ACT math practice

Front

What is vector addition?

Back

Vector addition is the process of adding two or more vectors together to determine a resultant vector. For example, if vector a = (3, 6) and vector b = (2, -5), then a + b = (3+2, 6-5) = (5, 1).

Front

How do you calculate the slope of a line given two points?

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1). For example, for points (-3, 1) and (5, 4), the slope is m = (4 - 1) / (5 - (-3)) = 3/8.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative. For example, 4x + 8y = 16 is in standard form.

Front

How do you express x in terms of y from a linear equation?

Back

To express x in terms of y from an equation like 4x + 8y = 16, isolate x: 4x = 16 - 8y, thus x = -2y + 4.

Front

What are positive factors of a number?

Back

Positive factors of a number are the integers that can be multiplied together to produce that number. For example, the positive factors of 10 are 1, 2, 5, and 10.

Front

How do you find the area of a rectangle?

Back

The area of a rectangle is calculated by multiplying its length by its width. For example, if a bathroom is 5 feet by 13 feet, the area is 5 * 13 = 65 square feet.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction. For example, √2 is irrational.

Front

How do you calculate the perimeter of a rectangle?

Back

The perimeter (P) of a rectangle is calculated by the formula P = 2(length + width). For example, for a rectangle with length 5 and width 3, P = 2(5 + 3) = 16.