 7 < 13.

  1. x < 3
  2. x > 5
  3. x > 3
  4. x < 5 Correct answer.

Explanation

Add 7 to both sides to get 4x < 20. Dividing both sides by the positive number 4 keeps the inequality direction, giving x < 5.

Question 25Mathematical Literacy - Number, Algebra and Computation

A jacket is sold for $64 after a 20% discount. What was the original price?

  1. $128
  2. $76.80
  3. $80 Correct answer.
  4. $84

Explanation

A 20% discount means the sale price is 80% of the original price. Let the original price be P; then 0.8P = 64, so P = 64 ÷ 0.8 = 80.

Question 26Mathematical Literacy - Number, Algebra and Computation

Divide $180 in the ratio 2 : 3 : 4. What is the largest share?

  1. $90
  2. $80 Correct answer.
  3. $40
  4. $60

Explanation

The ratio 2 : 3 : 4 has 2 + 3 + 4 = 9 equal parts. Each part is $180 ÷ 9 = $20, so the largest share is 4 × $20 = $80.

Question 27Mathematical Literacy - Number, Algebra and Computation

Factorise fully 6x^2 + 9x.

  1. 3x(2x + 3) Correct answer.
  2. 3x(2x + 9)
  3. x(6x + 9)
  4. 3(2x^2 + 3x)

Explanation

The highest common factor of 6x^2 and 9x is 3x. Taking 3x out gives 6x^2 + 9x = 3x(2x + 3).

Question 28Mathematical Literacy - Number, Algebra and Computation

Solve (x/3) + (x/4) = 7.

  1. x = 84
  2. x = 7
  3. x = 21
  4. x = 12 Correct answer.

Explanation

Multiply every term by the common denominator 12: 4x + 3x = 84. Then 7x = 84, so x = 12.

Question 29Mathematical Literacy - Number, Algebra and Computation

The value of a car depreciates by 15% in the first year and then by 10% in the second year. If its original price is $24,000, what is its value after two years?

  1. $18,360 Correct answer.
  2. $18,000
  3. $19,200
  4. $20,400

Explanation

A 15% depreciation leaves 85% of the value, and a further 10% depreciation leaves 90% of that amount. Multiply: 24,000 × 0.85 × 0.9 = 18,360.

Question 30Mathematical Literacy - Number, Algebra and Computation

Solve 2^(x+1) = 8^(x−1).

  1. x = 3
  2. x = 1
  3. x = 4
  4. x = 2 Correct answer.

Explanation

Write 8 as 2^3, so 8^(x−1) = 2^(3x−3). Equating exponents in 2^(x+1) = 2^(3x−3) gives x + 1 = 3x − 3, hence 4 = 2x and x = 2.

Question 31Mathematical Literacy - Number, Algebra and Computation

Work out 15% of 240.

  1. 36 Correct answer.
  2. 24
  3. 32
  4. 48

Explanation

15% is 10% plus 5%. Ten percent of 240 is 24 and 5% is half of that, 12; adding gives 36. Alternatively, 0.15 × 240 = 36.

Question 32Mathematical Literacy - Number, Algebra and Computation

Expand and simplify 4(2x − 3) + 5x.

  1. 13x + 12
  2. 7x − 12
  3. 13x − 12 Correct answer.
  4. 8x − 12

Explanation

Multiply each term inside the bracket by 4: 4(2x − 3) = 8x − 12. Then collect like terms: 8x − 12 + 5x = 13x − 12. The x terms combine to 13x and the constant stays −12.

Question 33Mathematical Literacy - Number, Algebra and Computation

Find the lowest common multiple (LCM) of 18 and 24.

  1. 144
  2. 36
  3. 6
  4. 72 Correct answer.

Explanation

Write 18 = 2 × 3² and 24 = 2³ × 3. The LCM uses the highest power of each prime: 2³ × 3² = 72. It is the smallest number divisible by both 18 and 24.

Question 34Mathematical Literacy - Number, Algebra and Computation

Solve the simultaneous equations 3x + 2y = 16 and x − y = 2.

  1. (4, 2) Correct answer.
  2. (2, 4)
  3. (5, 3)
  4. (3, 1)

Explanation

From x − y = 2, we get x = y + 2. Substituting into 3x + 2y = 16 gives 3(y + 2) + 2y = 16, so 5y = 10 and y = 2; then x = 4. The solution pair is (4, 2).

Question 35Mathematical Literacy - Number, Algebra and Computation

Work out (3/4) ÷ (2/5), giving your answer as a fraction in its simplest form.

  1. 6/20
  2. 8/15
  3. 3/10
  4. 15/8 Correct answer.

Explanation

Dividing by 2/5 is the same as multiplying by its reciprocal 5/2. So (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8. This improper fraction equals 1 7/8, but 15/8 is the simplest fractional form.

Question 36Mathematical Literacy - Number, Algebra and Computation

Expand and simplify (x + 5)(x − 3).

  1. x² + 8x − 15
  2. x² − 15
  3. x² + 2x − 15 Correct answer.
  4. x² − 2x − 15

Explanation

Use the distributive law twice: (x + 5)(x − 3) = x² − 3x + 5x − 15. Collecting the middle terms gives x² + 2x − 15. The constant term is 5 × (−3) = −15.

Question 37Mathematical Literacy - Number, Algebra and Computation

Calculate (2.5 × 10³) + (4.1 × 10²), giving your answer in standard form.

  1. 2.91 × 10³ Correct answer.
  2. 2.91 × 10⁵
  3. 6.6 × 10⁵
  4. 6.6 × 10³

Explanation

Convert to the same power of ten: 4.1 × 10² = 0.41 × 10³. Then add 2.5 × 10³ + 0.41 × 10³ = 2.91 × 10³. The result is already in standard form because 2.91 lies between 1 and 10.

Question 38Mathematical Literacy - Number, Algebra and Computation

£2000 is invested at 3% compound interest per year. What is the value after 2 years?

  1. £2,060.00
  2. £2,121.80 Correct answer.
  3. £2,120.00
  4. £2,183.60

Explanation

Each year the amount is multiplied by 1.03. After two years the value is 2000 × 1.03² = 2000 × 1.0609 = 2121.80. Compound interest means the second year's 3% is earned on the first year's interest as well as the original amount.

Question 39Mathematical Literacy - Number, Algebra and Computation

A quadratic sequence begins 5, 12, 23, ... Find its nth term.

  1. 2n² + 5n − 2
  2. n² + 6n − 2
  3. 2n² + n + 2 Correct answer.
  4. 2n² + 3n

Explanation

The first differences are 7 and 11, so the second difference is 4. For a quadratic sequence the coefficient of n² is half the second difference, so it is 2. Writing the nth term as 2n² + bn + c and using n = 1 and n = 2 gives b = 1 and c = 2, hence 2n² + n + 2.

Question 40Mathematical Literacy - Number, Algebra and Computation

Solve the simultaneous equations y = x + 1 and x² + y² = 25.

  1. (−4, 4) and (3, −3)
  2. (−3, −4) and (4, 3)
  3. (−4, −3) and (3, 4) Correct answer.
  4. (−5, −4) and (2, 3)

Explanation

Substitute y = x + 1 into x² + y² = 25: x² + (x + 1)² = 25. This simplifies to 2x² + 2x − 24 = 0, or x² + x − 12 = 0, giving x = −4 or x = 3. The corresponding y-values from y = x + 1 are −3 and 4, so the solutions are (−4, −3) and (3, 4).

Question 41Mathematical Literacy - Number, Algebra and Computation

Work out the value of (−3)^2 − 4 × (−2).

  1. −1
  2. −17
  3. 1
  4. 17 Correct answer.

Explanation

Using the order of operations, square first: (−3)^2 = 9. Then multiply: 4 × (−2) = −8, so the expression becomes 9 − (−8) = 9 + 8 = 17.

Question 42Mathematical Literacy - Number, Algebra and Computation

Round 0.004786 to 2 significant figures.

  1. 0.004
  2. 0.0048 Correct answer.
  3. 0.00479
  4. 0.005

Explanation

The leading zeros are not significant, so the first two significant figures are 4 and 7. The next digit is 8, so the 7 rounds up to 8, giving 0.0048.

Question 43Mathematical Literacy - Number, Algebra and Computation

Work out (4.2 × 10^5) × (2.5 × 10^3), giving your answer in standard form.

  1. 1.05 × 10^9 Correct answer.
  2. 1.05 × 10^10
  3. 1.05 × 10^8
  4. 1.05 × 10^7

Explanation

Multiply the coefficients: 4.2 × 2.5 = 10.5. Multiply the powers of ten: 10^5 × 10^3 = 10^8, so the result is 10.5 × 10^8, which is 1.05 × 10^9 in standard form.

Question 44Mathematical Literacy - Number, Algebra and Computation

Express the recurring decimal 0.363636... as a fraction in its simplest form.

  1. 11/30
  2. 36/100
  3. 4/11 Correct answer.
  4. 9/25

Explanation

Let x = 0.363636... Then 100x = 36.363636... Subtracting gives 99x = 36, so x = 36/99 = 4/11.

Question 45Mathematical Literacy - Number, Algebra and Computation

Make x the subject of the formula y = (3x − 5)/2.

  1. (3y + 5)/2
  2. (2y − 5)/3
  3. 2y + 5
  4. (2y + 5)/3 Correct answer.

Explanation

Multiply both sides by 2 to get 2y = 3x − 5. Add 5 to both sides: 2y + 5 = 3x, then divide by 3 to obtain x = (2y + 5)/3.

Question 46Mathematical Literacy - Number, Algebra and Computation

Solve the quadratic equation x² − 7x + 12 = 0 by factorising.

  1. x = 2 and x = 6
  2. x = −3 and x = −4
  3. x = 1 and x = 12
  4. x = 3 and x = 4 Correct answer.

Explanation

Two numbers with product 12 and sum −7 are −3 and −4. Hence x² − 7x + 12 = (x − 3)(x − 4), so the solutions are x = 3 and x = 4.

Question 47Mathematical Literacy - Number, Algebra and Computation

y is directly proportional to the square of x. When x = 3, y = 36. Find y when x = 5.

  1. 20
  2. 180
  3. 60
  4. 100 Correct answer.

Explanation

Direct proportion to the square of x means y = kx². Substitute x = 3 and y = 36 to get 36 = 9k, so k = 4. When x = 5, y = 4 × 25 = 100.

Question 48Mathematical Literacy - Number, Algebra and Computation

Simplify fully (2x^3 y^−2)^3 ÷ (4x^2 y^4).

  1. 2x^7 y^10
  2. 8x^7/y^10
  3. 2x^5/y^10
  4. 2x^7/y^10 Correct answer.

Explanation

Cube the numerator: (2x^3 y^−2)^3 = 8x^9 y^−6. Dividing by 4x²y⁴ gives (8/4)x^(9−2)y^(−6−4) = 2x^7 y^−10, which is 2x^7/y^10.

Question 49Mathematical Literacy - Number, Algebra and Computation

A rectangle has side lengths 8 cm and 5 cm, each measured to the nearest centimetre. Work out the lower bound of its area.

  1. 33.75 cm² Correct answer.
  2. 33.50 cm²
  3. 40.00 cm²
  4. 35.00 cm²

Explanation

A measurement to the nearest centimetre has a lower bound half a centimetre below the stated value. The lower bounds are 7.5 cm and 4.5 cm, so the lower bound of the area is 7.5 × 4.5 = 33.75 cm².

Question 50Mathematical Literacy - Number, Algebra and Computation

In a sale, a jacket is reduced by 15% and now costs £68. Work out the price of the jacket before the sale.

  1. £102.00
  2. £81.60
  3. £80.00 Correct answer.
  4. £78.20

Explanation

A 15% reduction means the sale price is 85% of the original price. If the original price is P, then 0.85P = 68, so P = 68 ÷ 0.85 = 80. Therefore the jacket originally cost £80.00.