Mathematics 1 Reference Sheet

Flashcards containing key mathematical concepts, formulas, and definitions in various areas of mathematics.

Standard Form

The format of a linear equation written as Ax + By = C, where A, B, and C are constants.

Slope-Intercept Form

The equation of a line written as y = mx + b, where m is the slope and b is the y-intercept.

Point-Slope Form

The equation of a line written as y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Quadratic Formula

The formula used to solve for the roots of a quadratic equation, given as x = (-b ± √(b² - 4ac))/(2a).

Midpoint

The point that is equidistant from both endpoints of a line segment, calculated as ((x1 + x2)/2, (y1 + y2)/2).

Distance Formula

The formula used to calculate the distance between two points (x1, y1) and (x2, y2), given as d = √((x2 - x1)² + (y2 - y1)²).

Area of Triangle

The area of a triangle calculated using the formula A = 1/2 * base * height.

Area of Parallelogram

The area of a parallelogram calculated using the formula A = base * height.

Volume of Cylinder

The volume of a cylinder calculated using the formula V = πr²h, where r is the radius and h is the height.

Circumference of Circle

The distance around a circle, calculated using the formula C = 2πr, where r is the radius.

Pythagorean Theorem

In a right triangle, the relation a² + b² = c², where c is the length of the hypotenuse.

Simple Interest

Interest calculated on the principal amount only, given as I = P * r * t, where P is the principal, r is the rate, and t is the time.

Direct Variation

A relationship where y varies directly with x, expressed as y = kx, where k is a constant.

Indirect Variation

A relationship in which y varies inversely with x, expressed as y = k/x, where k is a constant.

Surface Area of Sphere

The total area of the surface of a sphere, given by the formula SA = 4πr².

Standard Form

The format of a linear equation written as Ax + By = C, where A, B, and C are constants.

Slope-Intercept Form

The equation of a line written as y = mx + b, where m is the slope and b is the y-intercept.

Point-Slope Form

The equation of a line written as y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Quadratic Formula

The formula used to solve for the roots of a quadratic equation, given as x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Midpoint

The point that is equidistant from both endpoints of a line segment, calculated as \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right).

Distance Formula

The formula used to calculate the distance between two points (x1, y1) and (x2, y2), given as d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Area of Triangle

The area of a triangle calculated using the formula A = \frac{1}{2} \cdot \text{base} \cdot \text{height}.

Area of Parallelogram

The area of a parallelogram calculated using the formula A = \text{base} \cdot \text{height}.

Volume of Cylinder

The volume of a cylinder calculated using the formula V = \pi r^2h, where r is the radius and h is the height.

Circumference of Circle

The distance around a circle, calculated using the formula C = 2\pi r, where r is the radius.

Pythagorean Theorem

In a right triangle, the relation a^2 + b^2 = c^2, where c is the length of the hypotenuse.

Simple Interest

Interest calculated on the principal amount only, given as I = P \cdot r \cdot t, where P is the principal, r is the rate, and t is the time.

Direct Variation

A relationship where y varies directly with x, expressed as y = kx, where k is a constant.

Indirect Variation

A relationship in which y varies inversely with x, expressed as y = \frac{k}{x}, where k is a constant.

Surface Area of Sphere

The total area of the surface of a sphere, given by the formula SA = 4\pi r^2.

Slope Formula

The formula used to calculate the slope (m) of a line passing through two points (x1, y1) and (x2, y2), given as m = \frac{y2 - y1}{x2 - x1}.

Volume of Cone

The volume of a cone calculated using the formula V = \frac{1}{3} \pi r^2h, where r is the radius of the base and h is the height.

Volume of Sphere

The volume of a sphere calculated using the formula V = \frac{4}{3} \pi r^3, where r is the radius.

Area of Trapezoid

The area of a trapezoid calculated using the formula A = \frac{1}{2} (b1 + b2)h, where b1 and b2 are the lengths of the parallel bases and h is the height.

Standard Form

The format of a linear equation written as Ax + By = C, where A, B, and C are constants.

Slope-Intercept Form

The equation of a line written as y = mx + b, where m is the slope and b is the y-intercept.

Point-Slope Form

The equation of a line written as y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Quadratic Formula

The formula used to solve for the roots of a quadratic equation, given as x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Midpoint

The point that is equidistant from both endpoints of a line segment, calculated as \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right).

Distance Formula

The formula used to calculate the distance between two points (x1, y1) and (x2, y2), given as d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Area of Triangle

The area of a triangle calculated using the formula A = \frac{1}{2} \cdot \text{base} \cdot \text{height}.

Area of Parallelogram

The area of a parallelogram calculated using the formula A = \text{base} \cdot \text{height}.

Volume of Cylinder

The volume of a cylinder calculated using the formula V = \pi r^2h, where r is the radius and h is the height.

Circumference of Circle

The distance around a circle, calculated using the formula C = 2\pi r, where r is the radius.

Pythagorean Theorem

In a right triangle, the relation a^2 + b^2 = c^2, where c is the length of the hypotenuse.

Simple Interest

Interest calculated on the principal amount only, given as I = P \cdot r \cdot t, where P is the principal, r is the rate, and t is the time.

Direct Variation

A relationship where y varies directly with x, expressed as y = kx, where k is a constant.

Indirect Variation

A relationship in which y varies inversely with x, expressed as y = \frac{k}{x}, where k is a constant.

Surface Area of Sphere

The total area of the surface of a sphere, given by the formula SA = 4\pi r^2.

Slope Formula

The formula used to calculate the slope (m) of a line passing through two points (x1, y1) and (x2, y2), given as m = \frac{y2 - y1}{x2 - x1}.

Volume of Cone

The volume of a cone calculated using the formula V = \frac{1}{3} \pi r^2h, where r is the radius of the base and h is the height.

Volume of Sphere

The volume of a sphere calculated using the formula V = \frac{4}{3} \pi r^3, where r is the radius.

Area of Trapezoid

The area of a trapezoid calculated using the formula A = \frac{1}{2} (b1 + b2)h, where b1 and b2 are the lengths of the parallel bases and h is the height.

Area of Circle

The area of a circle calculated using the formula A = \pi r^2, where r is the radius.

Compound Interest

Interest calculated on the principal amount and also on the accumulated interest from previous periods, given as A = P(1 + \frac{r}{n})^{nt}, where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

nth term of an Arithmetic Sequence

The formula for the nth term of an arithmetic sequence, given as an = a1 + (n-1)d, where a_1 is the first term, n is the term number, and d is the common difference.

nth term of a Geometric Sequence

The formula for the nth term of a geometric sequence, given as an = a1 r^{n-1}, where a_1 is the first term, n is the term number, and r is the common ratio.

Vertex of a Parabola

The coordinates of the vertex of a parabola for a quadratic function y = ax^2 + bx + c, given as \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right).

Surface Area of Cylinder

The total area of the surface of a cylinder, calculated using the formula SA = 2\pi r h + 2\pi r^2, where r is the radius and h is the height.