ACT Math Review

Front

What is the formula for calculating the probability of an event?

Back

The probability of an event is calculated using the formula: P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}.

Front

How do you find the distance between two points in a coordinate plane?

Back

The distance d between two points (x1, y1) and (x2, y2) is given by the formula: d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Front

What is the probability of drawing a number less than 9 from the numbers 1 to 15?

Back

The probability is P(E) = \frac{8}{15}, since there are 8 favorable outcomes (1 to 8) out of 15 total outcomes.

Front

How many arrangements can be made by selecting 3 plants from 6 different types?

Back

The number of arrangements is given by the permutation formula: P(n, r) = \frac{n!}{(n - r)!}. For 6 plants and 3 spots, it is P(6, 3) = 6! / (6 - 3)! = 120.

Front

What is the area of a rectangle?

Back

The area A of a rectangle is calculated using the formula: A = \text{length} \times \text{width}.

Front

How do you calculate the area of a shaded region in a rectangle?

Back

To find the area of a shaded region, subtract the area of the unshaded part from the total area of the rectangle.

Front

What is the total number of marbles in a bag containing 8 red, 9 yellow, and 7 green marbles?

Back

The total number of marbles is 8 + 9 + 7 = 24.

Front

If the probability of drawing a red marble is \frac{3}{5}, how many red marbles are needed?

Back

To find the number of red marbles needed, set up the equation: \frac{R}{R + 24} = \frac{3}{5} and solve for R.

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n objects taken r at a time is given by P(n, r) = \frac{n!}{(n - r)!}.

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of n objects taken r at a time is given by C(n, r) = \frac{n!}{r!(n - r)!}.