ACT Math Prep 1

Front

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

Back

The probability is 8/15, since there are 8 numbers (1 to 8) that are less than 9 out of a total of 15.

Front

What is the result of combining like terms in the expression -4x^3 - 12x^3 + 9x^2?

Back

The result is -16x^3 + 9x^2.

Front

What is the absolute value of the expression |6 - 4| - |3 - 8|?

Back

The result is 7, since |6 - 4| = 2 and |3 - 8| = 5, thus 2 - 5 = -3.

Front

How do you calculate the number of students who earned a C if 1/4 earned an A and 1/3 earned a B in a class of 180 students?

Back

First, calculate the number of A's: 180 * (1/4) = 45. Then, calculate the number of B's: 180 * (1/3) = 60. The total number of students who earned A or B is 45 + 60 = 105. Therefore, students who earned C = 180 - 105 = 75.

Front

What is the formula for calculating probability?

Back

Probability = (Number of favorable outcomes) / (Total number of outcomes).

Front

What are like terms in algebra?

Back

Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms.

Front

What is the definition of absolute value?

Back

Absolute value is the distance of a number from zero on the number line, regardless of direction. It is always non-negative.

Front

How do you simplify the expression -4x^3 - 12x^3?

Back

Combine the like terms: -4x^3 - 12x^3 = -16x^3.

Front

What is the total number of outcomes when rolling a six-sided die?

Back

The total number of outcomes is 6, as there are six faces on the die.

Front

What is the probability of rolling an even number on a six-sided die?

Back

The probability is 3/6 or 1/2, since there are three even numbers (2, 4, 6) out of six possible outcomes.