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BGCSE Mathematics 0563 study materials
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BGCSE Mathematics 0563 practice questions

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Question 1Number and Numeration

In the number 4 706 285, what is the value of the digit 7?

  1. 700 000 Correct answer.
  2. 70 000
  3. 7 000 000
  4. 7 000

Explanation

Reading from the right, the digits occupy the ones, tens, hundreds, thousands, ten-thousands, hundred-thousands and millions columns. The 7 sits in the hundred-thousands column, so its value is 7 × 100 000 = 700 000.

Question 2Number and Numeration

Write 0.004567 correct to 3 significant figures.

  1. 0.0046
  2. 0.00457 Correct answer.
  3. 0.005
  4. 0.004567

Explanation

Counting significant figures starts at the first non-zero digit, so the first three significant figures here are 4, 5 and 6. The next digit is 7, which is 5 or more, so the 6 rounds up to 7 and the answer is 0.00457.

Question 3Number and Numeration

A shirt costs P240. In a sale the price is reduced by 15%. What is the sale price?

  1. P225
  2. P36
  3. P204 Correct answer.
  4. P216

Explanation

A reduction of 15% means the customer pays 100% − 15% = 85% of the original price. Multiplying gives 0.85 × P240 = P204, which is the amount actually paid at the till.

Question 4Number and Numeration

Express (3.2 × 10^5) × (4 × 10^-3) in standard form.

  1. 1.28 × 10^3 Correct answer.
  2. 1.28 × 10^8
  3. 12.8 × 10^2
  4. 1.28 × 10^2

Explanation

Multiply the number parts and add the indices: 3.2 × 4 = 12.8 and 10^5 × 10^-3 = 10^2. So the product is 12.8 × 10^2, which is 1280, and standard form requires a first factor between 1 and 10, giving 1.28 × 10^3.

Question 5Number and Numeration

Two bells ring at intervals of 18 minutes and 24 minutes. They ring together at 08:00. At what time will they next ring together?

  1. 08:36
  2. 08:42
  3. 09:00
  4. 09:12 Correct answer.

Explanation

The bells coincide again after a time equal to the lowest common multiple of 18 and 24 minutes. Since 18 = 2 × 3^2 and 24 = 2^3 × 3, the LCM is 2^3 × 3^2 = 72 minutes, and 72 minutes after 08:00 is 09:12.

Question 6Number and Numeration

P560 is divided between two people in the ratio 2 : 5. What is the larger share?

  1. P400 Correct answer.
  2. P350
  3. P160
  4. P280

Explanation

The ratio 2 : 5 means the money is split into 2 + 5 = 7 equal parts. One part is P560 ÷ 7 = P80, so the larger share is 5 × P80 = P400.

Question 7Number and Numeration

Simplify (2^5 × 2^-8) ÷ 2^-1, leaving your answer as a fraction or whole number.

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

Explanation

Multiplying powers of the same base means adding the indices: 2^5 × 2^-8 = 2^-3. Dividing by 2^-1 means subtracting the index −1, so 2^-3 ÷ 2^-1 = 2^(−3+1) = 2^-2 = 1/4.

Question 8Number and Numeration

Which of the following expresses 360 as a product of its prime factors?

  1. 2^2 × 3^3 × 5
  2. 2^2 × 3^2 × 10
  3. 2^3 × 3^2 × 5 Correct answer.
  4. 2^3 × 3 × 15

Explanation

Repeated division by the smallest primes gives 360 = 2 × 2 × 2 × 3 × 3 × 5, that is 2^3 × 3^2 × 5. A valid prime factorisation may contain only prime numbers as factors.

Question 9Number and Numeration

The length and width of a rectangle are measured as 8.4 cm and 5.6 cm, each correct to 1 decimal place. What is the lower bound of the area, in cm²?

  1. 47.04
  2. 47.7425
  3. 47.1775
  4. 46.3425 Correct answer.

Explanation

A measurement given to 1 decimal place can be up to half of 0.1, that is 0.05, below the stated value. The lower bounds are 8.35 cm and 5.55 cm, so the smallest possible area is 8.35 × 5.55 = 46.3425 cm².

Question 10Number and Numeration

Express the recurring decimal 0.131313… as a fraction in its simplest form.

  1. 13/99 Correct answer.
  2. 13/90
  3. 13/100
  4. 131/999

Explanation

Let x = 0.131313…, then 100x = 13.131313… because the block of two digits repeats. Subtracting gives 99x = 13, so x = 13/99, and this cannot be cancelled since 13 is prime and does not divide 99.

Question 11Number and Numeration

Write 0.000406 in standard form.

  1. 4.06 × 10^-4 Correct answer.
  2. 4.06 × 10^4
  3. 4.06 × 10^-3
  4. 40.6 × 10^-5

Explanation

Standard form requires a number between 1 and 10 multiplied by a power of 10. Move the decimal point 4 places to the right to get 4.06, so the exponent is −4. Check: 4.06 × 10^−4 = 0.000406.

Question 12Number and Numeration

Round 7.846 to 2 decimal places.

  1. 7.846
  2. 7.85 Correct answer.
  3. 7.8
  4. 7.84

Explanation

To round to 2 decimal places, look at the third decimal digit, which is 6. Since 6 is 5 or more, increase the second decimal digit 4 to 5, giving 7.85.

Question 13Number and Numeration

Which of these numbers is the largest?

  1. 0.58
  2. 0.6
  3. 0.599
  4. 0.605 Correct answer.

Explanation

Compare digits column by column after the decimal point. 0.605 has 6 tenths and then 0 hundredths, while 0.6 has 6 tenths but no further nonzero digits; 0.605 is greater than 0.600. The others, 0.599 and 0.58, are less than 0.6.

Question 14Number and Numeration

A car travels 240 km in 3 hours. What is its average speed in metres per second?

  1. 13.3 m/s
  2. 0.08 m/s
  3. 80 m/s
  4. 22.2 m/s Correct answer.

Explanation

Convert 240 km to 240000 m and 3 hours to 3 × 3600 = 10800 s. Speed = distance ÷ time = 240000 ÷ 10800 ≈ 22.2 m/s.

Question 15Number and Numeration

Increase 450 by 12%.

  1. 504 Correct answer.
  2. 486
  3. 462
  4. 540

Explanation

12% of 450 is 0.12 × 450 = 54. Add this to 450 to get 504. Alternatively, multiply 450 by 1.12 to get 504.

Question 16Number and Numeration

Simplify (3/4) ÷ (2/5).

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

Explanation

To divide by a fraction, multiply by its reciprocal: (3/4) × (5/2) = 15/8. This can also be written as 1 7/8.

Question 17Number and Numeration

Find the highest common factor (HCF) of 84 and 126.

  1. 252
  2. 21
  3. 42 Correct answer.
  4. 14

Explanation

Write 84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. The HCF uses the lowest power of each common prime factor: 2 × 3 × 7 = 42.

Question 18Number and Numeration

A sum of money is invested at 5% simple interest per year. After 3 years the interest is P180. What was the principal?

  1. P1080
  2. P3000
  3. P600
  4. P1200 Correct answer.

Explanation

Simple interest I = PRT/100, so 180 = P × 5 × 3 / 100 = 0.15P. Dividing gives P = 180 ÷ 0.15 = 1200.

Question 19Number and Numeration

Work out (2.5 × 10^-3) ÷ (5 × 10^-7), giving your answer in standard form.

  1. 5 × 10^4
  2. 0.5 × 10^3
  3. 5 × 10^-10
  4. 5 × 10^3 Correct answer.

Explanation

Divide the numbers: 2.5 ÷ 5 = 0.5. Subtract the indices: 10^(−3 − (−7)) = 10^4. So the value is 0.5 × 10^4 = 5 × 10^3, which is in standard form.

Question 20Number and Numeration

The number N = 2^4 × 3^3 × 5^2 is written as a product of prime factors. What is the smallest positive integer by which N must be multiplied to make it a perfect square?

  1. 5
  2. 15
  3. 3 Correct answer.
  4. 9

Explanation

A perfect square has even exponents in its prime factorisation. In N, 2^4 and 5^2 already have even exponents, but 3^3 has an odd exponent, so one more factor of 3 makes the exponent 4. Therefore the smallest multiplier is 3.

Question 21Number and Numeration

Write five million, three hundred thousand and forty-two in figures.

  1. 5 003 042
  2. 5 030 042
  3. 5 300 042 Correct answer.
  4. 53 000 042

Explanation

Group the words into millions, thousands and units: five million is 5 000 000, three hundred thousand is 300 000, and forty-two is 42. Adding these gives 5 300 042.

Question 22Number and Numeration

Which fraction is equivalent to 0.375?

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

Explanation

Write 0.375 as 375/1000, then divide the numerator and denominator by 125. This gives 3/8, so 0.375 and 3/8 are equivalent.

Question 23Number and Numeration

What is 68 542 rounded to the nearest thousand?

  1. 68 500
  2. 70 000
  3. 68 000
  4. 69 000 Correct answer.

Explanation

The thousands digit is 8, and the hundreds digit is 5, so the number rounds up to 69 000. The 542 is enough to move the thousand value from 68 to 69.

Question 24Number and Numeration

At 05:00 the temperature was −7 °C. By noon it had risen by 12 °C, and by midnight it had fallen by 5 °C. What was the temperature at midnight?

  1. 0 °C Correct answer.
  2. 12 °C
  3. −12 °C
  4. −5 °C

Explanation

Start at −7 °C and add 12 °C to get 5 °C. Then subtract 5 °C, which gives 0 °C at midnight.

Question 25Number and Numeration

After a 20% discount, a meal costs P48. What was the price before the discount?

  1. P60 Correct answer.
  2. P57.60
  3. P68
  4. P40

Explanation

Let the original price be x. Paying P48 after a 20% discount means 80% of x equals 48, so 0.8x = 48. Dividing gives x = 60, so the original price was P60.

Question 26Number and Numeration

What is the least number of sweets that can be shared equally among 12, 15 or 20 children with none left over?

  1. 60 Correct answer.
  2. 120
  3. 180
  4. 30

Explanation

The number must be a common multiple, and the least one is the LCM. Since 12 = 2² × 3, 15 = 3 × 5 and 20 = 2² × 5, the LCM is 2² × 3 × 5 = 60.

Question 27Number and Numeration

Work out 1.25 × 0.08.

  1. 0.01
  2. 0.8
  3. 0.1 Correct answer.
  4. 10

Explanation

Multiply 125 by 8 to get 1000. There are two decimal places in 1.25 and two in 0.08, so place the decimal point four places from the right: 0.1000, which is 0.1.

Question 28Number and Numeration

Simplify (5⁴ × 5⁻²) ÷ 5³, giving your answer as a fraction or whole number.

  1. 25
  2. 5
  3. 1/25
  4. 1/5 Correct answer.

Explanation

For the product, add the exponents: 4 + (−2) = 2, giving 5². For the division, subtract the exponent 3: 2 − 3 = −1, so the result is 5⁻¹ = 1/5.

Question 29Number and Numeration

A sum of money is divided among three people in the ratio 3 : 4 : 5. The largest share is P80 more than the smallest share. What is the total sum of money?

  1. P400
  2. P960
  3. P480 Correct answer.
  4. P240

Explanation

The total number of ratio parts is 3 + 4 + 5 = 12. The largest and smallest shares differ by 5 − 3 = 2 parts, and these 2 parts equal P80, so one part is P40. The total is 12 × P40 = P480.

Question 30Number and Numeration

The mass of a metal block is 4.80 kg, correct to 3 significant figures. What is the lower bound of the mass in grams?

  1. 4795 g Correct answer.
  2. 4799 g
  3. 4750 g
  4. 4800 g

Explanation

A mass of 4.80 kg given to 3 significant figures is rounded to the nearest 0.01 kg. Half of 0.01 kg is 0.005 kg, so the lower bound is 4.80 − 0.005 = 4.795 kg. Converting to grams gives 4795 g.

Question 31Ratio, Proportion, Percentage and Consumer Arithmetic

Write the ratio 48 : 36 in its simplest form.

  1. 5 : 4
  2. 3 : 4
  3. 8 : 6
  4. 4 : 3 Correct answer.

Explanation

Both parts of a ratio must be divided by the same number to simplify it. The highest common factor of 48 and 36 is 12, so 48 ÷ 12 = 4 and 36 ÷ 12 = 3. The ratio in simplest form is therefore 4 : 3.

Question 32Ratio, Proportion, Percentage and Consumer Arithmetic

A jacket costs $240. In a sale the price is reduced by 15%. What is the sale price of the jacket?

  1. $36
  2. $276
  3. $225
  4. $204 Correct answer.

Explanation

To find a percentage of an amount, multiply by the percentage written as a decimal: 240 × 0.15 = 36. This is the size of the reduction. Subtracting the reduction from the original price gives 240 − 36 = 204, which is the sale price.

Question 33Ratio, Proportion, Percentage and Consumer Arithmetic

A shop sells the same fruit juice in three sizes: 500 ml for $1.60, 750 ml for $2.25, and 1 litre for $2.80. Which size gives the lowest price per millilitre?

  1. They all cost the same per millilitre
  2. 1 litre Correct answer.
  3. 750 ml
  4. 500 ml

Explanation

Comparing value for money means finding the cost of the same unit, here one millilitre. Divide each price by its volume: 1.60 ÷ 500 = 0.0032, 2.25 ÷ 750 = 0.0030 and 2.80 ÷ 1000 = 0.0028 dollars per millilitre. The 1 litre bottle has the lowest unit cost.

Question 34Ratio, Proportion, Percentage and Consumer Arithmetic

A recipe for 12 biscuits needs 180 g of flour. How much flour is needed to make 30 biscuits at the same rate?

  1. 360 g
  2. 540 g
  3. 450 g Correct answer.
  4. 420 g

Explanation

In a direct proportion both quantities increase together, so the amount of flour per biscuit stays the same. One biscuit needs 180 ÷ 12 = 15 g of flour. Multiplying 15 g by 30 gives 450 g of flour for 30 biscuits.

Question 35Ratio, Proportion, Percentage and Consumer Arithmetic

Six workers take 10 days to build a wall. Working at the same steady rate, how long would 15 workers take to build the same wall?

  1. 25 days
  2. 2.5 days
  3. 4 days Correct answer.
  4. 9 days

Explanation

This is an inverse proportion: as the number of workers rises, the time needed falls, while the total amount of work stays fixed. The job needs 6 × 10 = 60 worker-days. Dividing 60 worker-days by 15 workers gives 4 days.

Question 36Ratio, Proportion, Percentage and Consumer Arithmetic

A trader buys a bicycle for $320 and sells it for $368. What is the percentage profit?

  1. 48%
  2. 15% Correct answer.
  3. 13%
  4. 12.5%

Explanation

Profit is the selling price minus the cost price: 368 − 320 = 48 dollars. Percentage profit is always compared with the cost price, so divide 48 by 320 and multiply by 100. This gives 15%.

Question 37Ratio, Proportion, Percentage and Consumer Arithmetic

A sum of $2500 is invested at 4% simple interest per year. How much interest is earned in 3 years?

  1. $250
  2. $300 Correct answer.
  3. $100
  4. $400

Explanation

Simple interest is calculated on the original sum only, using interest = principal × rate × time. Here it is 2500 × 0.04 × 3 = 300 dollars. The interest is the same each year, so the total is three times the annual $100.

Question 38Ratio, Proportion, Percentage and Consumer Arithmetic

A dress is reduced by 20% in a sale. At the till, a further 10% is taken off the reduced price. What single percentage reduction is this equivalent to?

  1. 25%
  2. 28% Correct answer.
  3. 32%
  4. 30%

Explanation

Successive percentage changes are not added, because each one acts on a new amount. After 20% off, the customer pays 80%, and a further 10% off leaves 90% of that: 0.80 × 0.90 = 0.72. The dress therefore costs 72% of the original price, which is a single reduction of 28%.

Question 39Ratio, Proportion, Percentage and Consumer Arithmetic

After a 15% discount, a table costs $340. What was the price of the table before the discount?

  1. $355
  2. $391
  3. $460
  4. $400 Correct answer.

Explanation

The $340 is the price after a 15% discount, so it represents 85% of the original price. To reverse a percentage change, divide by the decimal: 340 ÷ 0.85 = 400. Checking, 15% of $400 is $60, and 400 − 60 = 340.

Question 40Ratio, Proportion, Percentage and Consumer Arithmetic

$2000 is invested at 5% per year compound interest. What is the total value of the investment after 2 years?

  1. $2100
  2. $2210
  3. $2205 Correct answer.
  4. $2200

Explanation

Compound interest adds each year's interest to the principal, so the second year earns interest on a larger amount. The multiplier for 5% growth is 1.05, and applying it twice gives 2000 × 1.05² = 2000 × 1.1025 = 2205 dollars. The total is the same as 2000 + 105 + 110.25.

Question 41Ratio, Proportion, Percentage and Consumer Arithmetic

Share $720 between Amina and Ben in the ratio 4 : 5. How much does Amina receive?

  1. $320 Correct answer.
  2. $360
  3. $400
  4. $300

Explanation

The ratio has 4 + 5 = 9 equal parts. Each part is $720 ÷ 9 = $80, so Amina receives 4 × $80 = $320.

Question 42Ratio, Proportion, Percentage and Consumer Arithmetic

In a test, Maria answered 18 questions correctly out of 24. What percentage of the questions did she answer correctly?

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

Explanation

Write the score as a fraction of the total: 18/24. This simplifies to 3/4, and 3/4 = 0.75 = 75%.

Question 43Ratio, Proportion, Percentage and Consumer Arithmetic

A map has a scale of 1 : 25 000. On the map, the distance between two villages is 4 cm. What is the actual distance, in kilometres?

  1. 10 km
  2. 100 km
  3. 1 km Correct answer.
  4. 0.1 km

Explanation

Multiply the map distance by the scale: 4 × 25 000 = 100 000 cm. Since 100 000 cm = 1 000 m = 1 km, the actual distance is 1 km.

Question 44Ratio, Proportion, Percentage and Consumer Arithmetic

A car uses 12 litres of petrol to travel 150 km. At the same rate, how many litres will it use to travel 250 km?

  1. 16 L
  2. 22 L
  3. 18 L
  4. 20 L Correct answer.

Explanation

Find the unit rate first: 12 litres ÷ 150 km = 0.08 litres per km. Then multiply by 250 km: 0.08 × 250 = 20 litres.

Question 45Ratio, Proportion, Percentage and Consumer Arithmetic

$4800 is invested at 7.5% simple interest per year. The investment earns $1080 in interest. For how many years was the money invested?

  1. 3 years Correct answer.
  2. 2 years
  3. 5 years
  4. 4 years

Explanation

Use I = P × R × T. The interest for one year is 4800 × 0.075 = $360, so T = 1080 ÷ 360 = 3 years.

Question 46Ratio, Proportion, Percentage and Consumer Arithmetic

A salesperson earns a commission of 4.5% on total sales. In one month the salesperson's sales are $12,000. What commission is earned?

  1. $540 Correct answer.
  2. $5,400
  3. $54
  4. $450

Explanation

Commission is a percentage of total sales. Multiply $12,000 by 0.045: 12,000 × 0.045 = $540. So the salesperson earns $540.

Question 47Ratio, Proportion, Percentage and Consumer Arithmetic

The price of a television, including 15% VAT, is $690. What is the price before VAT is added?

  1. $621.00
  2. $586.50
  3. $600.00 Correct answer.
  4. $575.00

Explanation

The price including VAT is 115% of the price before VAT. Divide $690 by 1.15: 690 ÷ 1.15 = $600. Subtracting 15% of $690 would be incorrect because VAT is calculated on the lower original price.

Question 48Ratio, Proportion, Percentage and Consumer Arithmetic

A worker is paid $12 per hour for a normal 40-hour week. Overtime is paid at 1.5 times the normal rate. In one week the worker works 46 hours. What is the total pay for that week?

  1. $588 Correct answer.
  2. $552
  3. $480
  4. $624

Explanation

Normal pay for 40 hours is 40 × $12 = $480. Overtime is 6 hours at 1.5 × $12 = $18 per hour, giving $108. Total pay is $480 + $108 = $588.

Question 49Ratio, Proportion, Percentage and Consumer Arithmetic

A car is bought for $18,000. Its value depreciates by 15% each year. What is its value after 3 years, to the nearest dollar?

  1. $15,300
  2. $13,005
  3. $9,900
  4. $11,054 Correct answer.

Explanation

Each year the car keeps 85% of its value, so multiply by 0.85 for each year. 18,000 × 0.85³ = 11,054.25, which rounds to $11,054. Depreciation compounds, so the reduction is not a fixed $2,700 each year.

Question 50Ratio, Proportion, Percentage and Consumer Arithmetic

Three friends share a sum of money in the ratio 3 : 4 : 5. The friend with the largest share receives $240 more than the friend with the smallest share. What is the total sum of money shared?

  1. $1,800
  2. $1,200
  3. $960
  4. $1,440 Correct answer.

Explanation

The difference between the largest and smallest shares is 5 − 3 = 2 parts. Since 2 parts equal $240, one part is $120. Total parts = 3 + 4 + 5 = 12, so total = 12 × $120 = $1,440.