Number — IGCSE Mathematics (0580) questions by topic

Write the number 10069 in words.

A bag of sweets costs $0.34. Arun buys 10 bags of sweets. Work out how much change he receives from $5.

Two numbers have a sum of -2 and a product of -15. Work out the two numbers.

From the list of numbers 7, 27, 39, 49, 99, 112, write down an even number.

Write down the reciprocal of 5.

Put one pair of brackets into the calculation to make it correct. 7 - 5 x 4 + 8 = 16

Write 90% as a fraction in its simplest form.

Work out. -5 x -4

3^p x 3^4 = 3^10 Find the value of p.

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of (42.8 + 17.4) / (1.97 x 5.79)

A = 2^3 x 3 B = 3^2 x 5 Find the highest common factor (HCF) of A and B.

Work out 1 1/3 + 1 3/4. Give your answer as a mixed number in its simplest form.

Write 32500 in standard form.

Write the number sixteen thousand and sixty-two in figures.

Write three-quarters as a decimal.

Write down the value of sqrt(36).

Complete this statement. 10 weeks is ............... days.

The diagram shows a rectangle divided into a grid of small squares (5 columns by 7 rows, giving 35 small squares of equal size). Shade 2/5 of the rectangle.

Find the value of the reciprocal of 1/3.

Put one pair of brackets into the calculation to make it correct. -12 + 4 / 2 - 3 = -16

Write these fractions in order, starting with the smallest. 5/8 11/12 2/3 3/4 13/24 ............... < ............... < ............... < ............... < ...............…

Tim has a method for multiplying a number by 99. He shows his method for 53 x 99. 53 x 99 = 53 x 100 - 53 = 5300 - 53 = 5247 Work out 85 x 99 using Tim's method.

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of (17.8 + 10.3) / 5.5

Find the highest common factor (HCF) of 66 and 110.

P is a prime number. Write down the value of P that satisfies the inequality 13 < P < 19.

The Venn diagram shows the universal set E (script E) and two overlapping sets J and K, drawn as two intersecting circles inside a rectangle. The shaded region is the whole of…

Work out 2 7/9 x 1 1/5. Give your answer as a mixed number in its simplest form.

The mass, m kg, of a stone is 3.2 kg, correct to the nearest 100 g. Complete this statement about the value of m. ............... <= m < ...............

Write the number 70 000 000 in words.

Write down sqrt(169) .

Find the next term in each sequence. 1, 5, 10, 16, 23, ...

70 students study one of French, Spanish and German. The ratio number who study French : number who study Spanish = 3 : 7. 15 students study French. Find the number of students…

A music group has 30 members. 7 members play a flute (F) and play a clarinet (C). 12 members play a flute. 1 member does not play a flute and does not play a clarinet. Use this…

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of 62.5 / (9.7 × 0.52) .

On Monday the cost of a concert ticket is $x. On Tuesday the cost of a ticket for the same concert is 20% more than the cost on Monday. Jack buys 4 tickets on Monday and 5 tickets…

Find the highest common factor (HCF) of 36 and 54.

Work out 3 1/2 - 1 4/7. Give your answer as a mixed number in its simplest form.

Sally invests $1500 at 3% per year simple interest. Work out the total value of her investment at the end of 6 years.

Work out. 5/6 - 2/3 x 3/8

Write the recurring decimal 0.2 6-recurring (i.e. 0.2666... where the 6 repeats) as a fraction. Give your answer in its simplest form.

Expand and simplify. (2 - sqrt(5))(1 - 3 sqrt(5))

Find the value of 27^(-2/3).

Simplify. (2x^2 + 10x)/(x^2 - 25)

Find the highest common factor (HCF) of 36 and 54.

Write 0.007 08 in standard form.

Write 0.25 recurring (the 5 is recurring, i.e. 0.2555...) as a fraction.

Find the value of 125^(2/3).

Rationalise the denominator of 9/sqrt(3). Give your answer in its simplest form.

Write as a single fraction in its simplest form. (5a/6) x (3b/a)

Work out. 5/6 − 7/12 Give your answer as a fraction in its simplest form.

Write 42 as a product of its prime factors.

Find the lowest common multiple (LCM) of 15xy^3 and 18x^4y.

Simplify. sqrt(27) + sqrt(12)

Write 0.3̇2̇8̇ as a fraction in its simplest form. (The recurring decimal is 0.3 with 2 and 8 recurring, i.e. 0.3282828...)

Simplify. (7x − x^2) / (49 − x^2)

Find the value of sqrt(1.96).

Calculate the number of months in 5 years.

3/7 0.41 17/41 42% Write these numbers in order, starting with the smallest. ............ < ............ < ............ < ............ smallest

A plane leaves Seattle at 07 30 on Tuesday and arrives in Seoul 10 hours and 55 minutes later. The local time in Seoul is 16 hours ahead of the local time in Seattle. Work out the…

Tom needs 225 g of flour to make 10 cakes. A shop sells flour in 500 g bags. Work out the number of bags of flour Tom needs to make 70 cakes.

Dara changes 5700 Thai baht to dollars. The exchange rate is $1 = 34.18 Thai baht. Calculate the amount that Dara receives. $ ............

Anil invests $2000 and Baz invests $7500. Write the ratio money invested by Anil : money invested by Baz in its simplest form. ............ : ............

The population of an island increases from 18 400 to 19 780. Calculate the percentage increase. ............ %

Li asks 28 students if they speak English (E) and if they speak Spanish (S). 15 students speak English. 12 students speak Spanish. 6 do not speak English and do not speak Spanish.…

The height, h metres, of a building is 105 m, correct to the nearest metre. Complete this statement about the value of h. ............ <= h < ............

Apples cost $1.20 per kilogram and one banana costs 35 cents. Work out the total cost, in dollars, of 3 kg of apples and 7 bananas.

A student scores 58 out of 80 in a test. Calculate their percentage score.

Calculate 57% of 45.

The exchange rate is $1 = 0.923 euros. Calculate the difference between 750 euros and $846. Give your answer in euros correct to 2 decimal places.

Sam spends $187 on electricity and gas. The ratio electricity : gas = 8 : 3 . Work out how much Sam spends on electricity.

Rick invests $6000 for 5 years at a rate of 9% per year compound interest. Calculate the total interest earned during the 5 years.

Write 0.000 000 0347 in standard form.

Here is a list of numbers: 2 6 16 18 24 26 27 33 From this list, write down the number that is a multiple of 12.

Put one pair of brackets into this calculation to make it correct. 80 ÷ 8 + 2 × 3 = 24

Calculate. (2.8^5 − 0.3^2) / sqrt(5) Give your answer correct to 2 decimal places.

The local time in Japan is 3 1/2 hours ahead of the local time in India. Find the time in Japan when it is 21 45 in India.

Mia changes $350 into euros. The exchange rate is $1 = 0.92 euros. Calculate the amount Mia receives.

In May a shop makes a profit of $542. In June the shop makes a profit of $600. Calculate the percentage increase in the profit from May to June.

Meg invests $2500 at a rate of 4.6% per year simple interest. Calculate the total amount of her investment at the end of 3 years.

The table gives information about the costs of hiring bikes. Type of bike Cost for first day Cost for each extra day --- --- --- Road $25 $20 Mountain $40 $35 Electric $70 $50…

These are the distances above the surface of the Earth of five satellites, A, B, C, D and E. Each distance is in kilometres. A = 35 800 B = 7.8 × 10^2 C = 1.5 × 10^6 D = 535 E = 2…

Work out. (16.71 + 46.13) / sqrt(8.6^2 - 3.5^2) Give your answer correct to 2 significant figures.

In the USA, one gallon of fuel costs $4.83. In the UK, one litre of fuel costs £1.62. The exchange rate is £1 = $1.215. 1 gallon = 3.785 litres In which country does 1 litre of…

Write down the inequality in y shown by the number line. The number line for y runs from -2 to 5. There is a filled (closed) circle at y = -1.5 with the line shaded to the right,…

Hadi buys a dishwasher. He can either pay a single payment of $980 or he can pay using a monthly plan. The monthly plan is 20% of $980 plus 12 payments of $75.25. Hadi uses the…

In a sale, the original price of a sewing machine is reduced by $38. This is an 8% reduction in the original price. Work out the original price of the sewing machine.

Write down all the factors of 18.

Mateo invests $1250 at a rate of r% per year compound interest. At the end of 6 years the total value of his investment is $1484. Calculate the value of r.

(16^(5m)) / 4 = 64^(2n) Find m in terms of n.

I = V/R V is 50, correct to the nearest 10. R is 13, correct to the nearest integer. Calculate the upper bound of I.

Mass of box A : Mass of box B = 4 : 7 The mass of box B is 2.4 kg more than the mass of box A. Calculate the mass of box A and the mass of box B.

Scott changes $300 into pounds (£). The exchange rate is £1 = $1.20. Calculate the amount Scott receives.

Calculate. (2.1^2 - 1.9) / 0.5

In a sale, the original price of a shirt is reduced by 15%. The sale price of the shirt is $23.63. Find the original price of the shirt.

The length of a rectangle is 16 cm, correct to the nearest centimetre. The width of the rectangle is 14 cm, correct to the nearest centimetre. Calculate the lower bound of the…

Alex invests $400 at a rate of 2.3% per year simple interest. Find the total amount Alex has at the end of 5 years.

Simplify. (h^2 + 4h) / (h^2 - 16)

From this list, write down a natural number. The list is: 2/5 sqrt(15) 23 sqrt(144) -2 0.8

One titanium atom has a mass of 7.95 x 10^-23 grams. Calculate the number of titanium atoms in 1 kg of titanium. Give your answer in standard form.

E (universal set) = {x : x is an integer and 1 <= x <= 12} E = {even numbers} M = {multiples of 3} Find n(M).

sqrt( 10^400 / (10^220 x 10^80) ) = 10^k Find the value of k.

Jess invests $1400 in an account. The account pays compound interest at a rate of r% per year. At the end of 4 years the value of her investment is $1523.15. Find the value of r.

In the Venn diagram, shade the region (A union B) (intersection) C'. (The Venn diagram shows three intersecting circles labelled A (top left), B (top right) and C (bottom centre)…

A metal cube has mass 14.2 g, correct to 1 decimal place. Find the lower bound of the mass of the cube.

A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes.

Write these numbers in order, starting with the smallest: 15/213, 0.071, 0.7, 7%.

Write the fraction 24/84 in its simplest form.

By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of (6.7 × 2.1) / (18 − 5.9). You must show all your working.

The length, l metres, of a piece of wood is 3.6 metres, correct to the nearest 10 centimetres. Complete this statement about the value of l: ... ⩽ l < ...

Calculate 1 ÷ (6.4 × 10⁻⁵). Give your answer in standard form.

Without using a calculator, work out 2 1/7 ÷ 5/9. You must show all your working and give your answer as a mixed number in its simplest form.

𝓔 = {a, b, c, d, e, f, g, h, i, j, k}, F = {f, a, c, e}, B = {b, a, c, k}. Complete the Venn diagram (two overlapping sets F and B within the universal set).

Write down all the factors of 18.

Kai and Ava each have a piece of wood 57 cm long. Kai cuts his piece into 4 equal length parts. Find the length of one part.

Find the temperature that is 8 °C colder than −5 °C.

There are two prime numbers in this list: 27, 47, 57, 61, 75, 93. Work out the sum of these two prime numbers.

The distance from town A to town B on a map is 3.5 cm. The scale on the map is 1 : 250 000. Find the actual distance, in kilometres, from town A to town B.

𝓔 = {x 1 ⩽ x ⩽ 20}, E = {even numbers}, M = {multiples of 5}. Find n(M).

Without using a calculator, work out 4/7 ÷ 1 5/21. You must show all your working and give your answer as a fraction in its simplest form.

Write 45 000 in standard form.

Buses at a station go to the port or to the town. Buses leave every 28 minutes for the port. Buses leave every 48 minutes for the town. At 10 18 a bus for the port and a bus for…

The mass, m kilograms, of object A is 350 kg, correct to the nearest 10 kg. Complete this statement about the value of m: ... ⩽ m < ...

Write 928 correct to the nearest ten.

Write down a fraction that is equivalent to 7/9.

Work out −4 + 6 × 3.

Write down the reciprocal of 16 as a decimal.

Olga thinks that 87 is a prime number. Is Olga correct? Give a reason for your answer.

A film lasts for 2 hours 50 minutes. The film ends at 23 05. Find the time the film starts.

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of (6.8 × 10.6) / (3.2 − 0.98). You must show all your working.

Maddie changes 4000 Swiss francs into dollars when the exchange rate is $1 = 0.913 Swiss francs. Work out how many dollars she receives.

Find the highest common factor (HCF) of 32 and 120.

Vanessa invests $8500 at a rate of 3.5% per year compound interest. Calculate the value of her investment at the end of 6 years. Give your answer correct to the nearest dollar.

Without using a calculator, work out 5 11/12 + 2 1/4. You must show all your working and give your answer as a mixed number in its simplest form.

A train journey starts at 21 43. It takes 8 hours and 32 minutes. Find the time the journey finishes.

By writing each number in the calculation correct to 1 significant figure, work out an estimate for the value of (6.7 × 2.1) / (18 − 5.9). You must show all your working.

The scale of a map is 1 : 125 000. On a map, the length of an island is 9.4 cm. Calculate the actual length of the island, giving your answer in kilometres.

Without using a calculator, work out 2 1/7 ÷ 5/9. You must show all your working and give your answer as a mixed number in its simplest form.

Anya invests $6000 in an account that pays compound interest at a rate of r % per year. At the end of 8 years, the account has earned $621.70 in interest. Calculate the value of r.

Find the temperature that is 8 °C colder than −5 °C.

There are two prime numbers in this list: 27, 47, 57, 61, 75, 93. Work out the sum of these two prime numbers.

The distance from town A to town B on a map is 3.5 cm. The scale on the map is 1 : 250 000. Find the actual distance, in kilometres, from town A to town B.

𝓔 = {x 1 ⩽ x ⩽ 20}, E = {even numbers}, M = {multiples of 5}. Find n(M).

Without using a calculator, work out 4/7 ÷ 1 5/21. You must show all your working and give your answer as a fraction in its simplest form.

Write 0.6̅2̅1 (i.e. 0.6 recurring 21) as a fraction in its simplest form. You must show all your working.

In the Venn diagram, shade the region A ∩ B′ ∩ C.

A film lasts for 2 hours 50 minutes. The film ends at 23 05. Find the time the film starts.

At the end of the day, a shopkeeper has 12 tins of cat food left. This is 3/13 of the number he had at the beginning of the day. Calculate the number of tins he had at the…

Without using a calculator, work out 5 11/12 + 2 1/4. You must show all your working and give your answer as a mixed number in its simplest form.

𝓔 = {a, b, e, g, l, m, o, r, t, y}, P = {a, b, e, g, l, r}, Q = {e, g, m, o, r, t, y}. Complete the Venn diagram (two overlapping sets P and Q).

Calculate 4² + ³√0.4 (i.e. 16 + cube root of 0.4). [As printed: 4² + 3 of 0.4 with the 3 a cube-root index.]

Write 0.5̅8̅1 (0.5 recurring 81) as a fraction. You must show all your working and give your answer in its simplest form.

The number of trees in a forest is decreasing exponentially at a rate of 1.75% per year. Eleven years ago there were 980 trees. Calculate the number of trees in the forest now.…

A train travels between two stations. The distance between the stations is 220 km, correct to the nearest kilometre. The speed of the train is 125 km/h, correct to the nearest 5…

Write the number forty thousand and thirty-three in figures.

Antonio buys a restaurant for $240 000. This is 5/8 of the amount he has available to spend. Show that he has $144 000 left after buying the restaurant.

Write the number three hundred thousand and three in figures.

Bananas cost $1.20 per kilogram and apples cost $2.25 per bag. Work out the total cost of 3.5 kg of bananas and 2 bags of apples.

The length, l m, of a piece of wire is 18.7 metres, correct to the nearest 10 centimetres. Complete the statement about the value of l: ... ⩽ l < ...

An orchard has 1250 trees in the ratio apple : pear : cherry = 12 : 9 : 4. Calculate the number of apple trees.

The Venn diagram shows set X and set Y. X contains r, t, l, e, a; Y contains h, e, s, c, a (with e, a in the intersection). List the elements of X.

Anil changes $830 into euros when the exchange rate is 1 euro = $1.16. He spends 500 euros. He then changes the remaining money back into dollars at the same exchange rate. Work…

Tomas sells a computer, a bike and a phone. The amounts he receives are in the ratio computer : bike : phone = 14 : 17 : 9. Calculate the amount he receives for the phone as a…

Write down the value of the 8 in the number 58 317.

Find the value of the cube root of 5832 (∛5832).

A watch costs $12 400. In a sale there is a discount of 16%. Calculate the amount of the discount.

Arjun lives in Delhi and Haru lives in Tokyo. They play a computer game online at the same time. They start at 14 45 Tokyo local time. The game lasts 3 hours 50 minutes. The local…

Write 0.03682 correct to 2 significant figures.

The table shows some information about Amir's shopping. Complete the table. Fruit Cost per kilogram Number of kilograms Amir buys Cost --- --- --- --- Oranges $2.35 3.2 $...…

Find the highest common factor (HCF) of 140 and 126.

By writing each number in the calculation correct to 1 significant figure, find an estimate for the value of (36.9 + 24.2) / (3.8 − 1.2). You must show all your working.

Indira invests $6000 at a rate of r% per year simple interest. At the end of 4 years the value of her investment is $6840. Find the value of r.

Write 45 000 in standard form.

The length, s metres, of a ship is 287 m, correct to the nearest metre. Complete this statement about the value of s: ........... ≤ s < ...........

Write 8/10 as a decimal.

Work out 2/5 of 180.

Write these numbers in order, starting with the smallest: 3/16, 18.7%, 0.19, 9/50.

Write down the number that is 9 greater than −23.

Write 24.07839 correct to 2 decimal places.

Change 62 000 millimetres into kilometres.

Explain why 111 is not a prime number.

Filip invests $4000 for 3 years at a rate of 2.5% per year simple interest. Calculate the value of his investment at the end of the 3 years.

Without using a calculator, work out 3 1/8 − 1 3/4. You must show all your working and give your answer as a mixed number in its simplest form.

ξ = {students in a class}, C = {students who play cricket}, F = {students who play football}. There are 36 students in the class. 15 students play cricket. 20 students play…

Bell A rings every 22 minutes. Bell B rings every 14 minutes. Both bells ring at 09 00. Work out the next time both bells ring together.

Write down all the factors of 32.

From this list, write down a cube number: 61, 63, 64, 66, 68, 69.

Tara goes on a journey by train. The train leaves at 06 48. The journey takes 12 hours and 35 minutes. Find the time when Tara arrives.

Without using a calculator, work out 1 5/6 ÷ 11/15. You must show all your working and give your answer as a mixed number in its simplest form.

Shubhu invests $750 in a savings account for 5 years. The account pays simple interest at a rate of 1.8% per year. Calculate the total interest she earns during the 5 years.

ξ = {2, 4, 8, 9, 10, 12}, Q = {square numbers}, R = {multiples of 4}. Use this information to complete the Venn diagram (sets Q and R).

Find the highest common factor (HCF) of 48 and 80.

The table shows some information about Amir's shopping. Complete the table. Fruit Cost per kilogram Number of kilograms Amir buys Cost --- --- --- --- Oranges $2.35 3.2 $...…

The exchange rate between Singapore dollars and euros is 1 Singapore dollar = 0.62 euros. Find the value of 161.20 euros in Singapore dollars.

Calculate 7 3/11 × 3 3/10.

Find the highest common factor (HCF) of 140 and 126.

Write 0.42̇ (0.4 recurring 2) as a fraction in its simplest form. You must show all your working. (The recurring decimal is 0.4222...)

At the end of 2021 there were 27 000 rhinos living in the wild. The number of rhinos is expected to decrease exponentially by 3% each year. Work out the number of rhinos expected…

The Venn diagram shows information about the number of elements in sets A, B and ξ. The regions are: A only = 5x, A∩B = x + 5, B only = 12 − x, and outside both = 15. n(ξ) = 52.…

P = 2w + 2h. w = 11 and h = 9.5, both correct to 2 significant figures. Find the lower bound and the upper bound for P.

Write as a single fraction in its simplest form. (10x² − 60x) / (x² − x − 30)

Write 24.07839 correct to 2 decimal places.

Write down the number that is 9 greater than −23.

Change 62 000 millimetres into kilometres.

Explain why 111 is not a prime number.

Without using a calculator, work out 3 1/8 − 1 3/4. You must show all your working and give your answer as a mixed number in its simplest form.

Write 90 as a product of its prime factors.

On the Venn diagram (sets P and Q in universal set ξ), shade the region P ∪ Q'.

Find the lowest common multiple (LCM) of 12x⁸ and 8x¹².

The area of a rectangle is 55.2 cm², correct to 1 decimal place. The length of the rectangle is 9 cm, correct to the nearest cm. Calculate the upper bound of the width of the…

Simplify. (ax − 2a − x + 2) / (a² − 1)

Tara goes on a journey by train. The train leaves at 06 48. The journey takes 12 hours and 35 minutes. Find the time when Tara arrives.

From this list, write down a cube number: 61, 63, 64, 66, 68, 69.

Shubhu invests $750 in a savings account for 5 years. The account pays simple interest at a rate of 1.8% per year. Calculate the total interest she earns during the 5 years.

Without using a calculator, work out 1 5/6 ÷ 11/15. You must show all your working and give your answer as a mixed number in its simplest form.

Find the highest common factor (HCF) of 48 and 80.

Oliver sent 22% more messages in June than in May. He sent 305 messages in June. Find how many more messages he sent in June than in May.

Simplify. (64y²⁷)^(2/3)

F is proportional to the product of m and a. Calculate the percentage change in F when m is increased by 40% and a is decreased by 15%.

Write the number six and a half million in figures.

A railway line has three stations: Town, Port and Cove. Train A leaves Town for Cove and train B leaves Cove for Town. Both trains stop at Port. The travel graph shows distance…

Pure gold costs $42 per gram. The fraction of pure gold in an object is measured in carats. One carat means 1/24 of the mass of an object is pure gold. Henry buys a 9-carat gold…

Write the number fourteen thousand and ninety-seven in figures.

Elize, Lily and Marco start a business. Elize invests $5000, Lily invests $8000, Marco invests $3000. After one year they make a profit of $40 000. They share this profit in the…

Tom has a restaurant bill: Soup $..., Pasta $13.30, Ice cream $4.80, Drinks $3.81, Total cost $25.40. Complete the bill to show the cost of soup.

Aneel has 80 tea bags, 1/2 kg of sugar and 1 litre of milk. To make a cup of tea he uses 1 tea bag, 8 grams of sugar, 40 millilitres of milk. In the morning, Aneel makes 15 cups…

The table shows information about some planets (Earth, Mars, Jupiter, Saturn, Neptune) with their diameter (km) and average distance from the Sun (km). The average distance of…

Complete the table for the three sequences (find the 5th term and the nth term for each). Sequence 1st 2nd 3rd 4th 5th nth --- --- --- --- --- --- --- A −7 −3 1 5 B 7 13 23 37 C…

The value of Priya's car decreases by 10% every year. The value today is $7695. Calculate the value of the car after one year.

The table shows the amount received when exchanging $100 in some countries: Wales 77.05 pounds, India 7437.05 rupees, China 671.20 yuan, Spain 85.35 euros. Brad changes $250 to…

The table shows the number of each type of bird seen in a garden on Monday. Type of bird Frequency Pie chart sector angle --- --- --- Goldfinch 8 96° Jay 6 Starling 11 Robin 5…