college level

Solve for x: 2x + 5 = 15

x = 5

Factor: x² - 9x + 18

(x - 6)(x - 3)

Solve for x: x² - 16 = 0

x = ±4

What is the quadratic formula?

x = (-b ± √(b² - 4ac)) / 2a

Solve for x: 3x - 7 = 2x + 5

x = 12

What is the slope-intercept form of a line?

y = mx + b, where m is the slope and b is the y-intercept

Find the slope between points (2,5) and (6,9)

m = (9 - 5) / (6 - 2) = 1

What is the vertex of y = (x - 3)² + 2?

(3, 2)

Find the x-intercepts of y = x² - 4

x = ±2

If a function is increasing, what does its graph look like?

The graph rises from left to right.

Simplify: (x³)(x⁵)

x⁸

Simplify: (2x²)³

8x⁶

Convert to radical form: x^(1/2)

√x

Simplify: 16^(3/4)

8

What is the rule for dividing exponents with the same base?

x^m / x^n = x^(m-n)

Convert to exponential form: log₂8 = 3

2³ = 8

Solve for x: log₃81 = x

x = 4

What is the logarithmic identity log_b(MN) equal to?

logb M + logb N

What is log 1 equal to?

0

Solve for x: log₅x = 2

x = 25

Find the hypotenuse of a right triangle with legs of 6 and 8.

10 (using the Pythagorean theorem)

What is the sine of a 30-degree angle?

1/2

What is the formula for the area of a circle?

A = πr²

Convert 45° to radians.

π/4

What is the cosine of 0°?

1

What is the probability of rolling a 3 on a fair six-sided die?

1/6

What is the formula for standard deviation?

σ = √(Σ(xᵢ - x̄)² / n)

What does a normal distribution curve look like?

A symmetric, bell-shaped curve.

What is the median of the data set {3, 5, 7, 9, 11}?

7

If a data set has a mean of 50 and a standard deviation of 5, what is one standard deviation above the mean?

55