UCS JH Algebra I SEM 2 REVIEW GUIDE #1 1 Mike invests $2500 at 3% compounded monthly. How much will he have after 16 years?

A $4011.77 C $4037.77

B $88817.84 D $728932.22

2 In the following sequence, what expression can be used to find the term? 4, 8, 12, 16 . . .

A n + 4 C 4n + 4

B 4n D n 2

3 Mike is given the explicit rule for a sequence as shown below.

What is the recursive rule for this sequence?

A

C

B

D

4 The following formula defines a sequence recursively. a1 = 4 an = an-1 + -2 What is the fourth term of this sequence?

A -2 C -32

B 10 D 2

5 After the expression below is simplified, what is the coefficient of 𝑛2 ?

(𝑛2 − 3) − (7 − 𝑛 + 3𝑛2) − (4𝑛 + 1 − 8𝑛2)

A – 4 C 3

B – 3 D 6

6 What is the complete factorization of 64𝑎2 − 25𝑏4 ?

A (8𝑎 − 5𝑏2)(8𝑎 + 5𝑏2) C (8𝑎2 − 5𝑏2)(8𝑎2 + 5𝑏2)

B (8𝑎 − 5𝑏2)(8𝑎 − 5𝑏2) D Cannot be determined

7 Mrs. Kim drew this figure on the blackboard and said, “The area of this rectangle is 2𝑥2 +7𝑥 + 3. What is the length of this rectangle?”

A 𝑥 + 7

B 2𝑥 + 1

C 2𝑥 + 7

D 2𝑥2 + 62

8 What is the sum of the x-intercepts of the function:

𝑓(𝑥) = 2𝑥2 + 3𝑥 − 5

A 3 C −

3

2

B 3

2

D -3

9 What is the minimum point for the following equation found by completing the square? 𝑦 = 𝑥2 + 2𝑥 − 3

A (1, 0) because an equivalent equation is 𝑦 = (𝑥 − 1)2

B (−3, 0) because an equivalent equation is 𝑦 = (𝑥 + 3)2

C (1, 4) because an equivalent equation is 𝑦 = (𝑥 − 1)2 − 3

D (−1, −4) because an equivalent equation is 𝑦 = (𝑥 + 1)2 − 4

10 What is the perimeter of this triangle?

A 15𝑎 − 1

B 29𝑎 − 2

C 24𝑎2 + 11𝑎 − 1

D 34𝑎2 − 8𝑎 + 1

11 A rectangular box has a volume of 280 in3. Its dimensions are 4 in, (𝑛 + 2) in, and (𝑛 + 5) in. Find n. Use the formula 𝑉 = 𝑙𝑤ℎ.

A -12 C 5

B -5 D 12

12 Which equation represents the following graph?

A 𝑦 = 2𝑥2 − 3 C 𝑦 = 2𝑥2 + 3

B 𝑦 = −2𝑥2 − 3 D 𝑦 = −2𝑥2 + 3

13 Given the following equation, solve for 𝑥. 𝑦 = −16𝑥2 + 64

A

𝑥 = ±√𝑦 − 64

−16

C

𝑥 = ±√𝑦 − 64

16

B

𝑥 = ±√𝑦 + 64

−16

D

𝑥 = ±√𝑦 + 64

16

14 What is the solution of 𝑥2 + 64 = 0 ?

A -8 only C -8 and 8

B 8 only D No real solution

15 Use the method of completing the square to rewrite the following quadratic in vertex form:

𝑦 = 𝑥2 + 6𝑥 + 15

A 𝑦 = (𝑥 − 3)2 + 6 C 𝑦 = (𝑥 + 3)2 + 6

B 𝑦 = (𝑥 + 3)2 − 6 D 𝑦 = (𝑥 − 3)2 − 6

16 If 𝑥2 − 6𝑥 + 8 = 0 is solved by completing the square, which equation could be part of this method of solving?

A 𝑥2 − 6𝑥 + 9 = −8 C 𝑥2 − 6𝑥 + 9 = −8 + 9

B 𝑥2 − 6𝑥 + 9 = 9 D 𝑥2 − 6𝑥 + 8 + 9 = −8 + 9

17 The path that an eagle drops a newly caught salmon back into the river can be modeled

by the equation 𝑦 = −16𝑥2 + 𝑣𝑥 + 𝑐, where 𝑣 is the initial velocity, and 𝑐 is the initial height. When will the fish hit the water if the initial velocity is 0 ft/s and the initial height is 100 ft.

A -2.5 seconds C 6.25 seconds

B 2.5 seconds D .625 seconds

18 Which is a solution for the system of equations? 𝑦 = 𝑥2

𝑦 = −2𝑥 + 15

A (-3,9) C (3,9)

B (5,25) D (-5,3)

19 Which function contains the ordered pair (−1, −6)?

A 𝑦 = −𝑥2 + 3𝑥 + 5 C 𝑦 = −3𝑥2 + 2𝑥 − 1

B 𝑦 = 3𝑥2 − 6 D 𝑦 = −2𝑥2 + 𝑥 − 5

20 What is the minimum value of the function: 𝑓(𝑥) = 𝑥2 + 4𝑥 + 6

A 6 C 4

B 2 D -6

21 Which of these is the domain and range of this graph?

A Domain = all real numbers Range = all real numbers

B Domain = all real numbers

Range = 𝑦 ≤ 8 C Domain = 1 ≤ 𝑥 ≤ 3

Range = −9 ≤ 𝑦 ≤ 8 D Domain = all real numbers

Range = 𝑦 > 8

22 What are the coordinates of the maximum point of a parabola whose equation is

𝑦 = −𝑥2 − 5?

A (0, -5) C (0,-2.5)

B (0, 5) D (-5, 0)

23 What are the coordinates for the vertex of the parabola 𝑔(𝑥) = 𝑥2 − 8𝑥 + 13.

A (−4, −3) C (−3, 4)

B (4, −3) D (4, 0)

24 Which statement describes the effect on the graph of 𝑓(𝑥) = 𝑥2, if it is changed to

𝑓(𝑥) =1

2𝑥2 ?

A The graph will be reflected across the x-axis.

C The graph will be narrower.

B The graph will be reflected across the y-axis.

D The graph will be wider.

25 Tyler writes a complex number whose real part is 7 and imaginary part is √−16 .

Which of these correctly represents this complex number?

A 7 – 4i C 4 + 7i

B 7 + 4i D -4 + 7i

26 If the given expression is represented in the form of a + bi, what are the values of a and b?

(-2 + 5i) – (7 – 4i)

A a = -9, b = 9 C a = 5, b = 1

B a = 9, b = -9 D a = -9, b = 1

27 Which of the following is a cubic polynomial with coefficients of 4, 3, and 1.

A 𝑦 = 7𝑥4 + 6𝑥3 + 4𝑥 + 2 C 𝑦 = 3𝑥3 + 4𝑥2 + 𝑥 + 2

B 𝑦 = 3𝑥3 + 4𝑥2 − 𝑥 + 2 D 𝑦 = 7𝑥3 + 6𝑥2 + 4𝑥

28 Factor the expression completely: 100𝑥2 − 25𝑤2

A (10𝑥 + 5𝑤)(10𝑥 − 5𝑤) C 25(10𝑥 + 5𝑤)(10𝑥 − 5𝑤)

B 25(2𝑥 + 𝑤)(2𝑥 − 𝑤) D 25(2𝑥 + 𝑤)2

29 How could you solve this system of equations by graphing.

{𝑓(𝑥) = 3𝑥2 + 2𝑥 − 6

𝑔(𝑥) =1

4𝑥 + 2

A Examine the y-intercepts C Examine the points of intersection

B Examine the x-intercepts D Add the vertex coordinates

30 Which statement describes the range of ?

A The range is all real numbers.

B The range is all real numbers between and .

C The range is all real numbers greater than or equal to .

D The range is all real numbers greater than or equal to .

31 The path of a ball follows the following equation: h(t) = -4.9t2 + 15t + 3

where h(t) is the height of an object in meters and t is time in seconds. How high is the ball at 1 second?

A 13.1 meters C 10.1 meters

B 22.9 meters D 3 meters

32 Solve using the Quadratic Formula: 0 = 2𝑥2 − 8𝑥 + 5

A 𝑥 =

8 ± √24

4

C 𝑥 =

−8 ± √104

4

B 𝑥 =

8 ± √24

−4

D 𝑥 =

8 ± √104

4

33 Which is the correct equation for the graph?

A y = 2(x -2)2 (x + 1) C y = 2(x – 2)(x + 1)2

B y = -2(x – 2)2(x + 1) D y = -2(x – 2)(x + 1)2

34 State the crossing zeros, touching zeros, and y-intercept for the function:

y = 1

25(x + 5)2(x + 1)(x – 2)(x – 4)

A Crossing: -5; touching: -1, 2, 4; y-intercept: 200

B Crossing: -5; touching: -1, 2, 4; y-intercept: 8

C Crossing: -1, 2, 4; touching: -5; y-intercept: 200

D Crossing: -1, 2, 4; touching: -5; y-intercept: 8

36 The box-and-whisker plot shows the weight distribution among 200 professional football players.

Which of these is the BEST estimate of the number of players that weigh less than 210 pounds?

A 25 C 75

B 50 D 100

35 State the end behavior for the following polynomial function: y = 5x7 – 3x2

A (↑, ↑) as x → -∞, f(x) → +∞ and as x→ +∞, f(x) → +∞.

B (↓, ↓) as x → -∞, f(x) → -∞ and as x→ +∞, f(x) → −∞.

C (↑, ↓) as x → -∞, f(x) → +∞ and as x→ +∞, f(x) → −∞.

D (↓, ↑) as x → -∞, f(x) → -∞ and as x→ +∞, f(x) → +∞.

37 A college is surveying its graduates to calculate some statistics to use in its literature. A group of graduates reported their age at the time they graduated, as follows. 23, 22, 22, 21, 24, 24, 21, 21, 22, 31, 22 What was the mean age of this group at graduation?

A 21 C 23

B 22 D 24

38 Larry and Jimmy both play on the basketball team. Larry scored the following number of points in the first five games: 12, 5, 8, 10, 7. Jimmy scored the following number of points in the first five games: 11, 12, 17, 4, 2. Which statement correctly compares the data of these two players?

A Jimmy’s range is 4 points higher than Larry’s range.

B Jimmy’s mean score is 0.8 higher than Larry’s mean score.

C Larry’s mode score is 3 points higher than Jimmy’s mode score.

D Larry’s median score is 3 points higher than Jimmy’s median score.

39 The owner of a vacuum cleaner company gave a survey to his customers, asking them to rate the quality of the three vacuum cleaners he sells. Each respondent rated the quality as high, medium, or low. He compiled the data and created a two-way frequency table showing the relative frequency by row. What is the probability that a person who responded to the survey gave the vacuum cleaner a rating of “medium”?

A 0.25

B 0.40

C 0.43

D 0.50

40 The line plot shows the test scores for the students in Mr. Wright’s science class on their last test. Which statement BEST describes the distribution of the scores?

A The scores are symmetrical C The scores show an outlier at 50

B The scores are skewed to the left D The scores are clustered around 80

Mr. Wright’s Science Test Scores

50 55 60 65 70 75 80 85 90 95 100

Test Scores

41 If the correlation coefficient for a data set is 0.16, which statement describes the relationship of the values in the data set?

A The numbers are random.

B The numbers are correlated perfectly.

C The numbers are strongly correlated where both sets of values increase.

D The numbers are strongly correlated where one set of values increases and the other set decreases.

42 This table shows the number of hours each employee at Menchie’s worked and the amount of money each earned.

Employee’s

Name

Hours

Worked

Amount

Earned

Agatha 6 $35.10

Casper 16 $93.60

Dwight 8 $46.80

Georgina 15 $87.75

Manuel 12 $70.20

Xavier 9 $52.65

If the information in this table is graphed on a coordinate plane and the slope of the line is calculated, which statement is false?

A Each employee earned $5.85 per hour.

B The y-intercept would be $0.

C If Renee worked 10 hours, she would earn $58.50.

D The y-intercept would be $5.85.

43 The Cake Baker is a bakery that specializes in cakes. During a recent month, the owner created the graph below comparing the number of cakes sold with the price of a cake. Which statement BEST describes the relationship between the price of a cake and the number of cakes sold?

A There is no correlation between the price of a cake and the number of cakes sold,

and a higher cake price does not cause a decrease in the number of cakes sold.

B There is no correlation between the price of a cake and the number of cakes sold,

but a higher cake price most likely will cause a decrease in the number of cakes

sold.

C There is a correlation between the price of a cake and the number of cakes sold, but a higher cake price does not cause a decrease in the number of cakes sold.

D There is a correlation between the price of a cake and the number of cakes sold, and a higher cake price most likely will cause a decrease in the number of cakes sold.

44 The water temperature in a lake was tested on 20 different rates. The scatterplot shows the results and the line of best fit for the data. According to the data, what is the best prediction for the water temperature on June 30?

A 53° C 55°

B 54° D 56°