Algebra 1- Spring Midterm Review

Exponential Functions (Interpret and Write) and Sequences

  1. The graph of the exponential function is shown on the grid below.
    For what values of is ?

2. The exponential function model is f(x) = a(b)x. What is the meaning of a and b in this function?

A. a is the time and b is the rate.

B. a is the rate and b is the initial value.

C. a is the initial value and b is the rate.

D. a is the rate and b is the time.

3. Each year, Maria’s rabbit population doubles. What is the growth rate as a percent?

A. 2%B. 20%

C. 200%D. ½ %

4. Julie deposits $600 in an account that pays 8.5% interest compounded annually. She makes no additional deposits or withdrawals. Which of the following could be used to calculate the amount of money, M, that will be in Julie’s account at the end of 3 years?

A. 600 = M(1 – 0.85)3B. M = 600(1 – 0.85)3

C. 600 = M(1 + 0.085)3D. M = 600(1 + 0.085)3

5. Bacteria in a culture are growing exponentially with time, as show in the table below.

Months / Amount of Bacteria
1 / 1
2 / 7
3 / 49
4 / 343
5 / 2401

Which of the following equations expresses the number of bacteria, y, present at any time, t?

  1. y = 7tB. y = ()t

C. y = ()7tD. y = 7t + 1

6. The amount of medication in a patient’s bloodstream decreases exponentially from the time the medication is administered. A patient is administered a 1,000 cc dose of medication that decreases by 30% in the bloodstream each hour. Which function models this situation?


7. The population of the Giant Panda is currently 1,864. In 10 years, the population will be 1004. If the population continues to decrease by 6% annually, which function can be used to determine the number of Giant Pandas, y, after, t, years?

A. y = 1864(1.06)tB. y = 1864(.94)t

C. y = 1239(6)tD. y = 1239(.94)10

8. Which is a geometric sequence?

A. 2, 4, 6, 8, 10B. 5, 7, 11, 17, 25

C. 5, 10, 20, 40, 80D. 49, 39, 29, 19, 9

9. The first five terms in a pattern are shown below:

If the pattern continues, which expression can be used to find the th term?

Graphing and Predicting using Exponential Functions

10. A teacher spent a total of $328 on classroom supplies this year. In order to save money, she plans to decrease the amount she spends on classroom supplies by 5% every year. If this situation were represented by a graph, what would be the meaning of the -intercept?

  1. Sheonly spends 95% of the previous year’s amount on fast food.
  2. She spent $328 at the start of their savings plan.
  3. She only spends 5% of the previous year’s amount on fast food.
  4. They will spend $311.60 after the first year of their savings plan.

11. Which of the following graphs represents an exponential decay function with an initial value of and an asymptote at ?

A.

B.

C.

D.

  1. For the exponential growth function:

-intercept?

What does the-intercept represent?

  1. The following table shows the blue jay population in a national park after decades:

Decade, / 0 / 1 / 2 / 3 / 4
Population, / 20 / 23 / 29 / 35 / 42

Predict the blue jay population after 70 years.

  1. 51
  2. 64
  3. 70
  4. 85

14. Given the radical expression 2√6 + √54, which of the following is NOT an equivalent expression?

a. 2√6 + 3√6

b. 5√6

c. 2√60

d. √24 + √54

15. Simplify the following expression:

25a7b2c-3

5a5b4

  1. 20a2

b2c3

  1. 5a2c3

b2

  1. 20a2c3

b2

  1. 5a2

b2c3

16. The radius r of a sphere is given by the equation:

Where V is volume of the sphere. To the nearest foot, find the radius of a basketball that has a volume of 2144 cubic feet. Use 3.14 for ∏.

  1. 12 ft.
  2. 5 ft.
  3. 10 ft.
  4. 8 ft.

17. Find the area of a square with a side length of

inches.

  1. x6y8

9z4

  1. x9y16

9z4

  1. x12y16

81z8

  1. x5y6

6z4

Operations on Polynomials

  1. Sarah wants to build two separate congruent pens for her horses. Which polynomial below represents the amount of fencing (perimeter) she would need to enclose both pens?

  1. Xavier wants to install a pool in his backyard. The pool will have a width of and length of . The backyard has a width of and length of . What is the area of the yard that is left after the pool is installed?

  1. A rectangle pool table has an area of . The length of one side is
    . What is the length of the other side?
  1. Multiply: