ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
1
3
1. (1.4) Evaluate g ( x)  (6  12 x) when x  .
3
4
2. (1.5) Which choice is equivalent to the following expression:
2a(a  5)  3(a  5b  2)  b(6  a)
(A) 2a 2  ab  6a  9b  6
(B) 5a 2  ab  7a  21b  6
(C) 5a 2  ab  6a  21b  6
(D) 2a 2  ab  7a  9b  6
For questions 3 and 4, refer to the scenario below.
Let the cost of a meal at a restaurant be c. The tax and tip on the meal are generally a
percentage of the price of the meal. The total cost of the meal is the price of the meal plus
tax plus tip.
3. (1.5, 1.6) What is an expression for the total cost of a meal where the tax is 8% and the tip is
15%? Select all that apply.
(A) c  0.08  0.15
(B) c  0.08c  0.15c
(C) 1.23c
(D) 0.24c
4. (1.5, 1.6) Write an expression for the total cost of the meal where the tax is x% and the tip
g% .
(A) c  xc  gc
(B) c  x  g
(C)
c  xc  gc
100
(D) c 
x
g
c
c
100
100
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
5. (1.7) The second step is missing in the solution process. Write the correct second step for the
solution process.
Step 1: 5x  6  2x  7 x  6
Step 2:
Step 3: 6  4 x  6
Step 4: 12  4x
Step 5: 3  x
6. (1.8) Karen is putting a decorative border around her rectangle flower garden. The total
perimeter of the garden is 200ft.
(a) Draw three different rectangles that could represent Karen’s flower garden. Label the
dimensions of your rectangles.
(b) Use the table to show the lengths and widths of five different rectangles that could
represent Karen’s flower garden. Do not use any of your rectangles from part a.
Length
Width
Perimeter
(c) The length of Karen’s garden is 4 times its width. Explain how to use the perimeter
formula P  2l  2w to find the dimensions of the garden.
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
7. (2.1) Solve the inequality for x, given b  c
a  bx  cx  d
(A) x 
ad
bc
(B) x 
ad
cb
(C) x 
ad
cb
(D) x 
d  a
bc
8. (2.3, 2.4) The diameter of a perfect Krispy Kreme donut is approximately 10cm. The
diameter can vary by at most 8mm, before it gets thrown away. Solve an absolute value
inequality finding the range of a perfect diameter of the donut in centimeters.
9. (3.1) Jerome is constructing a table of values that satisfies the definition of a function.
Input
–13
20
0
–4
11
–1
17
Output
–15
–11
–9
–2
–1
5
5
13
Which number(s) can be placed in the empty cell so that the table of values satisfies the
definition of a function? Select all that apply.
(A) –5
(B) –1
(C) 0
(D) 2
(E) 11
(F) 17
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
10. (3.3) FIFA soccer tournaments award points for results in group play. Teams are awarded 3
points for a win and 1 point for a tie. Let w represent wins and t represent ties. Write a
function to find a team’s total points, P.
11. (4.3) This graph shows three lines named a, b, and c.
a
b
c
1
Which ratio of the lines’ slope equals ?
4
(A)
a
b
(B)
b
a
(C)
a
c
(D)
c
b
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
3
12. (4.4) A line is defined by the equation y   x  2 . Select all ordered pairs that represent a
5
solution to the equation.
7
(A) (1, )
5
7
(B) (1, )
5
4
(C) (2,  )
5
(D) (5,5)
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
13. (4.5) Which graph is a solution set of the inequality 4 x  5 y  20 ?
(A)
(B)
(C)
(D)
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
14. (5.1) Consider the function f ( x)  3x  6 . Find f 1 (2).
(A) 12
(B) 0
(C) 
4
3
(D) 
8
3
15. (5.4) Which piecewise function represents the graph?
  x  2 , x  2

(A) f ( x)  3
, 2  x  2
2 x  3 , x  2

 x  2 , x  2

(B) f ( x)  3
, 2  x  2
2 x  3 , x  2

, x  2
x

, 2  x  2
(C) f ( x)  3
2 x  1 , x  2

 x  2 , x  2

, 2  x  2
(D) f ( x)  3
 2 x  3 , x  2

ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
For questions 16 and 17, refer to the scenario below.
The student council sold cookies and brownies at a bake sale. They sold a total of 25 items
and made $67. They charged $2 for each cookie and $3 for each brownie.
16. (6.1) Let x represent the number of cookies and y represent the number of brownies. Which
equations can be used as a system to model the situation? Select all that apply.
(A) x  y  67
(B) x  y  25
(C) 2 x  3 y  25
(D) 3x  2 y  25
(E) 2 x  3 y  67
(F) 3x  2 y  67
17. (6.1) How many brownies did the student council sell?
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
For questions 18 - 20, refer to the scenario below.
Christopher has 28 coins in quarters and dimes. The total value of the coins is $4.45.
18. (6.1) If Christopher has q quarters and d dimes, which system of equations can be used to
find the number of each coin?
q  d  3
(A) 
0.25q  0.10d  4.45
q  d  3
(B) 
0.10q  0.25d  4.45
q  d  28
(C) 
0.10q  0.25d  4.45
q  d  28
(D) 
0.25q  0.10d  4.45
19. (6.1) How many quarters did Christopher have?
20. (6.1) How many dimes did Christopher have?
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
21. (6.1) Which graph matches the system?
5 x  y  9

10 x  7 y  18
(A)
(B)
(C)
(D)
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
For questions 22 - 24, use the equation 3x  2 y  32 .
22. (6.1, 6.2) Choose two points that are solutions to the equation.
(A) (2,19)
(B) (7,3)
(C) (10,1)
(D) (11, 4)
23. (6.1, 6.2) Which of the following linear equations has one answer from question 22 as a
solution, but not the other?
(A) y  2 x  5
(B) 10 x  7 y  107
(C) y  2 x  11
3
(D) y   x  16
2
24. (6.1, 6.2) Which the following linear equations has the solution (0,0), but has no solutions in
common with 3x  2 y  32 ?
(A) y  
10
17
x
7
7
(B) 2 x  y  11
(C) 4 x  11y  235
3
(D) y   x
2
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
25. (6.2) Given the system of equations
kx  2 y  6

2 x  4 y  m
Which values of k and m make the lines parallel?
(A) k  1 , m  8
(B) k  1 , m  4
(C) k  1 , m  6
(D) k  1 , m  12
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
For question 26, use the scenario below.
Ernesto would like to earn at least $180 per month. He delivers newspapers for $9 per hour
and coaches basketball for $18 per hour. Ernesto cannot work for more than 15 hours per
month. Let x represent the number of hours Ernesto delivers newspapers and y represent the
number of hours Ernesto coaches basketball.
26. (6.4) Which graph shows the set of points that represents the number of hours that Ernesto
can work in order to earn at least $180 and not work more than 15 hours per month?
Hours Coaching
(A)
Hours Delivering Papers
Hours Coaching
(B)
Hours Delivering Papers
Hours Coaching
(C)
Hours Delivering Papers
Hours Coaching
(D)
Hours Delivering Papers
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
For question 27, use the scenario below.
The basketball team is having a fundraiser and can purchase t-shirts for $12 and sweatshirts
for $18. The team has a budget of $1500. Due to shipping costs, no more than a total of 100
t-shirts and sweatshirts combined can be ordered. Let t represent the number of t-shirts sold
and s represent the number of sweatshirts sold. The constraints are illustrated in the graph
below.
The team makes a profit of $5 on each t-shirt and $8 on each sweatshirt.
The objective function for profit is p  5t  8s .
27. (6.5) What is the maximum amount of profit the team can make?
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
28. (7.1) Select the value of x such that
24 1
 .
2 x 16
(A) 4
(B) 8
(C) 0
(D) 8
1 1
2 2
29. (7.2) What is the value of (81 ) ?
(A) 81
(B) 3
(C) 9
(D) 4.5
30. (7.4) Determine the growth rate for the exponential function below.
(A) 100%
(B) 200%
(C) 300%
(D) 600%
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
31. (7.6) The number of bacteria in a dish is initially measured to be N. The population
decreases by 5% per hour. Which function best describes the bacteria population after h
hours?
(A) f (h)  N (1.05)h
(B) f (h)  N (1.5)h
(C) f (h)  N (0.95)h
(D) f (h)  N (0.9)h
32. (8.2, 8.3) Which of the following expressions will result in an irrational number? Select all
that apply.
(A) 5  9
(B) 4  6
(C) 3  8
(D) 3  12
(E) 7  3 25
(F) 4  3 27
(G) 2  3 33
(H) 6  3 8
33. (8.2, 8.3) Which of the following expressions will result in a rational number? Select all that
apply.
(A)
4
3
(B)
9
4
(C)
16
(D)
2 8
(E)
5 125
(F)
12 2
25
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
34. (8.3) Find the area of the given right triangle in the simplest form.
1 6
2
(A)
2  12
(B)
2 2 3
(C)
2
 3
2
(D)
2
2 3
2
35. (8.3) Which are equivalent to 24x 4 y 2 where x  0 and y  0 ? Select all that apply.
(A) 2 x 6 x 2 y 2
(B) 2 x 2 y 2 6
(C) 2 x 2 y 6
(D) 12x 2 y
36. (8.3) Which are equivalent to
(A) 16 5
(B) 4 10
(C) 4 5
(D) 2 20
80 ? Select all that apply.
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
37. (9.3) Let ( x  y)2  45 and x 2  y 2  23 . What is the value of xy?
(A) 11
(B) 11
(C) 22
(D) 68
38. (9.3) Find the area of the given triangle.
(A) 9x 13
(B) 8 x 2  44 x  48
(C) 4 x 2  22 x  24
(D) 24 x3  124 x 2  100 x  48
39. (9.4) Which of the following are equivalent to 16x 4  y 4 ? Select all that apply.
(A) (4 x 2  y 2 )(2 x  y)(2 x  y)
(B) (2 x  y)2 (4 x 2  y 2 )
(C) (4 x 2  y 2 )(4 x 2  y 2 )
(D) (2 x  y)3 (2 x  y)
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
40. (9.4) If ( x  5) is a factor of 3 x 2  14 x  k , what is the value of k?
(A) 9
(B) 5
(C) 5
(D) 9
41. (9.5) Given x 2  48  ( x  b)( x  b) , find the value of b?
(A) 24
(B) 8 3
(C) 4 3
(D) 2 6
42. (9.5) Which equation has roots of 3 and 5 ?
(A) ( x  3)( x  5)  0
(B) ( x  3)( x  5)  0
(C) ( x  3)( x  5)  0
(D) ( x  3)( x  5)  0
43. (10.1) Use the function f ( x)  x 2  5 x  4 .
(a) Identify the x-intercepts and the y-intercepts.
(b) Identify the axis of symmetry.
(c) Determine the coordinates of the vertex.
(d) Sketch the graph.
(e) State the domain and range.
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
44. (10.4) The function f ( x)  2 x 2  4 x  6 is being transformed into g ( x)  2 x 2  4 x  2 .
Choose the best description of the transformation.
(A) The function is translated down 8 units.
(B) The function is translated up 8 units.
(C) The function is translated to the right 8 units.
(D) The function is translated to the left 8 units.
45. (10.5) The area, A, of a rectangular attached garage is given by the function
A( x)  4 x 2  64 x , where x is the length in meters of the garage. If the function is graphed
in a coordinate plane, which statement would be true?
(A) The x-intercepts of the function are 0 and 8, which are a lower bound and an upper
bound for the possible values of the length of the garage.
(B) The x-intercepts of the function are 0 and 8, which are a lower bound and an upper
bound for the possible values of the width of the garage.
(C) The x-intercepts of the function are 0 and 16, which are a lower bound and an upper
bound for the possible values of the length of the garage.
(D) The x-intercepts of the function are 0 and 16, which are a lower bound and an upper
bound for the possible values of the width of the garage.
ALGEBRA I
2014-2015
PRACTICE MATERIALS
END OF COURSE EXAMS
For question 46, use the scenario below.
Data Set A
Data Set B
46. Select all the choices that are true.
(A) 50% of data set A is between 8 and 10.
(B) The median values for data set A and B are the same.
(C) The interquartile range of set A is larger than the interquartile range of set B.
(D) The mean of set B is larger than the mean of set A.
(E) 75% of the data is less than 10 in both data sets.
(F) Both sets of data have a range greater than 7.