Number

What is the value of $7^0$?

What is the $n$-th term of the sequence of odd numbers: $1, 3, 5, 7, \dots$?

In the geometric sequence $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$, what is the common ratio?

Identify the prime number that lies between 20 and 25.

Find the $n$th term of the sequence: $2, 4, 8, 16, \dots$

Which of these is the prime factorization of $210$?

What is the common difference of the sequence: $\frac{1}{2}, 1, \frac{3}{2}, 2, \dots$?

A sequence is defined by $u_n = n^2 - 10n + 30$. At which value of $n$ does the sequence reach its minimum value?

Find the sum of all the prime factors of 210.

A quadratic sequence starts with $u_1, u_2, 15, 24, 35, \dots$ where the second difference is constant. Find $u_1$.

If $L = \{x : x \text{ is a letter in "MATH"}\}$ and $M = \{x : x \text{ is a letter in "TEAM"}\}$, find $L \cap M$.

If $\mathcal{E} = \{2, 4, 6, 8, 10\}$ and $A = \mathcal{E}$, what is $A'$?

What is the intersection of set $A$ and the empty set?

If $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, find $n(A \cup B)$.

Given $A = \{x : x \in \mathbb{R}, 0 < x < 5\}$ and $B = \{x : x \in \mathbb{R}, 3 \leq x < 8\}$, what is $A \cup B$?

If $n(A) = 10, n(B) = 15$ and $A \cap B = A$, then $n(A \cup B)$ is:

Let $P = \{2, 4, 6\}$ and $Q = \{1, 2, 3, 4, 5\}$. Find the number of elements in $P \cup Q$.

The set of values of $x$ for which $(x-2)(x-5) > 0$ is denoted by $S$. The set of values for which $3 < x < 6$ is denoted by $T$. Find $S \cap T$ for $x \in \mathbb{R}$.

If $n(A) = 20, n(B) = 30$ and $n(A \cup B) = 40$, find $n(A \cap B')$.

Given $A = \{x : x \text{ is a letter in the word 'PROBABILITY'}\}$ and $B = \{x : x \text{ is a letter in the word 'STATISTICS'}\}$. Find $n(A \cap B)$.

Evaluate $\sqrt{0.0001}$.

Find the value of $16^2$.

Calculate $\sqrt{121} + \sqrt[3]{64}$.

What is the value of $0.4^2$?

Evaluate $\sqrt{1.44} + \sqrt[3]{0.008}$.

Evaluate $\sqrt[3]{-27} \times (-1)^2$.

Calculate $(\frac{1}{2})^2 \div (\frac{1}{2})^3$.

Simplify $(\sqrt{3} + \sqrt{2})^2 - (\sqrt{3} - \sqrt{2})^2$.

Simplify $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b})$.

A cube has a side length of $\sqrt[3]{16}$ cm. Find its total surface area.

Simplify $\frac{35}{100}$ to its lowest terms.

Increase $200$ by $5\%$.

Calculate $2.5 \times 0.4$.

Write $\frac{3}{8}$ as a decimal.

A deposit of $\$400$ earns $\$48$ simple interest over $3$ years. What was the annual interest rate?

Express $500$ grams as a percentage of $2.5$ kilograms.

If $\frac{2}{3}$ of $\frac{4}{5}$ of a number $x$ is $16$, find $x$.

Solve for $x$ in the equation: $0.\dot{x} = \frac{7}{9}$.

A rectangle has sides $x$ and $y$. If $x$ increases by $10\%$ and $y$ increases by $20\%$, find the percentage increase in the perimeter if the original $x = y$.

A sum of money doubles itself in $8$ years under simple interest. What is the annual interest rate?

A concrete mix uses sand and cement in the ratio $3:2$. If $25$ kg of the mix is prepared, how many kilograms of sand were used?

If $200$g of a product costs $\$3.20$, calculate the price per kilogram.

If $\frac{x}{4} = \frac{y}{7}$, what is the ratio $x:y$ in its simplest form?

A scale model has a ratio of $1:200$. If the actual height of a building is $15$ m, what is the height of the model in centimeters?

In a group of $80$ people, the ratio of adults to children is $5:3$. If $10$ more children join the group, find the new ratio of adults to children in its simplest form.

The variable $y$ varies directly as $x^2$ and inversely as $\sqrt{z}$. When $x = 2$ and $z = 9$, then $y = 4$. Find the value of $y$ when $x = 3$ and $z = 4$.

A map has a scale of $1:100,000$. A water reservoir has an actual volume of $5$ km$^3$. What is the volume of this reservoir on the map in cm$^3$?

A sum of $\$1300$ is divided among A, B, and C such that $\frac{2}{3}$ of A's share is equal to $\frac{3}{4}$ of B's share and $\frac{4}{5}$ of C's share. What is B's share?

$M$ is inversely proportional to $d^3$. When $d=2, M=2.5$. Find the value of $d$ when $M=0.02$.

An express train travels at an average speed of $100$ km/h, stopping for 3 minutes every 75 km. A local train travels at $60$ km/h, stopping for 1 minute every 20 km. How much longer does the local train take to travel $600$ km than the express train?

Calculate $(4.4 \times 10^8) \div 2$ and give your answer in standard form.

Convert $1.1 \times 10^{-5}$ into an ordinary number.

Convert $5.43 \times 10^1$ into an ordinary number.

Write $987,000,000$ in standard form.

Calculate $\frac{2.4 \times 10^{-4} \times 5 \times 10^{-2}}{3 \times 10^{-3}}$ and give the result in standard form.

Evaluate $(1.5 \times 10^4) + (2.5 \times 10^3) - (5 \times 10^2)$ and give your answer in standard form.

If $3 \times 10^x = 0.00003$, what is the value of $x$?

Evaluate $\frac{(5 \times 10^{-6})^2}{\sqrt{2.5 \times 10^{-11} \times 10}}$ and express in standard form.

A particle travels at $2.4 \times 10^4$ meters per second. How many kilometers will it travel in $5 \times 10^{-2}$ hours? Express in standard form.

Simplify $\frac{8 \times 10^5 + 2 \times 10^6}{4 \times 10^{-3}}$ and express in standard form.

A sum of $1000$ is invested at $2\%$ compound interest per year. What is the total amount after $5$ years?

Calculate the simple interest on $2000$ at $0.1\%$ per year for $10$ years.

If $300$ is invested at $5\%$ compound interest per year, what is the total value after $3$ years?

Find the simple interest earned on $1200$ at $6\%$ per year for $1.5$ years.

Find the total interest earned on $1,600 at $5\%$ compound interest per annum for $3$ years.

A computer system depreciates from $1,000 to $810 in $2$ years. Calculate the annual rate of depreciation.

A sum of $5,000 is invested at $3\%$ simple interest for $2$ years. The total amount is then reinvested at $3\%$ compound interest (compounded annually) for a further $2$ years. What is the final balance?

What sum of money will amount to $\$5,796.37$ in $2.5$ years at $6\%$ per annum compounded semi-annually?

A man borrows $\$10,000$ at $10\%$ simple interest per annum. He pays back $\$3,000$ at the end of each year. How much does he still owe at the end of the second year?

Calculate the compound interest on $\$12,000$ for $3$ years if the rate of interest is $5\%$ for the first year, $6\%$ for the second year, and $7\%$ for the third year.

An angle $\alpha$ is $90^{\circ}$ correct to the nearest degree. What is the upper bound of $\alpha$?

A length $l$ is $10.00\text{ cm}$ correct to $2$ decimal places. What is the lower bound of $l$?

A mass $g$ is $0.55\text{ kg}$ correct to $2$ decimal places. Which inequality represents $g$?

A distance $s$ is $4.8 \times 10^3\text{ m}$ correct to $2$ significant figures. What is the upper bound of $s$?

Let $y = 10 - x$, where $x = 4.2$ correct to 1 decimal place. Find the lower bound for $y$.

If $x = 0.8$ correct to 1 decimal place, find the upper bound for $x^2$.

In a right-angled triangle, sides $a = 3.0$ cm and $b = 4.0$ cm are both correct to 1 decimal place. Calculate the upper bound for the hypotenuse $c = \sqrt{a^2 + b^2}$.

A container holds $5.0$ kg of flour correct to 1 decimal place. $150$ g of flour (to the nearest 10 g) is removed. Calculate the lower bound for the remaining mass of flour in grams.

The pressure $P$ on a surface is $P = F/A$. $F = 600$ N correct to 1 significant figure and $A = 2.5$ m$^2$ correct to 1 decimal place. Calculate the upper bound for $P$.

The potential energy $U$ of a spring is $U = \frac{1}{2}kx^2$. If $k = 200$ N/m correct to the nearest 10 N/m and $x = 0.15$ m correct to 2 decimal places, find the lower bound for $U$.