UPCAT Math 3 Algebra 1

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113 Terms

1
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What are the solutions of 3x2 + 14x + 16 \= 0?
B
2
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The only solution of the equation x2 + bx + 16 \= 0 is x \= 4. What is the value of b?
b \= -8
3
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Which function has zeros at x \= −2 and x \= 5?
f(x) \= x2 − 3x − 10
4
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An equation has solutions of m \= -5 and m \= 9. Which could be the equation?
(m + 5)(m - 9) \= 0
5
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What are the solutions to x2 + 8x + 7 \= 0?
x \= -7 and x \= -1
6
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Which equations are true for x \= -2 and x \= 2? Check all that apply.
x2 - 4 \= 0
4x2 \= 16
7
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Which function has zeros at x \= 10 and x \= 2?
f(x) \= x2 - 12x + 20
8
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John has 48 square centimeter tiles he wants to use to create a mosaic. He wants the mosaic to be rectangular with a length that is 2 centimeters longer than the width.

Which equation could John solve to find w, the greatest width in centimeters he can use for the mosaic?
w(w + 2) \= 48
9
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For what values of x is x2 + 2x \= 24 true?
4 and -6
10
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What is the only solution of 2x2 + 8x \= x2 - 16?
-4
11
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Which is a solution to (x − 2)(x + 10) \= 13?
x \= 3
12
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Which is a solution to the equation?

(x −2)(x + 5) \= 18
x \= −7
13
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Which is a solution to (x - 3)(x + 9) \= -27?
x \= 0
14
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What are the solutions to the equation?

x2 + 6x \= 40
x \= −10 and x \= 4
15
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Two factors of -48 have a difference of 19. The factor with a greater absolute value is positive.

What is the sum of the factors?
13
16
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What are the solutions to the quadratic equation x2 - 16 \= 0?
x \= 4 and x \= -4
17
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What are the solutions to the quadratic equation 3(x − 4)2 \= 75?
x \= −1 and x \= 9
18
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What are the solutions of the quadratic equation (x + 3)2 \= 49?
x \= 4 and x \= -10
19
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What are the solution(s) to the quadratic equation x2 - 25 \= 0?
x \= 5 and x \= -5
20
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Which are the roots of the quadratic function f(b) \= b2 - 75? Check all that apply.
1and 2
21
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Theo started to solve the quadratic equation (x + 2)2 - 9 \= -5. He added 9 to both sides and the resulting equation was
(x + 2)2 \= 4. Next, he took the square root of each side.

Which was the resulting equation of that step?
x + 2 \= ±2
22
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Which are the roots of the quadratic function f(q) \= q2 - 125? Check all that apply.
1 and 2
23
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What are the solution(s) of the quadratic equation 98 - x2 \= 0?
C.
24
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What are the solutions to the quadratic equation (5y + 6)2 \= 24?
A.
25
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What value of c makes x2 − 24x + c a perfect square trinomial?
144
26
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Solve x2 + 14x \= −24 by completing the square.

What is the solution set of the equation?
{−12, −2}
27
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Solve x2 - 8x \= 3 by completing the square. Which is the solution set of the equation?
A.
28
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Which are the solutions of x2 \= 19x + 1?
B.
29
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What value of c makes x2 − 12x + c a perfect square trinomial?
36
30
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Solve x2 \= 12x - 15 by completing the square. Which is the solution set of the equation?
D.
31
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What value of c makes x2 + 6x + c a perfect square trinomial?
9
32
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Which are the solutions of x2 \= -7x - 8?
D.
33
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Atraeus is solving the quadratic equation by completing the square. What is the value of A.
7
34
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What are the zeros of the quadratic function f(x)\=2x2-10x-3
C
35
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Sienne is solving the quadratic equation by completing the square. What is the value of A.
3
36
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Patel is solving 8x2+16x+3\=0 check all that apply
1,2,5
37
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The first few steps in solving the quadratic equation 8x2+80x\=-5 by completing the square are shown.
200
38
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Atraeus is solving the quadratic equation by completing the square.

7x2 - 14x + 6 \= 0

7x2 - 14x \= -6

A(x2 - 2x) \= -6

What is the value of A?
7
39
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What are the zeros of the quadratic function f(x) \= 2x2 - 10x - 3?
c.
40
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Isoke is solving the quadratic equation by completing the square.

10x2 + 40x - 13 \= 0

10x2 + 40x \= 13

A(x2 + 4x) \= 13

What is the value of A?
10
41
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Sunil is solving the quadratic equation by completing the square. What should sunil do next.
C.
42
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What are the zeros of the quadratic function f(x)\=2x2+16x-9
Not b
43
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What are the zeros of the quadratic function f(x)\=6x2+12x-7
Not d
44
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What are the zeros of the quadratic function f(x)\=16x2+32x-9
B.
45
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Lie is solving a quadratic equation by completing the square. What should lie do next
B.
46
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Which is a zero of the quadratic function f(x)\=9x2-54x-19
Not b
47
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In which step did yvonne make a mistake.
A.
48
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In which step did tran first make an error.
Not d
49
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What should gio do first.
A.
50
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What should maya do first
C.
51
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Which statement is true about the quadratic equation 8x2 − 5x + 3 \= 0?
The leading coefficient is 8.
52
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Determine the discriminant for the quadratic equation 0 \= -2x2 + 3. Based on the discriminant value, how many real number solutions does the equation have?

Discriminant \= b2 - 4ac
2
53
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The first step for deriving the quadratic formula from the quadratic equation, 0 \= ax2 + bx + c, is shown.

Step 1: -c \= ax2 + bx

Which best explains or justifies Step 1?
subtraction property of equality
54
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What are the values of a, b, and c in the quadratic equation -2x2 + 4x - 3 \= 0?
a \= -2, b \= 4, c \= - 3
55
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What is the value of the discriminant for the quadratic equation -3 \= -x2 + 2x?

Discriminant \= b2 - 4ac
not c
56
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What are the values of a, b, and c in the quadratic equation 0 \= 5x - 4x2 - 2?
a \= -4, b \= 5, c \= -2
57
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Which shows the correct substitution of the values a, b, and c from the equation 0 \= - 3x2 - 2x + 6 into the quadratic formula?

Quadratic formula: x \=
not c or b
58
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What is the value of the discriminant for the quadratic equation 0 \= 2x2 + x - 3?

Discriminant \= b2 - 4ac
not a
59
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Which shows the correct substitution of the values a, b, and c from the equation 1 \= -2x + 3x2 + 1 into the quadratic formula?

Quadratic formula:
not d
60
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What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 \= x2 − 4x + 5, and what does it mean about the number of real solutions the equation has?
The discriminant is −4, so the equation has no real solutions
61
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What is the value of the discriminant for the quadratic equation 0 \= x + 2 + x2?

Discriminant \= b2 - 4ac
-7
62
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Which shows the correct substitution of the values a, b, and c from the equation -2 \= -x + x2 - 4 into the quadratic formula?

Quadratic formula: x \=
not c
63
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A student is deriving the quadratic formula. Her first two steps are shown.

Step 1: -c \= ax2 + bx

Step 2:

Which best explains or justifies Step 2?
factoring the binomial
64
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Alessandro wrote the quadratic equation -6 \= x2 + 4x - 1 in standard form. What is the value of c in his new equation?
not -1
65
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Some of the steps in the derivation of the quadratic formula are shown.

Step 4:

Step 5:

Step 6:

Step 7:

Which best explains why the expression cannot be rewritten as during the next step?
not d
66
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Which shows the correct substitution of the values a, b, and c from the equation 1 \= -2x + 3x2 + 1 into the quadratic formula?

Quadratic formula:
a.
67
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What are the values of a, b, and c in the quadratic equation 0 \= x2 - 3x - 2?
a \=1/2 , b \= -3, c \= -2
68
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Some of the steps in the derivation of the quadratic formula are shown.

Step 3: -c + \= a

Step 4a: -c + \= a

Step 4b: + \= a

Which best explains or justifies Step 4b?
converting to a common denominator
69
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Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation x2 + 4x + 8 \= 0. Which explanation could Anderson provide?
The equation has one real number solution because the discriminant is 0
70
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Rhett is solving the quadratic equation 0\= x2 - 2x - 3 using the quadratic formula. Which shows the correct substitution of the values a, b, and c into the quadratic formula?
D.
71
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Zacharias is using the quadratic formula to solve the equation 0 \= -2x2 + 5x - 3. He begins by substituting as shown.

Quadratic formula: x \=
Substitution: x \=
What error did Zacharias make?
not a
72
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Ramiya is using the quadratic formula to solve a quadratic equation. Her equation is x \= after substituting the values of a, b, and c into the formula. Which is Ramiya's quadratic equation?

Quadratic formula: x \=
0 \= x2 + 3x + 2
73
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What is the discriminant of the quadratic equation 3 - 4x \= -6x2?
not a
74
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Quincy uses the quadratic formula to solve for the values of x in a quadratic equation. He finds the solution, in simplest radical form, to be x \= .

Which best describes how many real number solutions the equation has?
not b or c
75
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In simplest radical form, what are the solutions to the quadratic equation 6 \= x2 - 10x?

Quadratic formula: x \=
not c
76
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What is the discriminant of the quadratic equation 0 \= 2x2 + 3x - 5?
not c
77
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What are the zeros of the function f(x) \= x2 + 5x + 5 written in simplest radical form?



Quadratic formula: x \=
c
78
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A quadratic equation of the form 0 \= ax2 + bx + c has a discriminant value of 0. How many real number solutions does the equation have?
1
79
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A quadratic equation has a discriminant of 12. Which could be the equation?
0 \= 2x2 + 6x + 3
80
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Nathaniel is using the quadratic formula to solve 0 \= x2 + 5x - 6. His steps are shown below.



What are the solutions to the equation?
x \= -6, 1
81
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A quadratic equation has exactly one real number solution. Which is the value of its discriminant?
not c or d
82
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In simplest radical form, what are the solutions to the quadratic equation 0 \= -3x2 - 4x + 5?

Quadratic formula: x \=
not b
83
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What is the discriminant of the quadratic equation 0 \= -x2 + 4x - 2?
8
84
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What is the discriminant of the quadratic equation 0 \= 2x2 + 3x - 5?
not b or c
85
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A quadratic equation of the form 0 \= ax2 + bx + c has a discriminant value of -16. How many real number solutions does the equation have?
not 2 or 1
86
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What is the positive solution to the equation 0 \= -x2 + 2x + 1?

Quadratic formula: x \=
not b
87
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What is the value of the discriminant of the quadratic equation −1 \= 5x2 −2x, and what does its value mean about the number of real number solutions the equation has?
not c
88
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Mattie uses the discriminant to determine the number of zeros the quadratic equation 0 \= 3x2 - 7x + 4 has. Which best describes the discriminant and the number of zeros?
The equation has two zeros because the discriminant is greater than 0.
89
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Which function has real zeros at x \= −10 and x \= −6?
f(x) \= x2 + 16x + 60
90
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What are the solutions to the quadratic equation 4(x + 2)2 \= 36
x \= −5 and x \= 1
91
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Solve x2 + 6x \= 7 by completing the square. Which is the solution set of the equation?
{-7, 1}
92
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What is a solution to (x + 6)(x + 2) \= 60?
x \= 4
93
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What are the zeros of the quadratic function f(x) \= 2x2 + 8x - 3?
A.
94
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Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is -99.

Which equation can be used to find m, the midpoint of the two numbers?
m2 - 100 \= -99
95
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Mariya is solving the quadratic equation by completing the square.

4x2 - 20x + 3 \= 0

4x2 - 20x \= -3

A(x2 - 5x) \= -3

What is the value of A?
4
96
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Mischa wrote the quadratic equation 0 \= -x2 + 4x - 7 in standard form. What is the value of c in her equation?
-7
97
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Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 \= 121, x represents the side measure of the cropped photo.

What are the dimensions of the cropped photo?
9 inches by 9 inches
98
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Which is the graph of a quadratic equation that has a negative discriminant?
D.
99
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Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x \= -6. Which function could Heather be writing?
f(x) \= -x2 - 12x - 36
100
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The first step in solving the quadratic equation -5x2 + 8 \= 133 is to subtract from each side.
8