Number

What is the sum of all the factors of $8$?

Which of the following sets is equal to $\{2, 4, 6\}$?

If $A \cup B = B$, then:

If $\mathcal{E} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ and $C = \{x : x \text{ is a composite number}\}$, find $n(C)$.

If $\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, $A = \{x : x \text{ is even}\}$ and $B = \{x : x \text{ is a multiple of 5}\}$, find $n(A' \cap B)$.

Given $n(A) = 10, n(B) = 15$. If $n(A \cup B) = 25$, what can be said about $A$ and $B$?

Let $n(\xi) = 45$. If $n(A') = 20$, find $n(A)$.

A survey of 60 students found that 30 play the piano ($P$), 25 play the guitar ($G$), and 20 play the violin ($V$). It is known that 12 students play both piano and guitar, 8 play both guitar and violin, 10 play both piano and violin, and 4 students play all three instruments. How many students play none of these instruments?

Given the universal set $\xi = \{x \in \mathbb{Z} : 1 \le x \le 30\}$, let $A$ be the set of multiples of 4, $B$ be the set of multiples of 6, and $C$ be the set of square numbers. Find $n((A \cup B) \cap C)$.

Given $U = \{1, 2, 3, \dots, 20\}$. Let $A$ be the set of multiples of 2, $B$ the set of multiples of 3, and $C$ the set of multiples of 5. Find $n(A \cap B' \cap C)$.

Write $0.625$ as a fraction in its simplest form.

Simplify the fraction $\frac{18}{24}$ to its lowest terms.

What is $20\%$ of $0.5$?

Convert $\frac{21}{25}$ to a percentage.

Write $125\%$ as a mixed number in its simplest form.

A bank pays $2.5\%$ simple interest per year. How much total interest will be earned on $\$\$3000$ after $4$ years?

Increase $\$120$ by $12.5\%$.

Evaluate $\frac{(0.2)^3}{0.04 \times 0.5}$ and express the result as a fraction in simplest form.

A water tank is $\frac{2}{3}$ full. After $20$ liters are removed, the tank is $\frac{1}{2}$ full. What is the total capacity of the tank in liters?

Calculate the exact sum of the recurring decimals $0.1\dot{6}$ and $0.8\dot{3}$.

Simplify the ratio $\frac{1}{2} : \frac{1}{3}$ to its simplest integer form.

If $1\text{ inch} = 2.54\text{ cm}$, how many centimetres are in $10\text{ inches}$?

If $x:y = 3:8$ and $y=40$, find the sum of $x$ and $y$.

A gear with $12$ teeth is connected to a gear with $20$ teeth. When the $12$-tooth gear makes $50$ turns, how many turns does the $20$-tooth gear make?

The three interior angles of a triangle are in the ratio $3:4:5$. Calculate the size of the largest angle.

The time period $T$ of a pendulum is proportional to the square root of its length $L$. If a pendulum of length $1.44$ m has a period of $2.4$ s, find the period of a pendulum with length $0.81$ m.

A $500$ g box of cereal costs $\$3.20$ and a $750$ g box of the same cereal costs $\$4.50$. Calculate the difference in price per $100$ g of cereal.

A liquid is flowing through a pipe at a rate of $2.5 \text{ litres per second}$. How many cubic metres will flow through the pipe in 1 hour?

The ratio of the heights of two similar cylinders is $2 : 3$. If the volume of the smaller cylinder is $40 \text{ cm}^3$, find the volume of the larger cylinder.

If $x$ is inversely proportional to $y^2$, and $x$ is increased by $300\%$, by what percentage does $y$ decrease?

Simplify $9^2 \times 9^0$.

Write $0.000000001$ in standard form.

Express $700,000,000$ in standard form.

Simplify $k^0 \times k^5$.

Simplify the expression $(m^{\frac{1}{2}} n^{\frac{1}{3}})^6$.

Evaluate $16^{0.75} - 8^{\frac{1}{3}}$.

Calculate $(2.5 \times 10^8) \div (5 \times 10^3)$, giving your answer in standard form.

If $x = 2 \times 10^5$, find $x^{-3}$ in standard form.

Simplify $(\frac{1}{2})^{-2} + (\frac{1}{3})^{-2} + (\frac{1}{4})^{-2}$.

Solve $2^{x-1} \times 5^{x-1} = 0.001$.

Simplify $\sqrt{48}$ completely.

What is the simplest form of $\sqrt{125}$?

Express $\sqrt{200}$ in the form $10\sqrt{k}$.

Divide the surd: $8\sqrt{3} \div 2$.

Simplify the product $2\sqrt{7} \times 3\sqrt{14}$ into the form $a\sqrt{2}$.

Expand and simplify $(\sqrt{10} + \sqrt{2})(\sqrt{10} - \sqrt{2})$.

Rationalize the denominator and simplify $\frac{\sqrt{11} - 1}{\sqrt{11} + 1}$.

Find the value of $n$ such that $\sqrt{3^n} = 81$.

Given $x = \frac{1}{\sqrt{2}+1}$ and $y = \frac{1}{\sqrt{2}-1}$, find $x+y$.

The side of an equilateral triangle is $2\sqrt{3}$. Find its altitude.

How much compound interest is earned on $\$400$ at $5\%$ per year for $2$ years?

Calculate the total amount in an account if $\$1000$ is invested at $2.5\%$ simple interest per year for $4$ years.

Find the total value after $2$ years when $\$6000$ is invested at $2\%$ per year compound interest.

Calculate the total amount after $5$ years if $\$800$ is invested at $3\%$ simple interest per year.

The population of a town is 120,000 and is decreasing at a compound rate of $3\%$ per year. What will the population be after 5 years, to the nearest whole number?

Calculate the difference between simple interest and compound interest on $3000 for 2 years at an annual rate of $5\%$.

A deposit of $900 earns $108 in simple interest over 2 years. What was the annual interest rate?

A man borrows $\$10,000$ at $10\%$ compound interest. At the end of each year, he pays back $\$2,000$. How much does he owe after the second payment?

A sum of money was invested at $10\%$ compound interest for $3$ years. If the difference between the interest for the third year and the second year is $\$110$, find the principal.

A painting's value increases by $10\%$ in Year 1 and $20\%$ in Year 2. What is the single equivalent annual compound growth rate over these two years?

The power of a motor is $1600$ W, correct to the nearest $100$ W. What is the lower bound of the power?

The height of a door is $1.82$ m, correct to the nearest centimetre ($0.01$ m). What is the upper bound of the height?

A fabric width is $1.1$ m, correct to one decimal place. What is the lower bound of the width?

A lesson lasts for $40$ minutes, correct to the nearest $10$ minutes. What is the lower bound of the duration?

The length and width of a rectangle are both $20$ cm, measured to the nearest $10$ cm. What is the lower bound of the perimeter?

If $k = 1/x$ and $x = 0.4$ correct to $1$ decimal place, calculate the lower bound of $k$ to $2$ decimal places.

A reading $x$ is $4.56$ correct to $2$ decimal places. Find the upper bound of $x$.

A cylinder has radius $r=5.0$ cm and height $h=10.0$ cm (both correct to 1 decimal place). Calculate the difference between the upper bound and the lower bound of its volume in $\text{cm}^3$ to 1 decimal place.

Given $x = \frac{a-b}{c}$, where $a = 100$, $b = 50$, and $c = 10$, all correct to the nearest integer, calculate the upper bound of $x$ to 3 decimal places.

The resistivity $\rho$ is given by $\rho = \frac{RA}{L}$. If $R = 20$ $\Omega$, $A = 0.5$ $\text{m}^2$, and $L = 10$ m, all measured to the nearest integer, calculate the lower bound of $\rho$ to 4 decimal places.

Find the value of $\sqrt[3]{216}$.

Calculate the value of $\sqrt{144} + \sqrt{25}$.

Simplify the expression $a^5 \times a^3$.

Evaluate the value of $3^4$.

Simplify the expression $\frac{y^7 \div y^{-2}}{y^3}$.

Solve the equation $5^{x+1} = 125$ for $x$.

Evaluate the expression $27^{-\frac{2}{3}}$.

Simplify the expression $\frac{4^n \times 2^{n-1}}{8^n}$ to its simplest numerical form.

Simplify the expression $\sqrt{50} + \sqrt{18}$ into the form $k\sqrt{2}$, where $k$ is an integer. Find the value of $k$.

1. Powers and Roots: practice question 1 for Number?

1. Ordering: practice question 1 for Number?

1. Ordering: practice question 2 for Number?

1. Ordering: practice question 3 for Number?

1. Ordering: practice question 4 for Number?

1. Ordering: practice question 5 for Number?

1. Ordering: practice question 6 for Number?

1. Ordering: practice question 7 for Number?

1. Ordering: practice question 8 for Number?

1. Ordering: practice question 9 for Number?

1. Ordering: practice question 10 for Number?

Work out the value of $1.5 \times 4 - 0.8 \div 0.2$.

Calculate the value of $2 \times 5^2 - 10$.

Evaluate the expression $-7 + (-3) - (-5)$.

Find the value of $\frac{5}{6} \times \frac{3}{10}$ and give your answer in its simplest form.

Work out the value of $\sqrt{1.44} \div 0.3 + (0.2)^3$

Find the result of the calculation: $(2.5)^2 - 1.5 \times 3 + \sqrt{0.49}$

Calculate the value of $1 \frac{3}{4} + 2 \frac{1}{2} \div \frac{5}{6}$ and give your answer as a mixed number.

A retailer buys a box of 60 gadgets for GBP 480. It is found that 15% of the gadgets are faulty and cannot be sold. At what price must the retailer sell each of the remaining gadgets to make a total profit of 19% on the original cost of the box?

Work out the value of the expression: $\left( \frac{3}{8} - 0.625 \right) \div \left( \frac{1}{2} \right)^3 + 15.5$.

A manufacturing machine produces 1200 bolts per hour. For every 4 hours of production, it must be stopped for a 20-minute maintenance break. If the machine begins operating at 08:00, calculate the total number of bolts produced by 23:00 on the same day.

Calculate $3.5 \times 10^4 + 2.1 \times 10^3$.

Convert the fraction $\frac{7}{16}$ into a decimal.

Calculate $\sqrt{2.56} + 1.2^2$.

Calculate the value of $12.5 + 4.2 \times (6.8 - 2.3)$.

Calculate the value of $\frac{1}{\sqrt{0.04}} + 3^2 \times 0.2$.

Calculate $\frac{2}{3} + \frac{5}{8} \times \frac{4}{15}$ and give your answer as a fraction in its simplest form.

Find the value of $\sqrt[3]{17.576} \times (1.5)^3$.

Evaluate $\frac{(3.2 \times 10^5) \times (1.5 \times 10^{-2})}{2.5 \times 10^2 - 1.2 \times 10^2}$ correct to 1 decimal place.

Evaluate $\frac{15.4 \times \sin(30^{\circ})}{\sqrt{4.5^2 + 6.2^2}}$ correct to 3 significant figures.

1. Using a Calculator: practice question 1 for Number?

1. Exponential Growth and Decay: practice question 1 for Number?

1. Exponential Growth and Decay: practice question 2 for Number?

1. Exponential Growth and Decay: practice question 3 for Number?

1. Exponential Growth and Decay: practice question 4 for Number?

1. Exponential Growth and Decay: practice question 5 for Number?

1. Exponential Growth and Decay: practice question 6 for Number?