Download 232 Algebra 2 Semester 1 Exam

January 2015
Name ___________________
232A Semester 1 Practice Exam
1) Simplify. 3(2y - x) – 5(3x - 2y + 4x2)
2) x2 + 2xy if x = 3 and y = 4
a) 30
b)
57
c) 23
d) 33
e) 40
3) Solve:
7 
2
x5
3

a)
-8
b) -3
c) -18
d) 18
e)
4
3
4) Solve:
10  2 x  3  5  x  
a)
1
 4 x  8
2
-3
b)
1
c) 3
3

d)
1
3
e) 13
5) Solve for z:
A  2 xy  xz
z
a)
A
 2 xy
x
z
b)
A
 xy  x
2
z
c)
x
A  2 xy
z  A  2 xy  x
d)
z
e)
A  2 xy
x
6) x  5  3x  7
a)
x6
b)
x  1
c) x  6
d) x  6
e) x  1
c) 1  x  2
1
5
 x
2
2
d)
7) 3  4x  1  9
a) 1  x  2
8) Solve.
5x  2  8
b)
6
5
b)
a) x  
9)
Solve.
1  x  2

e) 1  x  2
d) x  2, 
c) x  2
3x  4  2
a) -2 ≤ x ≤ 
2
3
b) 0 ≤ x ≤ 
2
3
c) x ≤ -2 or x ≥ 
2
3
d) x ≥ -2 or x ≤ 
2
3
6
5
10)
3x  6  9
a) x  1 or x  5
b) x  1 or x  5
c) x  1 or x  5
11) Which of the following relations is not a function?
a) (0 , 0) , (1,1) , (2 , 4)
c) (0 , 0) , (1,1) , (1,  1) , (2 , 4) , (2 ,  4)
d) x  1 or x  5
b) (0 , 0) , (1,1) , (1,1) , (2 , 4) , (2 , 4)
d) (0 , 0) , (1,1) , (1,  1) , (2 , 4) , (2 ,  4)
12) Which of the following graphs does not represent a function?
a)
b)
c)
5
e) x  5 or x  1
d)
5
5
5
10
10
-10
-5
-5
-5
-5
13) Find the slope of the line through (-6, 7) and (2, 9)
a)
1
4
b) -2
c) 4
d) -4
e) 
1
2
14) Line that passes through (2, 6) and is parallel to y = 3x + 1
a) y  3x  2
y  3 x
b) y  3x
c)
y  3x  6
d) y  3x  2
e)
15) Find the slope of the line perpendicular to the line through (4, -4) and (10, -1).
a)

1
2
b)
2
c) -2
16) Find the equation of the line through (-3,5) and (1, 13)
1
a) y  2 x  11
b) y   x  11
c) y  2 x  11
2
d)
1
6
d) y 
e)
1
x  11
2
1
2
e) y  2 x  11
17) In 2005 a public library had 16,000 books. In 2009, it had 19,000 books. Find the average rate of
change per year.
750books
3000books
3000books
1year
750books
year
year
4
years
4
a) 750books
b)
c)
d)
e)
18) Which of the following equations describes this graph?
3
2
1
-2
2
4
-1
a) 3x  2 y  6
b) 2 x  3 y  6
c)  3x  2 y  6
d)  2 x  3 y  6
19) For y = x2 + 6x + 2, what is the equation of the Axis of Symmetry?
20) Write an equation for the horizontal line passing through the point (-3, 5).
a) x  3
b) y  3
c) x  5
d) y  5
21) Given: y varies directly as x; y = 20 when x = 8. Write a direct variation equation that relates y and x.
a) y  2.5 x
b) x  2.5 y
c) y  8 x
d) y  0.4 x
22) In 1990, 13 students belonged to the ping-pong club. By 2000, the membership had grown to 33
students. Write a linear equation in slope-intercept form that describes the average growth in the
membership from 1990 to 2000. Let x = 0 represent the year 1990 and let y represent the number of
members.
a) y  0.5 x  13 b) y  0.5 x  34
c) y  2 x  13
d) y  2 x  34
23) The graph below approximates the line-of-best-fit for the average price of men’s sneakers, y, where
x = 0 represents the year 1960. Write an equation for this line using the points (10, 18) and (20, 35).
35
(2 0 ,3 5 )
PRICE OF M EN'S SNEAKERS
30
25
Ave rage
pric e
of me n's
s ne ak ers ,
in dolla rs
20
(1 0 , 1 8 )
15
10
5
10
20
30
Y e a rs s in c e 1 96 0
a) y  1.7 x  5
b) y  1.7 x  1
c) y 
10
x5
17
d) y 
10
x 1
17
24) Write a system of linear equations to represent this problem:
You want to burn 400 calories during 30 minutes of exercise. You burn 10 calories per minute while roller
skating and 15 calories per minute playing basketball. Let x = # minutes roller skating and y = # minutes
playing basketball.
x  y  400
x  y  30
x  y  15
x  y  30
a)
b)
c)
d)
10 x  15 y  30
15 x  10 y  400
400 x  30 y  10
10 x  15 y  400
25) Simplify:
a)
8
27
2 6
9
26) Simplify: 4 6  10
a) 4 60
b)
4 6
9
c)
b) 6 15
2
6
3
d)
4 2
9 3
c) 8 15
d) 12 15
c) (x + 2)(x – 2)
d) (x – 1)(x + 4)
c) (x – 5)(x + 9)
d) (x – 15)(x + 3)
c) (3x + 4)(x – 2)
d) (3x – 2)(x + 4)
27) Factor completely: x2 – 4
a) (x + 2)(x + 2)
b) (x – 2)(x – 2)
28) Factor completely: x2 – 4x – 45
a) (x – 4)(x + 45)
b) (x + 5)(x – 9)
29) Factor completely: 3x2+ 10x – 8
a) (x + 12)(x – 2)
b) (3x + 2)(x – 4)
30) Factor completely: 12x2 – 25x + 12
a) (12x – 1)(x – 12)
31) Solve using square roots:
a)  3 5
b) (3x – 4)(3x – 4)
d) (3x – 4)(4x – 3)
x  32  3  2
b) 3  5
32) Solve using the quadratic formula. x 2  2 x  4  0
a) 1 2i
b)  1 2i
33)
c) (3x – 3)(4x – 4)
c) 3  5i
d)  3 5
c) 1 3i
d)  1  i 3
If the discriminant of a quadratic equation is negative, then the equation will have:
a) 1 real solution
c) 2 real solutions
b) 1 real double solution
d) 2 complex solutions (imaginary)
34) Simplify. (5  3i )  (7  2i )
a)  2  5i
b)  2  i
35) Simplify.
c) 12  5i
d) 12  i
c) 20  2i
d) 4  2i
10
2i
a) 4  10i
b)
20 10
 i
3
3
15 x 1
36) Simplify.
(3x 3 ) 2
a)
5
3x 7
37) Simplify.
b)
a) 9x2-16y2
b) 4
c) 4x2
b) x2y2
c)
b) -x2+13x-13
4
x2 y
1
y2
d)
x
y2
d)
b) x3-5x2-5x-4
c) x3+3x2+5x-4
d) x3-3x2-5x-4
x2+13x-13
b) 9x2+12xy+16y2
c)9x2-24xy+16y2
d) 9x2-12xy+16y2
c) x  9,  9i
d) x   3,  3i
(3x-4y)2
x 4  81  0
b) x   3,  i 3
43) Solve over the complex numbers:
a) x =  3
d)
c) x2+13x-3
42) Solve over the complex numbers:
a) x  3,  3i
1
45 x 7
(x+4) (x2-x –1)
a) x3+3x2-5x-4
41) Simplify.
d)
(3x2+4x-8) – (2x2-9x+5)
a) x2-5x-3
40) Simplify.
45 x7
xy 1
xy
a) y2
39) Simplify.
c)
4(x2 y)0
a) 1
38) Simplify.
5
x7
x 4  10 x 2  9  0
b) x =  1,3
c) x = 1, 3
d) x =  1, 9
January 2015
Name ____________________
232A Algebra 2
Free Response: Show all work on this paper.
44) Solve and graph: 2 x  3  9
0
45) Complete the table of values and graph:  2 x  y  5
y
x
-1
0
1
2
46) Solve this system using the substitution or linear combination method:
4 x  y  26
y  2x  8
answer: _______________________
47) Factor completely. 2x3y – 18xy
answer: ________________________
48) Solve by completing the square. x2 – 4x – 3 = 0
answer: ________________________
49) Solve by the quadratic formula.
3x2 – 4x + 5 = 0
NO DECIMALS!
Write your answer in simplest radical form.
answer: ________________________
50) Solve:
x 3  27  0
Make sure all solutions are written
on the answer line. NO DECIMALS!
Write your answer in simplest radical form.
answer: ________________________