Maths

What is the Pythagorean Theorem?

The Pythagorean Theorem states that for a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides: $a^2 + b^2 = c^2$.

Define an algebraic expression.

An algebraic expression is a combination of numbers, variables, and operations (addition, subtraction, multiplication, and division) without an equality sign.

What is a linear equation?

A linear equation is an equation of the first degree, meaning it can be written in the form $ax + b = c$, where a, b, and c are constants.

What is a function?

A function is a relation that assigns exactly one output for each input from a set. It can be represented as $f(x)$.

Explain what a probability is.

Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1.

What is the formula for the area of a circle?

The area of a circle is given by the formula: $A = \\frac{\text{π}d^2}{4}$ or $A = \text{π}r^2$, where r is the radius.

Define the term 'mean.'

The mean, or average, of a set of numbers is calculated by adding all the numbers together and dividing by the total count of numbers.

What is an inequality?

An inequality is a mathematical statement that compares two values or expressions, showing that one is larger or smaller than the other, using symbols such as $<$, $>$, $≤$, or $≥$.

What is the quadratic formula?

The quadratic formula is used to find the solutions of a quadratic equation and is given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Define a prime number.

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

What is a rational number?

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

What is the slope of a line?

The slope of a line in the Cartesian plane represents the steepness of the line and is calculated as: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Explain what coordinates are.

Coordinates are a set of values that show an exact position on a graph or in space, typically represented as (x,y) in 2D.

What is an exponent?

An exponent indicates how many times a number, known as the base, is multiplied by itself. For example, in $a^n$, 'a' is the base and 'n' is the exponent.

Define a composite number.

A composite number is a natural number greater than 1 that is not prime, meaning it has divisors other than 1 and itself.

What is the difference between mean and median?

The mean is the average of a set of numbers, while the median is the middle number when the numbers are arranged in order.

What is a histogram?

A histogram is a graphical representation of the distribution of numerical data, where the data is grouped into bins.

Explain what a polynomial is.

A polynomial is an algebraic expression that consists of variables raised to whole number powers and coefficients, e.g., $2x^3 + 4x^2 + 7.$

What are complementary angles?

Complementary angles are two angles whose measures add up to 90 degrees.

Define circumference of a circle.

The circumference is the distance around the circle, calculated using the formula: $C = \text{π}d$, where d is the diameter.

What is the mode in statistics?

The mode is the number that appears most frequently in a data set.

Define integers.

Integers are whole numbers that can be positive, negative, or zero, without any fractional or decimal part.

What is the formula for the area of a rectangle?

The area of a rectangle is calculated using the formula: $A = l imes w$, where l is the length and w is the width.

What is the formula for the volume of a cylinder?

The volume of a cylinder is given by the formula: $V = ext{π}r^2h$, where r is the radius and h is the height.

What is the formula for the perimeter of a rectangle?

The perimeter of a rectangle is calculated using the formula: $P = 2(l + w)$, where l is the length and w is the width.

What is the formula for the area of a triangle?

The area of a triangle is calculated using the formula: $A = \frac{1}{2}bh$, where b is the base and h is the height.

What is the formula for the surface area of a sphere?

The surface area of a sphere is given by the formula: $A = 4 ext{π}r^2$, where r is the radius.

What is the formula for the quadratic equation?

A quadratic equation can be expressed in standard form as: $ax^2 + bx + c = 0$, where a, b, and c are constants.

What is the formula for simple interest?

The formula for calculating simple interest is: $I = P imes r imes t$, where I is the interest, P is the principal amount, r is the rate of interest, and t is the time in years.

What is the formula for the distance between two points?

The distance between two points $(x<em>1, y</em>1)$ and $(x<em>2, y</em>2)$ in a plane is given by: $d = \sqrt{(x<em>2 - x</em>1)^2 + (y<em>2 - y</em>1)^2}$.