UCS Algebra I Semester 1 Exam Review Guide #1

1 Which family of function is not shown below?

A Quadratic C Square RootB Absolute Value D Exponential

2 What is the constant in the expression 12 x3−2x2+x+5

A 3, 2, and 1 C 5B 12, – 2, and 1 D There is no constant value

3 Which relation is a function?

A

B

C

D

4 Function g is defined below.

g ( x )=−12x+7

If the range of function g is {4.325 ,6.225 }, what is the domain of function g ?

A {4.8375 ,3.8875 } C {−1.55 , .5.35 }

B {1.55 ,5.35 } D {−4.325 ,−6.225 }

5 Read the article at the left.

Suppose $24 had been invested in 1626 in an account paying 4.5% interest compounded annually. Which amount is closest to the balance in 2000?

A $339 million C $9400

B $89 million D $8900

6 Mrs. Springer purchased a house 15 years ago for $150,000. Since her purchase, her home has increased in value an average of $5,000 per year. If she wanted to graph the total value of her home in each of the past 15 years, which of these would describe the range of her graph?

A {all positive realnumbers }

B {real numbers between0∧15 inclusively }

C {real numbers greater than∨equal¿150,000 }

D { postivie realnumbers than∨equal¿5,000 }

7 A taxi cab driver charges $25 per ride plus $1.99 per mile and can be modeled by this function:

c (m )=1.99m+25

 Which set of numbers describes the domain of this function?

A All Positive Integers C All Real Numbers

B All Non-Negative Real Numbers D All Real Numbers greater than 25

8 The graph represents Brigham’s bicycle trip to Sara’s house for a Super Bowl party.

Which of the following statements would be a proper description for the section B to C?

A Brigham is pedaling at his fastest rate

B Brigham is cruising at a constant speed

C Brigham stops at the store to buy chips

D Brigham arrives at Sara’s house

9 On an algebra test, the highest grade was 38 points higher than the lowest grade. The sum of the two grades was 142. Find the lowest grade.

A 90 C 38B 71 D 52

10 Which relationship would BEST be modeled with a linear function?

A the weight of a dog and the age of the dog

B the number of $1 toppings on a pizza and the total cost of the pizza

C the value of a car that depreciates 10% every year and the age of the car

D the height of a projectile above the surface of Earth and the time after it

is launched

11 The graph shows how the price of a laptop computer is changing over time.

Which statement BEST describes how the price is changing?

A The price is decreasing by $900 every 6 months.

B The price is decreasing by $100 every month.

C The price is decreasing by $50 every month.

D The price is decreasing by $25 every month.

12 You just got a new puppy. Bones cost $2.00 each, and toys cost $6.00 each. Write an equation to relate the number of bones b and toys t you are able to buy your puppy with $30.00.

A 6c – 2t = 30 C 6c + 2t = 30

B 2c + 6t = 30 D 30 + 2c = 6t

13 Identify the x and y intercepts

A x−∫ : (−4,0 ) y−∫ :(0 ,−2) B x−∫ :(−2,0) y−∫ :(0 ,−4)

14 The value of a stock, in dollars per share, during a one-year period is shown on the graph below.

Which of these statements BEST describes the change in value of the stock?

A The lowest rate of change occurred from months 0 to 2.

C The rate of change was lower during months 4 to 6 compared to months 10 to 12.

B The highest rate of change occurred from months 10 to 12.

D The rate of change was higher during months 6 to 8 compared to months 2 to 4.

15 The formula for the perimeter of a rectangle is shown below. Solve the formula for the

variable w.P = 2l + 2w

A w=P−l C w=P−2l−2

B w= P2

−l D w= P−w2

16 The length of a rectangle is twice its width. If the perimeter of the rectangle is 30 in., find the length of the rectangle.

A length = 5 in. C length = 20 in.B length = 10 in. D length = 30 in.

17 There are at most 12 bicycles and tricycles in a school playground. There are at least 17 wheels altogether. Let b equal the number of bicycles and t equal the number of tricycles. Which system describes this situation?

A b + t < 122b + 3t ≥ 17

C b + t ≤ 12 2b + 3t ≥ 17

B b + t ≤ 122b + 3t > 17

D b + t ≤ 122b + 3t ≤ 17

18 State which inequalities have equivalent solution sets.

i. 13x≥ 2

3ii. −3 x≥−6iii. x+4≥6

A i. and ii. C ii. and iii.

B i. and iii. D i., ii., and iii.

19

Matt’s Explorer gets the same gas mileage as Eric’s teal car from his college days, but it has a smaller gas tank. Matt’s gas tank only holds 14 gallons

when full. The amount of gasoline Matt has left after driving x miles is shown in this graph.

A y=−150x+12 C y=−1

25x+12

B y=−150x+16 D y=−1

25x+16

20

Which graph shows the solution set of the inequality below?−3 x+3>−9

A

B

C

D

21 Simplify the following compound inequality.57≤3x−15≤75

A 14≤ x≤20 C 24≤ x≤30

B 14≥ x≥20 D 24≥ x≥30

22 Look at the system of equations below.

{4 x+3 y=112x+ y=5

Which of these shows a way the second equation could be rewritten in order to solve the system?

A 6 x−3 y=−15 C −6 x−3 y=−5

B −4 x+2 y=10 D −4 x−2 y=−10

23 Solve the system of equations.

−3 x−9 y=−32 x+9 y=11

A (1, 0) C (-1, -2)

B (1, 1) D (-8, 3)

24 Sophie graphed the line y = - 14 x + 3 on a coordinate plane. Which ordered

pair could not be on the line?

A (12, 0) C (- 14 , 3)

B (7, 54 ) D (16, -1)

25 Which of the following correctly shows the point of intersection for the functions below?

y=3 x+3y=−x−3

A

O 2 4–2–4 x

2

4

–2

–4

y C

O 2 4–2–4 x

2

4

–2

–4

y

B

O 2 4–2–4 x

2

4

–2

–4

y D

O 2 4–2–4 x

2

4

–2

–4

y

26 A company sells brass and steel machine parts. One shipment contains 3 brass and 10 steel parts and costs $48. A second shipment contains 6 brass and 12 steel parts and costs $72.

a) Find the cost of each type of machine part.b) How much would a shipment containing 10 brass and 13 steel

machine parts cost?A a) Brass $3, Steel $6;

b) $108C a) Brass $6, Steel $3;

b) $99B a) Brass $6, Steel $3;

b) $108D a) Brass $3, Steel $6;

b) $99

27 Which of the following graphs could represent the solution set of the inequality

y < 12x + 1?

A C

B D

28 To graph the equation shown below, Jeremy determined its x-intercept and y-intercept. 

 What are the intercepts of the graph of this equation?

Ax-intercept = ; y-intercept =

Cx-intercept = ; y-intercept =

Bx-intercept = ; y-intercept =

Dx-intercept = ; y-intercept =

29

Cindy has two part-time jobs. She earns $8 per hour as a cashier at Beta Market Foods and $6 per hour as a file clerk at Hal’s Insurance Company. Which graph best represents the amount of time she must work at each job to earn $120 per week?

A C

B D

30 Which statement is true about the graphs of y=25x+4 and ?

A They represent the same graph.

B They have different slopes and y-intercepts.

C They have different slopes but the same y-intercept.

D They have the same slope but different y-intercepts.

31 Which of the following equations represents the graph below?

A

y = x + 2

C y=2x+ 23

By = - x + 2

D y=−2x+ 23

32 If it rains 2 inches on Monday and it increases to 4 inches by Friday, what is the rate of increase in inches per day?

A (1/2 inch)/day C 1 inch/day

B 4 inches/day D 6 inches/day

33 Line a is given by the equation y=3 x−7 and line b contains points (0,5) and (2,9). Which of the two lines has a greater slope?

A Line a B Line b

34 Which situation BEST shows a constant rate of change?

A the number of eggs Rick gets in d dozen eggs

C the number of questions Jennifer misses on q quizzes

B the number of points per game Evan scores in b basketball games

D the number of friends Daisy makes each year for y years

35 Is the following a growth or decay function? How can you tell? f ( x )=0.5( 32 )

x

A Growth. The growth factor is greater than one.

C Decay. The growth factor is greater than one.

B Growth. The growth factor is less than one.

D Decay. The growth factor is less than one.

36 Given the expression f ( x )=4 (2 )X , what represents the growth factor ?

A x C 4

B 2 D None of These

37 The expression (x4 y−3 )−2can be rewritten as

Ax2 y−5

C y6

x8

Bx2 y6

D x−8

y6

38 The following graph shows the amount of gasoline used compared to miles driven on a recent vacation. Using the graph, identify the equation for the line.

Ay=−x+15 C y=−1

25x+15

B y=1525x+15 D y=−15x+ 3

5

39 What will be the function value at x=6?

A 64 C 12

B 6 D 36

40 Based on his records for his investments, John has determined thatthe equation A=609(1.0174)x represents the amount of money in hisbank account x years after he invested $609.

Which statement accurately describes the rate of change of John’s account balance

A The account is losing value at a rate of 1.74% each year.

C The account is growing at a rate of 1.74% each year.

B The account is losing value at a rate 101.74% each year.

D The account is growing at a rate of 101.74% each year.

41 The table below shows how the number of bacteria on a kitchen counter changes over time.

Day Number of Bacteria

0 1001 2002 4003 8004 1,600

A y=200(2)x C y=100 (2 x )

B y=100 (2)x D y=200(x)2

42 The value of a new car decreases exponentially. Suppose your mom buys a new car for $25,000. The value of the car decreases by 18% each year. Write an equation to model the value of the car x years after she buys it.

A Y = 25,000(1.18)x

B Y = 25,000(0.18)x

C Y = 25,000(0.82x)

D Y = 25,000(0.82)x

Which equation represents the relationship between the day (x) and the number of bacteria

43

Julie wants to purchase a new car for $18,000. She knows that after she purchases her car, it will depreciate (decrease in value) at a rate of 15% per year. Which graph models this situation?

A C

B D

44 Function  has the equation , and function  is described by

the table below.

How are these two functions alike?

A Both are linear functions.

B Both are exponential functions.

C Both have graphs with the same y-intercept.

D Both have graphs that approach as approaches .

45 Ms. Ricks, the principal of a new school, kept track of the school’s enrollment for the first four years. The results, which show an exponential relationship, are shown in the table below. Which equation models the data?

Year (f)

Number of Pupils (P)

0 2301 2482 2683 2904 313

A P=230 (0.08)t C P=248 (0.08)t

B P=230 (1.08)t D P=248 (1.08)t

46

An initial investment of $5 is expected to double in value every 10 years. Which graph BEST models the investment’s value?

A C

B D

47 Which graph shows the solution set of the inequality below?

|x+2|≥6

A C

B D

48 Erik is playing a video game in which he moves his character to avoid obstacles while collecting coins to earn points. There are 10 levels in the game. The table below shows the number of points earned for each coin collected by his character while playing on an easy Level 1 as

compared to playing on a more difficult Level 7.

If the patterns continue, what is the smallest coin number at which the points earned in Level 7 exceed the points earned in Level 1?

A 8 coins C 10 coins

B 9 coins D 12 coins

49 Write the equation of the graph below.

A y=|x−1|+2 C y=|x+1|−2

B y=−|x+1|+2 D y=|x−1|−2

50 Match the expression to the evaluation blocks pictured at the right.

A (5 - 6) + (3 * 7) C 5 - (6 + 3) *7

B (6 + (3 * 7) – 5 D 5 – (6 + (3 * 7))

51 Match the expression that models the evaluation blocks pictured at below:

A (6 – (2 * 5)) + (16/4) C 6 + (2 * 5) – (16/4)

B 6 – ((2 * 5) + (16/4)) D (2 *5) + (16/4) - 6