Number

If a number is denoted as $x \in \mathbb{Z}^+$, what does this mean?

Which of these decimals is the same as $1/2$?

Evaluate $|-3 \times 4|$.

Which set is formed by the union of rational and irrational numbers?

Which of these is the most accurate classification for $\sqrt{0.4}$?

If $x$ is a natural number, then $-x$ is always a(n):

The set of numbers $\{... -2, -1, 0, 1, 2 ...\}$ is specifically known as:

Determine the intersection $S \cap \mathbb{Q}$, where the set $S$ is defined as $S = \{ x \in \mathbb{R} \setminus \{\sqrt{5}\} \mid \frac{x^2 - 5}{x - \sqrt{5}} \in \mathbb{Q} \}$.

Which of the following expressions results in a rational number?

If $x$ and $y$ are both irrational, then $x/y$ is:

What is the complement of the universal set, $U'$?

If $A = \{1, 2, 3\}$ and $B = \{1, 2, 3, 4\}$, which of the following is the set $B \setminus A$ (elements in $B$ not in $A$)?

What is the cardinality of the set $Z = \{0\}$?

If $U$ is the set of all letters in the English alphabet and $V$ is the set of vowels, what does $V'$ represent?

Let $A = \{1, 2\}$. Which of the following is an element of $P(A)$, the power set of $A$?

In a group of 50 students, 20 like Math, 25 like English, and 30 like Science. 8 like Math and English, 10 like English and Science, 7 like Math and Science. 3 like all three. How many like Math only?

De Morgan's First Law states that $(A \cup B)'$ is equal to:

If $A, B$ are two sets such that $n(A \setminus B) = 12 + x$, $n(B \setminus A) = 3x$, and $n(A \cap B) = x + 2$, find the value of $x$ such that $n(A) = n(B)$.

Given $n(A \cap B) = 8, n(A \cap C) = 7, n(B \cap C) = 9$. If $n(A \cap B \cap C) = 3$, find $n((A \cap B) \cup (B \cap C) \cup (A \cap C))$.

The region $(A \cup B \cup C) \cap (A \cap B)' \cap (B \cap C)' \cap (A \cap C)'$ represents which of the following?

Simplify the expression $\frac{p^2}{p^9}$.

Simplify the expression $(5x^3)^2$.

Evaluate the expression $\sqrt{144/169}$.

Simplify the expression $b^3 \cdot b \cdot b^2$.

Simplify the product $(a^{1/2} + b^{1/2})(a^{1/2} - b^{1/2})$.

Evaluate $\frac{81^{3/4}}{27}$.

Simplify the expression $\frac{3^{n+2} - 3^n}{3^n}$.

Solve for $x$: $3^{2x} - 10 \cdot 3^x + 9 = 0$.

Simplify the nested radical $\sqrt{x \sqrt{x \sqrt{x}}}$.

If $a = 2 + \sqrt{3}$ and $b = 2 - \sqrt{3}$, find the value of $a^2 + b^2$.

Write $0.03 \times 10^{-2}$ in standard form.

Express $400 \times 10^{-5}$ in standard form.

Convert $0.5 \times 10^4$ to standard form.

Convert $12.5 \times 10^2$ to standard form.

Express $1.05 \times 10^3$ as an ordinary number.

Work out $(7 \times 10^4) \times (8 \times 10^{-6})$ and give your answer in scientific notation.

Convert the ordinary number $0.000000000034$ to standard form.

The pressure $P$ is given by $P = F/A$. If the force $F = 1.5 \times 10^3$ N and the area $A = 2.5 \times 10^{-4}$ m$^2$, calculate the pressure in standard form.

If the scale of a map is $1 : 2.5 \times 10^5$, what distance on the map (in cm) represents an actual distance of $75$ km?

Evaluate $\sqrt{1.44 \times 10^{-8}} \times (2 \times 10^5)$ and express in standard form.

If the ratio of boys to girls in a class is $1:4$, what percentage of the class are girls?

An amount of $600$ is invested at $4\%$ simple interest for $6$ months. How much interest is earned?

A pair of shoes costs $80$. The price is reduced by $20\%$ and then increased by $20\%$. What is the final price?

Calculate $0.5\%$ of $1,000$.

An employee receives a $4\%$ bonus on her annual salary of $45,000. How much is her bonus?

A savings bond pays $2.25\%$ simple interest annually. If the bond is worth $5,450 after $4$ years, what was the initial investment?

A retailer buys $200$ pens for $100. He sells $120$ pens at $0.80$each and the rest at \$0.50$ each. Calculate his total percentage profit.

An amount is deposited in a bank at $10\%$ compound interest, compounded annually. If the difference between the interest for the second year and the third year is Rs $121$, find the initial principal.

A rectangle's length is increased by $25\%$. By what percentage must the width be decreased to maintain the same area?

A salesman gets a commission of $5\%$ on total sales up to Rs $10,000$ and $8\%$ on sales exceeding Rs $10,000$. If he earned a total commission of Rs $1,300$, what were his total sales?

If $12$ items cost $\$4.80$, what is the cost of $5$ items?

Express the ratio of $10$ minutes to $2$ hours in its simplest form.

Solve for $x$ in the following proportion: $\frac{x}{5} = \frac{12}{10}$.

A drink is made by mixing $1$ part syrup with $5$ parts water. How many milliliters of syrup are needed to make $300$ ml of the drink?

Bronze is an alloy consisting of copper and tin in the ratio $9 : 1$ by mass. How many grams of tin are required to make $250$ g of bronze?

The density of mercury is approximately $13,600$ $kg/m^3$. Convert this density into $g/cm^3$.

The length of a shadow is directly proportional to the height of the object casting it. A person $1.5$ m tall casts a shadow $2.4$ m long. At the same time, a building casts a shadow $32$ m long. How tall is the building?

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Wire A is twice as long as wire B and has half the cross-sectional area. What is the ratio of the resistance of wire A to wire B?

A contractor employs 20 men to build a house in 30 days. After 10 days, he realizes that only $25\%$ of the work is done. How many more men must he employ to finish the work on time?

If $a : b = c : d$, then $\frac{a^2 + c^2}{b^2 + d^2}$ is equal to:

If $x = -2$, find the value of $|3x|$.

Evaluate $|-0.1|$.

Find the value of $|-6| - |-4|$.

Evaluate $3 - |-7|$.

Solve for $x$ in the equation $|2x - 3| = 0$.

Find the distance between $-12$ and $-19$ on the number line.

Simplify the following expression: $|-2| + |-3| - |-4| - |-1|$.

Solve the equation $|x + 2| - |x - 1| = 3$.

If $|x| < 1$, simplify the expression $|x - 1| + |x + 1|$.

Solve the equation $|x - 2| = |2x - 1|$.

Solve the inequality: $-3 \le x + 4 \le 3$.

What is the solution to $1 < 2x - 5 < 7$?

Solve: $x + 6 < 4$ or $x + 6 > 8$.

Solve the compound inequality: $3x \ge 9$ and $x - 5 \le 2$.

Solve the compound inequality: $x - 3 \geq 1$ or $x + 2 \leq -1$.

Find the largest integer $x$ such that $3x - 5 < 10$ and $x + 1 > -2$.

Solve for $x$: $-2 < \frac{x+5}{2} < 3$.

Find the range of $x$ such that $\frac{x}{2} + 5 > 7$ and $\frac{x}{3} - 1 < 2$.

If $2x + 3 < 15$ and $x$ is a prime number, how many solutions exist for $x > 0$?

Solve for $x$: $5(x - 2) \le 3(x + 4)$ and $x + 1 > -2$.

What is the value of $\sqrt{0}$?

What is the value of $\sqrt{1}$?

Simplify the expression $\sqrt{8} + \sqrt{18}$.

Simplify the expression $\sqrt{12} + \sqrt{27}$.

Simplify $\sqrt{x^2 y^4}$ where $x > 0$ and $y > 0$.

Expand $\sqrt{2}(\sqrt{8} - \sqrt{2})$.

Simplify the fraction $\frac{\sqrt{72}}{6}$.

Simplify the following expression:

$\frac{\sqrt{10} + \sqrt{15}}{\sqrt{10} + \sqrt{15} + \sqrt{20} + \sqrt{30}}$

Simplify the expression $\frac{1}{\sqrt{5}} + \frac{1}{\sqrt{20}}$ and rationalize the denominator.

If $a = \sqrt{3}$, what is the value of $a^6$?

Is the number $\sqrt{25}$ rational or irrational?

In scientific notation $a \times 10^k$, what is the restriction on $a$?

What is the value of $-3^2$?

What is the value of $(-3)^2$?

What is the intersection of the set of even numbers and the set of prime numbers?

Write the decimal $0.0000006$ in scientific notation.

Determine the number of significant figures in $0.00300$.

Which of the following sets is closed under the operation of subtraction?

Find the percentage error when $2/3$ is approximated as $0.67$.

The number $0.101101110...$ is an example of what type of number?

If $y = \frac{12}{x}$, find $y$ when $x = 0.5$.

If $y = \frac{2}{5}x$, find $y$ when $x = 15$.

The time $T$ to fill a pool is inversely proportional to the number of hoses $n$. If 2 hoses take 10 hours, how many hoses are needed to fill it in 4 hours?

If $y \propto \frac{1}{x}$ and $y=100$ when $x=1$, what is the value of $y$ when $x=25$?