Second Year Algebra Review

The expression –x² + 70x – 600 represents a company’s profit for selling x items. For which number(s) of items sold is the company’s profit equal to $0?

• 0 items

• 35 items

• 10 items and 60 items

• 20 items and 30 items

What are the solutions to the equation 2x² – 2x – 12 = 0?

• x = –4, x = 3

• x = –3, x = 4

• x = –2, x = 3

• x = –6, x = 2

What are the solutions to the equation x² – 5x = 14?

• x = –7, x = –2

• x = –14, x = –1

• x = –2, x = 7

• x = –1, x = 14

What explicit expression can be used to find the next term in this sequence?

• 2n

• 2n + 6

• 2n²

• 2n² + 1

A café’s annual income depends on x, the number of customers. The function I(x) = 4x² – 20x describes the café’s total annual income. The function C(x) = 2x² + 5 describes the total amount the café spends in a year. The café’s annual profit, P(x), is the difference between the annual income and the amount spent in a year. Which function describes P(x)?

• P(x) = 2x² – 20x – 5

• P(x) = 4x³ – 20x²

• P(x) = 6x² – 20x + 5

• P(x) = 8x⁴ – 40x³ – 20x² – 100x

Which statement BEST describes the graph of f(x + 6)?

• The graph of f(x) is shifted up 6 units.

• The graph of f(x) is shifted left 6 units.

• The graph of f(x) is shifted right 6 units.

• The graph of f(x) is shifted down 6 units.

A flying disk is thrown into the air from a height of 25 feet at time t = 0. The function that models this situation is h(t) = –16t² + 75t + 25, where t is measured in seconds and h is the height in feet. What values of t best describe the time when the disk is flying in the air?

• 0 < t < 5

• 0 < t < 25

• all real numbers

• all positive integers

What is the average rate of change of x over the interval –2 ≤ x ≤ 0?

• -10

• -5

• 5

• 10

Starting money = $350.
Interest rate = 2.5%
TIme = 3 years.
How much interest?

• $7.50

• $26.25

• $87.5

• $262.50

In a dilation what mathematical operation is used with the scale factor?

• addition 

• subtraction 

• multiplication 

• division