Name: ________________________ Class: ___________________ Date: __________
GA Milestone Review Units 4-6
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
____
____
____
1. Express 8 −84 in terms of i.
a. −16i 21
b.
−5376
c.
d.
−16 21
16i 21
2. Solve the equation 2x 2 + 18 = 0.
a. x = 3 ± i
b. x = ±3
c.
d.
x = ±3i
x = ±3 + i
3. Find the values of x and y that make the equation −9x + 8i = −54 + (16y)i true.
a.
x = 6, y = 2
b.
x=
1
6
, y=2
1
6
c.
x=
, y=
d.
x = 6, y =
1
2
1
2
4. Find the zeros of the function f(x) = x 2 + 6x + 18 .
a. x = 3i or –3i
c.
b. x = –3 + 3i or –3 – 3i
d.
x = –3 + 3i
x = –6 + 3i or –6 – 3i
5. Find the complex conjugate of 3i + 4.
a. −4 − 3i
b. −4 + 3i
c.
d.
4 + 3i
4 − 3i
6. Subtract. Write the result in the form a + bi .
(5 – 2i ) – (6 + 8i )
a. –1 – 10i
b. 7 – 2i
c.
d.
–3 – 8i
11 + 6i
1
ID: A
Name: ________________________
ID: A
____
7. Multiply 6i ( 4 − 6i ) . Write the result in the form a + bi .
a. −36 + 24i
c. 36 − 24i
b. −36 − 24i
d. 36 + 24i
____
8. Simplify −8i 20 .
a. 8i
b. –8i
c.
d.
8
–8
c.
− 17 –
d.
−5 –
____ 10. What expression is equivalent to (3 − 2i) 2 ?
a. 13 − 12i
b. 13
c.
d.
5 − 12i
9 + 4i
____ 11. Factor the trinomial a 2 + 14a + 48.
a. ( a + 14 ) ( a + 1 )
b. ( a + 6 ) ( a + 8 )
c.
d.
(a − 8) (a − 6)
( a + 1 ) ( a + 48 )
____ 12. Factor the trinomial r 2 + r − 20.
a. (r + 1)(r − 20)
b. (r − 5)(r − 4)
c.
d.
(r − 4)(r + 5)
(r − 1)(r − 20)
____ 13. Factor the trinomial x 4 + 50x 2 + 625.
a. (x + 25) 4
c.
(x 2 + 25) 2
d.
2(x 2 + 25) 2
____
9. Simplify −2 + 2i .
5 + 3i
2
a.
− 17 +
b.
−5 +
b.
2
8
17
2
3
i
i
(x 2 + 50) 2
2
2
2
8
17
2
3
i
i
Name: ________________________
ID: A
____ 14. Factor 2x 2 + 7x + 6.
a. ( x + 2 ) ( 2x − 3 )
b. ( x + 2 ) ( x + 3 )
c.
d.
( x + 3 ) ( 2x + 2 )
( x + 2 ) ( 2x + 3 )
____ 15. Factor the trinomial 42n 2 − n − 30.
a. (6n + 5)(7n − 6)
b. Cannot be factored
c.
d.
(6n + 6)(7n − 5)
(6n − 5)(7n + 6)
____ 16. Factor −3x 2 + 26x − 16.
a. − ( x + 8 ) ( 3x + 2 )
b. ( 3x − 2 ) ( x − 8 )
c.
d.
− ( x − 8 ) ( 3x − 2 )
( 3x − 2 ) ( x + 8 )
____ 17. Determine whether 16x 2 − 24x + 9 is a perfect square. If so, factor it. If not, explain why.
a. No, 16x 2 − 24x + 9 is not a perfect square. 16x2 and 9 are perfect squares, but 24x is not a
perfect square. So 16x 2 − 24x + 9 is not a perfect square.
b. Yes, 16x 2 − 24x + 9 is a perfect square. ( 4x + 3 ) 2
c.
Yes, 16x 2 − 24x + 9 is a perfect square. ( 4x − 3 ) 2
d.
Yes, 16x 2 − 24x + 9 is a perfect square. ( 16x − 9 ) 2
____ 18. A square piece of fabric has an area of 16x 2 + 40x + 25 square inches. The length of each side of the fabric is
cx + d , where c and d are whole numbers. Find an expression in terms of x for the perimeter of the piece of
fabric. Then find the perimeter when x = 2.
a. An expression for the perimeter is 16x + 5. The perimeter is 37 inches.
b. An expression for the perimeter is ( 4x + 5 ) ( 4x + 5 ) . The perimeter is 169 inches.
c. An expression for the perimeter is 16x + 20. The perimeter is 52 inches.
d. An expression for the perimeter is 16x + 20. The perimeter is 13 inches.
____ 19. Determine whether 81 − 49n 4 is a difference of two squares. If so, factor it. If not, explain why.
a. (9 − 7n 4 )(9 + 7n 4 )
b.
(9 + 7n 2 )(9 − 7n 2 )
c.
(9 − 7n 2 )(9 − 7n 2 )
d.
Not a difference of squares because –49n4 is not a perfect square.
3
Name: ________________________
____ 20. Graph f(x) = x 2 − 5x + 10 by using a table.
a.
b.
ID: A
c.
d.
____ 21. The parent function f(x) = x 2 is reflected across the x-axis, vertically stretched by a factor of 10, and
translated right 10 units to create g. Use the description to write the quadratic function in vertex form.
a. g(x) = 10(x + 10) 2
c. g(x) = 10(x − 10) 2
b.
g(x) = −10(x − 10) 2
d.
4
g(x) = −10(x + 10) 2
Name: ________________________
ID: A
____ 22. The minimum braking distance d in feet for a properly loaded truck on dry concrete is approximated by the
function d ( v ) = 0.065v 2 , where v is the vehicle’s speed in miles per hour. If the truck is overloaded, the
braking-distance function is d o ( v ) = 0.078v 2 . What kind of transformation describes this change, and what
does the transformation mean?
a. The value of a has increased from 0.065 to 0.078. The increase indicates a vertical
stretch by a factor of 1.2. Thus, an overloaded truck takes about 1.2 times as many feet to
stop as a properly loaded truck.
b. The value of a has increased from 0.065 to 0.078. The increase indicates a vertical
stretch by a factor of 1.2. Thus, a properly loaded truck takes about 1.2 times as many
feet to stop as an overloaded truck.
c. The value of a has increased from 0.065 to 0.078. The increase indicates a horizontal
stretch by a factor of 1.2. Thus, an overloaded truck takes about 1.2 times as many feet to
stop as properly loaded truck.
d. The value of a has increased from 0.065 to 0.078. The increase indicates a horizontal
stretch by a factor of 1.2. Thus, a properly loaded truck takes about 1.2 times as many
feet to stop as an overloaded truck.
____ 23. Identify the axis of symmetry for the graph of f(x) = x 2 + 2x − 3 .
a. x = −1
c. y = −1
b. y = −4
d. x = −4
____ 24. Find the minimum or maximum value of f(x) = x 2 − 2x − 6 . Then state the domain and range of the function.
a. The maximum value is 1. D: {all real numbers}; R: {y | y ≥ –7}
b. The minimum value is –7. D: {x | x ≥ –7 }; R: {all real numbers}
c. The maximum value is 1. D: {x | x ≥ –7 }; R: {all real numbers}
d. The minimum value is –7. D: {all real numbers}; R: {y | y ≥ –7}
5
Name: ________________________
ID: A
____ 25. What quadratic function does the graph represent?
a.
f(x) = x 2 + 8x − 14
c.
f(x) = −x 2 + 8x + 14
b.
f(x) = −x 2 + 8x − 14
d.
f(x) = −x 2 − 8x − 14
____ 26. Determine whether the data set could represent a quadratic function. Explain.
x
y
a.
b.
c.
d.
–4
15
–2
5
0
–1
2
–3
4
–1
The x-values are not evenly spaced, so this could not be a quadratic function.
The first differences between y-values are constant for equally spaced x-values, so it
could represent a quadratic function.
The 2nd differences between y-values are constant for equally spaced x-values, so it
could represent a quadratic function.
The 2nd differences between y-values are not constant, so this could not be a quadratic
function.
____ 27. Find the zeros of the function h ( x ) = x 2 + 23x + 60 by factoring.
a. x = 4 or x = 15
c. x = −4 or x = −15
b. x = −20 or x = −3
d. x = 20 or x = 3
6
Name: ________________________
ID: A
____ 28. A toy rocket is launched from the ground level with an initial vertical velocity of 96 ft/s. After how many
seconds will the rocket hit the ground?
a. 6 seconds
c. 0 seconds or 6 seconds
6 seconds
d. 0 seconds
b.
____ 29. Find the roots of the equation 30x − 45 = 5x 2 by factoring.
a. x = 9
c. x = 3
b. x = −9
d. x = −3
____ 30. Write a quadratic function in standard form with zeros 6 and –8.
a. 0 = x 2 + 2x − 48
c. f(x) = x 2 − 2x − 48
b.
f(x) = x 2 + 2x − 48
____ 31. Solve the equation x 2 − 10x + 25 = 54.
a. x = 5 ±3 6
b. x = 5 +3 6
d.
f(x) = x 2 − 4x + 4
c.
d.
x = 5 −3 6
x = 5±6 3
____ 32. Write the function f(x) = −5x 2 − 60x − 181 in vertex form, and identify its vertex.
a.
b.
f(x) = (x + 12) 2 − 181 ;
vertex: (–12, –181)
f(x) = −5(x + 6) 2 − 1 ;
vertex: (–6, –1)
c.
d.
f(x) = (x + 6) 2 − 1 ;
vertex: (–6, –1)
f(x) = −5(x + 12) 2 − 181 ;
vertex: (–12, –181)
____ 33. Find the zeros of f(x) = x 2 + 7x + 9 by using the Quadratic Formula.
a.
x = −7 ±
b.
x=
13
13
−7 ±
2
3±
c.
x=
d.
x = 3±
7
7
2
7
Name: ________________________
ID: A
____ 34. Find the zeros of g ( x ) = 4x 2 − x + 5 by using the Quadratic Formula.
a.
x=
1
2
±
b.
x=
1
8
±
79
2
79
8
i
i
c.
x=
1
8
±
81
8
i
d.
x=
1
8
±
79
8
i
____ 35. Find the number and type of solutions for x 2 − 9x = −8.
a. Cannot determine without graphing.
b. The equation has one real solution.
c. The equation has two nonreal complex solutions.
d. The equation has two real solutions.
____ 36. During the eruption of Mount St. Helens in 1980, debris was ejected at a speed of over 440 feet per second
(300 miles per hour). The height in feet of a rock ejected at angle of 75° is given by the equation
y ( t ) = −16t 2 + 425t + 8200 , where t is the time in seconds after the eruption. The rock’s horizontal distance in
feet from the point of ejection is given by x ( t ) = 113t . Assuming the elevation of the surrounding countryside
is 0 feet, what is the horizontal distance from the point of ejection to the where the rock would have landed?
Round your answer to the nearest foot.
a. 2,234 ft
c. 4,467 ft.
b. 8,932 ft
d. 1,117 ft
____ 37. Solve the system by graphing.
ÔÔÏÔ
ÔÔÔ y = 2x + 1
Ô
ÔÌÔÔ
ÔÔÔ y = (x + 3) 2 − 8
Ó
a.
b.
(0, 1)
(−4, − 7)
c.
d.
(−3, − 8)
(−4, − 7) and (0, 1)
c.
d.
(−5, − 5) and (−1, 3)
(−5, − 5)
____ 38. Solve the system by substitution.
ÏÔÔ
ÔÔÔÔ −8x + 4y = 20
Ô
ÔÌÔÔ
ÔÔÔ y + 6 = (x + 4) 2
Ó
a.
b.
(−4, − 6)
(0, 5)
8
Name: ________________________
ID: A
____ 39. A glass-enclosed elevator at a sports arena moves upward from the ground floor at a constant speed of h = 9t.
At the same time the elevator starts to rise, a cannon on the arena floor shoots a souvenir mini-basketball into
the air at an initial velocity of 60 feet per second. The height of the mini-basketball (neglecting air resistance)
can be modeled by the equation h = −16t 2 + 60t . In both equations, h is height in feet and t is time in seconds.
Find the time for the ball and the elevator to be at the same height again. If necessary, round your answer to
the nearest tenth of a second.
a. 1.7 seconds
c. 2.4 seconds
b. 3.2 seconds
d. 1.5 seconds
____ 40. The cost, C, of manufacturing and selling x units of a product is C = 19x + 21, and the corresponding revenue,
R, is R = x 2 − 45 . Find the break-even value(s) of x. (Hint: A break-even value is where the cost is equal to the
revenue.)
a. 25
c. 3
b. 22
d. 25 and 3
____ 41. Write the equation of a circle with center M(7, –10) and radius 2.
a. (x + 10) 2 + (y − 7) 2 = 4
c. (x − 7) 2 + (y + 10) 2 = 4
b.
(x − y) 2 + (7 + 10) 2 = 4
d.
(x − 7) 2 + (y + 10) 2 = 2
____ 42. A reflector is designed so that its cross section is a parabola. The equation for a cross section of the parabola
is x = 361 y 2 . How far is the parabola’s focus from its vertex?
a.
b.
36
16
c.
d.
9
9
4
Name: ________________________
____ 43. Graph the equation (x − 3) 2 + (y + 2) 2 = 25 .
a.
b.
ID: A
c.
d.
____ 44. Find the point(s) of intersection of the line x − y = −6 and the circle x 2 + y 2 = 18 by solving the system of
equations.
a. (3, − 3)
c. (−3, 3) and (3, − 3)
b. (−3, 3)
d. (−3, 3) and (3, 3)
____ 45. Write the equation in standard form for the parabola with vertex (0, 0) and directrix y = −14.
a. y = − 1 x 2
c. x = 1 y 2
56
56
b. y = 1 x 2
d. x = 56y 2
56
10
ID: A
GA Milestone Review Units 4-6
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
D
C
D
B
D
A
D
D
A
C
B
C
C
D
A
C
C
C
B
B
B
A
A
D
B
C
B
A
C
B
A
B
B
D
D
C
D
C
B
1
ID: A
40.
41.
42.
43.
44.
45.
B
C
C
C
B
B
2