Algebra 1- Spring Midterm Review

Algebra 1- Spring Midterm Review
Systems of Linear Equations
1.
There are 18 books stacked on a shelf. The
thickness of each book is either 1 inch or 4 inches.
The height of the stack of 18 books is 24 inches.
Write a system of equations that can be used
determine x, the number of 4-inch-thick books in
the stack, and y, the number of 1-inch-thick
books??
A.
𝑥 + 𝑦 = 24
𝑥 + 4𝑦 = 18
B.
𝑥 + 𝑦 = 18
3.
How many solutions are there to each graph?
1
4𝑥 + 𝑦 = 24
C.
𝑥 + 𝑦 = 18
𝑥 + 4𝑦 = 24
D.
𝑥 + 𝑦 = 24
4𝑥 + 𝑦 = 18
1
2. Moving companies typically charge a one-time fee
for the truck and then a per hour fee for the labor
of loading and unloading the truck. The table
below represents the cost of two moving
companies where 𝑥 represents the number of
hours required to load and unload the truck and 𝑦
represents the total cost.
𝑥
3
5
7
8
10
1
Company
𝑦1 $959 $1037 $1115 $1154 $1232
1
Company
𝑦2 $894 $990 $1086 $1134 $1230
2
Which system of equations represents these two
moving companies?
A. 𝑦1 = 39 + 842𝑥
𝑦2 = 48 + 750𝑥
B. 𝑦1 = 48 + 750𝑥
𝑦2 = 39 + 842𝑥
C. 𝑦1 = 750 + 48𝑥
𝑦2 = 842 + 39𝑥
D. 𝑦1 = 842 + 39𝑥
𝑦2 = 750 + 48𝑥
0
Algebra 1- Spring Midterm Review
8. Bacteria in a culture are growing exponentially with
time, as show in the table below.
4.
A high school band held a bake sale. The number
of muffins, m, sold was five less than twice the
number of cookies, c, sold. The band sold a total
of 49 muffins and cookies. How many cookies did
the band sell?
A. 27
B. 31
C. 28
D. 18
Amount of
Bacteria
Months
Exponential Functions (Interpret and Write) and Sequences
5. The graph of the exponential function 𝑓 is shown on
the grid below.
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
A. y = 7t
B.
For what values of 𝑥 is 𝑓(𝑥) > 8?
A.
𝑥 < −4
B.
𝑥 > −4
C.
𝑥>0
D.
𝑥 > 32
1
B. y = ( )t
7
t
y = ( )7
7
C.
y = 7t + 1
9. 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?
A. 𝑓(𝑥) = 1000(0.7)𝑥
B. 𝑓(𝑥) = 30(1000)𝑥
C. 𝑓(𝑥) = 1000(0.3)𝑥
6. 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.
7. Each year, Maria’s rabbit population doubles. What is
the growth rate as a percent?
A. 2%
B. 20%
C. 200%
D. ½ %
D. 𝑓(𝑥) = 1000(0.03)𝑥
10. 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)3
B. M = 600(1 – 0.85)3
C. 600 = M(1 + 0.085)3
D. M = 600(1 + 0.085)3
Algebra 1- Spring Midterm Review
11. 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)t
B. y = 1864(.94)t
C. y = 1004(6)t
D. y = 1004(.94)10
15. Which of the following graphs represents an
exponential decay function with an initial value of 1
and an asymptote at 𝑦 = 0?
A.
12. Which is a geometric sequence?
A. 2, 4, 6, 8, 10
B. 5, 7, 11, 17, 25
C. 5, 10, 20, 40, 80
D. 49, 39, 29, 19, 9
B.
13. The first five terms in a pattern are shown below:
0.4, 0.2, 0, −0.2, −0.4, . . .
If the pattern continues, which expression can be used to
find the 𝑛th term?
A.
−0.2𝑛 + 0.6
B.
0.8𝑛 + 0.6
C.
−0.2𝑛 − 0.4
D.
−0.6𝑛 + 0.2
C.
Graphing and Predicting using Exponential Functions
14. 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 𝑦-intercept?
A.
She only spends 95% of the previous year’s amount on
fast food.
B.
She spent $328 at the start of their savings plan.
C.
She only spends 5% of the previous year’s amount on
fast food.
D.
They will spend $311.60 after the first year of their
savings plan.
D.
Algebra 1- Spring Midterm Review
19. Simplify the following expression:
25a7b2c-3
5a5b4
16. For the exponential growth function:
𝑓(𝑥) = 815(1.03)𝑥
What is the 𝑦-intercept?
a. 20a2
b2c3
815
What does the 𝑦-intercept represent?
b. 5a2c3
b2
The initial value
c. 20a2c3
b2
17. The following table shows the blue jay population 𝑦
in a national park after 𝑡 decades:
Decade, 𝑡
Population, 𝑦
0
20
1
23
2
29
3
35
4
42
Predict the blue jay population after 70 years.
A.
51
B.
64
C.
70
D.
85
18. 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
d. 5a2
b2c3
20. The radius r of a sphere is given by the equation:
1
3𝑉 3
𝑟=( )
4𝜋
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 ∏.
a.
b.
c.
d.
12 ft.
5 ft.
10 ft.
8 ft.
Algebra 1- Spring Midterm Review
21. Find the area of a square with a side length of
𝑥3𝑦4
3𝑧 2
inches.
23. Xavier wants to install a pool in his backyard. The pool
will have a width of 3𝑥 and length of 2𝑥 + 1. The
backyard has a width of 6𝑥 + 2 and length of 10𝑥 + 4.
What is the area of the yard that is left after the pool is
installed?
a. x6y8
9z4
A. −66𝑥 2 − 47𝑥 + 12
b. x9y16
9z4
B. 66𝑥 2 + 47𝑥 + 8
A. 54𝑥 2 + 47𝑥 + 8
C. 54𝑥 2 + 41𝑥 + 8
c. x12y16
81z8
24. A rectangle pool table has an area of
2𝑥 2 + 7𝑥 + 6. The length of one side is
𝑥 + 2. What is the length of the other side?
d. x5y6
6z4
A. 2𝑥 + 3
Operations on Polynomials
22. 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?
B. 2𝑥 − 3
C. 𝑥 + 3
D. 𝑥 + 6
25. Multiply: (6𝑥 − 7)(4𝑥 + 2)
A. 10𝑥 2 − 5
A.
25𝑥 2 − 20𝑥
B.
20𝑥 − 8
C.
40𝑥 − 16
D.
2
50𝑥 − 40𝑥
B. 24𝑥 2 − 14
C. 24𝑥 2 − 16𝑥 − 14
10𝑥 2 + 28𝑥 − 14