Number

Work out \(2\frac{3}{4} - 1\frac{5}{6}\).

Work out \(\frac{3}{5} \div \frac{9}{10}\).

In a sale, the price of the jacket is reduced by 15%. Work out the sale price.

The shop bought the jacket for $40 and sells it at the normal price of $64. Work out the percentage profit.

Write 0.35 as a fraction in its simplest form.

Write \(\frac{3}{8}\) as a percentage.

Write these numbers in order of size, starting with the smallest.
0.38    \(\frac{3}{8}\)    37%    \(\frac{7}{20}\)

45% of the students walk to school. Work out how many students walk to school.

126 students cycle to school. Work out the percentage of students who cycle to school.

All the other students travel by bus. Write the fraction of students who travel by bus in its simplest form.

Work out the interest Kofi earns in 4 years.

Work out the total amount in the account after 4 years.

Write 0.0047386 correct to 3 significant figures.

By rounding each number to 1 significant figure, estimate the value of \(\frac{48.7 \times 3.12}{0.198}\).
Show all your working.

Work out how much Chen receives.

Chen then gives one quarter of his share to Amira.
Find the new ratio Amira : Ben : Chen in its simplest form.

Write down the lower bound and the upper bound of the side length.

Calculate the upper bound of the perimeter of the tile.

Change €250 into dollars.

Change $500 into euros. Give your answer correct to the nearest cent.

A jacket costs €85 in Paris and $95 in New York.
Find which city sells the jacket more cheaply and by how many dollars.

Work out the mass of flour needed for 15 muffins.

Lina has 7 eggs and plenty of every other ingredient.
Find the greatest number of muffins she can make.

all the prime numbers,

all the square numbers,

a cube number,

a multiple of 13.

Write 360 as a product of its prime factors. Give your answer in index form.

Find the smallest positive integer k such that 360k is a square number.

List all the factors of 18.

Find the highest common factor (HCF) of 18 and 24.

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

Find the next time both buses leave together.

Find how many times the two buses leave together from 08 00 to 13 00, including both of these times.

From this list, write down the irrational numbers.

√5    0.25    2π    √49    \(\frac{7}{9}\)    ∛27

Write down an integer between √50 and √70.

Write down the prime number between 40 and 50 that is 1 more than a multiple of 6.

\(x^5 \times x^3\)

\(\frac{y^{12}}{y^4}\)

\((2p^3)^4\)

Write 0.000 407 in standard form.

Write 6.3 ×10⁵ as an ordinary number.

Work out (4 ×10⁶) × (7 ×10⁻²). Give your answer in standard form.

Write down the value of \(7^0\).

Find the value of \(3^{-2}\) as a fraction.

Find the value of \(n\) when \(2^n = \frac{1}{32}\).

Work out the monthly rent before the increase.

The following year, the monthly rent of $1008 decreased by 12%. Work out the new monthly rent.

Work out the overall percentage change from the original rent to the rent in part (b). State whether it is an increase or a decrease.

Show that the fraction of her pay that she spends on food is \(\frac{3}{20}\).

Work out the fraction of her pay that is left after rent and food.

Amira has $360 left after paying for rent and food. Work out her monthly pay.

Work out the value of the car after 3 years.

Work out the total percentage of the original value that the car has lost after 3 years.

Work out the deposit.

Work out the total cost of buying the television on hire purchase.

Work out how much more the hire purchase cost is than the cash price, as a percentage of the cash price.

Work out how many days 12 workers would take to build the same wall.

The wall must be built in 6 days.
Find how many workers are needed in addition to the original 8.

Calculate the value of her investment at the end of 5 years. Give your answer correct to the nearest cent.

Sam also invests $4500 for 5 years, but at r% per year simple interest.
At the end of 5 years Sam's investment has the same value as Priya's.
Find r.

Find the number of red counters in the bag.

Some red counters are now removed from the bag. The ratio red : blue becomes 1 : 2.
Find how many red counters are removed.

Without using your calculator, estimate the value of E by rounding each number to 1 significant figure. Show your working.

Use your calculator to find the value of E. Give your answer correct to 3 significant figures.

Calculate the percentage error in your estimate, using the unrounded value of E.

Find the highest common factor (HCF) of A and B. Give your answer as an ordinary number.

Find the lowest common multiple (LCM) of A and B. Give your answer as an ordinary number.

Find the smallest positive integer n such that An is a cube number.

Find the largest possible side length of a tile.

Find the number of tiles needed when this largest tile is used.

Find the greatest number of bags that can be made.

Find the total number of sweets in each bag.

"The sum of any two prime numbers is always even."

"For every positive integer n, the number n² + n + 1 is prime."

"For every positive integer n, the number n² + n is even."

Find the lowest common multiple of 6, 8 and 15.

Find the smallest square number that is a multiple of 6, 8 and 15.

Find the smallest integer greater than 1000 that leaves a remainder of 1 when divided by 6, by 8 and by 15.

Write these numbers in order of size, starting with the smallest.
4.1 ×10⁻³    0.0039    3.9 ×10⁻⁴    0.04

Work out (8.4 ×10⁷) ÷ (2.1 ×10⁻³). Give your answer in standard form.

Work out 3.2 ×10⁴ + 5 ×10³. Give your answer in standard form.

Calculate the average number of people per km² of land.

On average, each person produces 0.74 kg of waste per day.
Calculate the total waste produced by the world's population in one year of 365 days. Give your answer in kilograms, in standard form.

1 tonne = 1000 kg. Write your answer to part (b) in tonnes, in standard form.

Work out the selling price of each of the lamps sold at a profit.

Work out the percentage loss on each of the remaining lamps.

Work out the capacity of the tank.

40% of the water in the tank is then used. Show that the tank is now exactly half full.

Work out how many litres of water are needed to fill the tank completely.

Find the ratio x : y : z in its simplest form.

Given that x + y + z = 155, find the values of x and z.

The same number, n, is added to both x and z. The ratio of the new values becomes 11 : 12.
Find n.

Write 5.0 litres in m³, in standard form.

Calculate the number of red blood cells in this adult's blood. Give your answer in standard form.

Each red blood cell lasts 120 days and is then replaced. The total number of red blood cells stays the same.
Calculate the number of red blood cells replaced each second. Give your answer in standard form, correct to 3 significant figures.

\(\sqrt{50}\)

\(\sqrt{12} + \sqrt{75}\)

\(\sqrt{3} \times \sqrt{27}\)

Show that \(0.\dot{2}\dot{7} = \frac{3}{11}\).

Write \(0.1\dot{8}\) as a fraction in its simplest form.

Hence write \(0.\dot{2}\dot{7} + 0.1\dot{8}\) as a single fraction in its simplest form.

The account pays 4% per year. Show that the value of the investment after 4 years is $5849.29, correct to the nearest cent.

A different account pays compound interest at \(r\)% per year. An investment of $5000 in this account is worth $6200 after 5 years.
Find the value of \(r\), giving your answer correct to 3 significant figures.

Find an expression for y in terms of x.

Find y when x = 4.

Find the positive value of x when y = 3.

Complete the statement for the distance, d km:
…… ≤ d < ……

Calculate the upper bound of the average speed of the car.

Explain why 50 cannot be one of the two integers.

One of the integers is 72. Find the other integer.

\(\frac{6}{\sqrt{3}}\)

\(\frac{4}{3-\sqrt{5}}\)

\(3^x = 81\)

\(2^{x+1} = 8^{x-1}\)

\(25^y = \frac{1}{125}\)

\((16x^8)^{\frac{1}{2}}\)

\(\frac{12a^5b^{-2}}{3a^{-1}b^3}\)

\(\left(\frac{8}{27x^6}\right)^{-\frac{1}{3}}\)

Find the perimeter of the rectangle.

Show that the area of the rectangle is a whole number of square centimetres, and find this area.

Find the exact length of a diagonal of the rectangle.

The price is increased by 20% and then decreased by 20%. Show that the overall effect is a decrease of 4%.

A different price is increased by \(x\)% and then decreased by \(x\)%. The overall effect is a decrease of 9%.
Find the value of \(x\).

Calculate the lower bound of the width of the bed.

Calculate the upper bound of the width of the bed.

Explain whether the width can be stated correctly to 2 significant figures.

Find the number of complete years after which the value of the car first falls below 40% of its value when new.
Show clear working.

After 4 years, the car is worth $11 230.
Calculate the value of the car when it was new. Give your answer correct to the nearest dollar.

Write 600 as a product of its prime factors.

Find the value of k.

Find the lowest common multiple of N and 600.

Find all the possible pairs of values of a and b.

Find the larger of the two possible values of the lowest common multiple of a and b.

Find how long it is until they are next together at the start line. Give your answer in minutes and seconds.

Find how many laps Priya has completed at this time.

A third runner, Kofi, joins them at the start. His lap time is t seconds, where t is an integer between 62 and 75.
All three runners are next together at the start line after exactly 2520 seconds.
Find the value of t.

Expand and simplify \((2+\sqrt{3})^2\).

Write \(\frac{5+\sqrt{3}}{2-\sqrt{3}}\) in the form \(a + b\sqrt{3}\), where \(a\) and \(b\) are integers.

Given that \(x = 2+\sqrt{3}\) and \(\frac{1}{x} = 2-\sqrt{3}\), find the value of \(x^2 + \frac{1}{x^2}\). You may use your answer to part (a).

Show that \(4^x \times 8^{x-1}\) can be written as \(2^{5x-3}\).

Hence solve \(4^x \times 8^{x-1} = \frac{1}{4\sqrt{2}}\).

Show that \(\frac{2^{n+3} - 2^{n+1}}{2^n}\) has the same value for every value of \(n\), and find this value.