Algebra 2

_____1.

Simplify.

_____2.

Find a quadratic function to model the values in the table. Predict the value of y for x = 6. 

______3.

A manufacturer of shipping boxes has a box shaped like a cube. The side length is 5a + 4b. What is the volume of the box in terms of a and b?

_____4.

In how many ways can 3 singers be selected from 5 who came to an audition?

_____5.

Solve the problem by writing an inequality. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts. Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at least $100.

Short Answer: Type your answer in the space below each question. Show your work when applicable.

6.

The velocity of sound in air is given by the equation  , where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity is 329 meters per second by graphing the equation. Round the answer to the nearest degree.

7.

The volume in cubic feet of a box can be expressed as  , or as the product of three linear factors with integer coefficients. The width of the box is 2 – x.

Factor the polynomial to find linear expressions for the height and the width.

8.

This table shows data on heating oil use for two years in three adjacent buildings on Spring Street.

9.

Solve the equation. Check for extraneous solutions. Type your answers in the blanks.

x = ______ or ______

Multiple Choice: Type your answer choice in the blank.

_____10.

Assign each letter and a blank space to a number as shown by the alphabet table below: 

Use to encode the phrase “FIT AS A FIDDLE”.

_____11.

A gem store sells beads made of amber and quartz. For 4 amber beads and 4 quartz beads, the cost is $46.00. For 1 amber bead and 3 quartz beads, the cost is $14.50. Find the price of each type of bead.

12.

In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

Multiple Choice: Type your answer choice in the blank.

_____13.

Evaluate the expression for the given value of the variable(s).

_____14.

Find a quadratic model for the set of values. 

(–2, –20), (0, –4), (4, –20)

15.

Simplify the expression. Type your answer in the blank.

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16.

Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.

Multiple Choice: Type your answer choice in the blank.

_____17.

Solve for x. State any restrictions on the variables.

18.

Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below.

19.

Verify that the matrix has no inverse. Type your answer below.

20.

Three friends recorded the amount of time each spent exercising and sleeping over the course of a week.