SAT/ACT Math Practice #14

Front

What does the inequality x ≤ -2 or x ≥ 4 represent on a number line?

Back

It represents the values of x that are either less than or equal to -2 or greater than or equal to 4.

Front

How do you simplify the expression 2(6x + 3) - 3(2x - 4)?

Back

By distributing, you get 12x + 6 - 6x + 12, which simplifies to 6x + 18.

Tags

CCSS.6.EE.A.3

Front

What is the result of multiplying (i + 2)(i + 4)?

Back

The result is 6i + 8.

Tags

CCSS.HSN.CN.A.2

Front

If 0 < m < 1, which expression has the largest value: m, m^2, or m^{-1}?

Back

m^{-1} has the largest value because it represents the reciprocal of m, which is greater than 1.

Tags

CCSS.8.EE.A.1

Front

How do you find f(g(1)) if f(x) = 2x + 4 and g(x) = x^2 - 1?

Back

First, find g(1) = 1^2 - 1 = 0, then find f(0) = 2(0) + 4 = 4.

Tags

CCSS.HSF-BF.A.1C

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.

Tags

CCSS.8.F.A.1

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax^2 + bx + c.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, for any two points x1 and x2 where x1 < x2, f(x1) < f(x2).

Front

What is the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting back to find y.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B