Free Printable Q1: Semester Exam Ch 1-3

1.

Which transformation maps $f(x)=x^2$ to $g(x)=3(x+2)^2$ ?

a)

Left 2, vertical stretch by 3

b)

Left 2, horizontal stretch by 3

c)

Right 2, vertical stretch by 3

d)

Right 2, vertical compression by 3

2.

Which transformation maps $f(x)=x^2$ to $g(x)=−(x−5)^2+1$ ?

a)

Right 5, reflect over x-axis, up 1

b)

Left 5, reflect over x-axis, down 1

c)

Left 5, reflect over y-axis, up 1

d)

Right 5, reflect over y-axis, down 1

3.

For g(x) = a(x−h)² + k, what point is the vertex?

a)

(k,h)

b)

(h,k)

c)

(h,−k)

d)

(−h,k)

4.

Which equation represents a parabola opening up with vertex at (3,−4)?

a)

$y=(x−4)^2+3$

b)

$y=−(x−3)^2−4$

c)

$y=(x+3)^2−4$

d)

$y=(x−3)^2−4$

5.

A quadratic is translated 4 units left and 3 units down from y=x². Which equation matches?

a)

$y=(x−4)^2+3$

b)

$y=(x+4)^2+3$

c)

$y=(x+4)^2−3$

d)

$y=(x−4)^2−3$

6.

What is the effect of the coefficient a in y=a|x|?

a)

Reflect across y-axis only

b)

Vertical stretch by a

c)

Shift left by a units

d)

Horizontal stretch by a

7.

Which absolute value function translates the graph up 7 and right 5?

a)

y=|x+5|+7

b)

y=|x−5|+7

c)

y=|x−7|+5

d)

y=|x+7|−5

8.

Which transformation takes y=|x| to y=−|x|+2?

a)

Reflect over y-axis, shift down 2

b)

Reflect over x-axis, shift right 2

c)

Reflect over x-axis, shift up 2

d)

Reflect over y-axis, shift up 2

9.

If y=2(x-1)²+5, which statement is true?

a)

Vertex at (1,5), vertical stretch

b)

Vertex at (−1,5), vertical stretch

c)

Vertex at (1,−5), vertical stretch

d)

Vertex at (1,5), vertical compression

10.

Identify the vertex and whether the graph opens up or down.

a)

(2, -3); opens up

b)

(-2, -3); opens down

c)

(2, 3); opens down

d)

(-2, 3); opens up

11.

Which change converts $y=x^2$ to $y=(x+3)^2$ ?

a)

Translate down 3 units

b)

Translate right 3 units

c)

Translate left 3 units

d)

Translate up 3 units

12.

Consider the arithmetic sequence 5, 12, 19, … . What is the common difference d?

a)

d = 12

b)

d = 7

c)

d = 6

d)

d = 5

13.

Given the arithmetic sequence find the explicit formula: $a_n=a_1+d\left(n-1\right)$

Example 1: 4, 7, 10, 13, 16, …

a)

$a_1\ =\ 3,\ \ \ d\ =\ 4$

b)

$a_1\ =\ 16,\ \ \ d\ =\ 3$

c)

$a_1\ =\ 4,\ \ \ d\ =\ 3$

d)

$a_1\ =\ 16,\ \ \ d\ =\ 13$

14.

For the arithmetic sequence 5, 12, 19, …, which explicit formula correctly gives the nth term a_n?

a)

a_n = 12 + 5(n − 1)

b)

a_n = 5 + 12(n − 1)

c)

a_n = 7 + 5(n − 1)

d)

a_n = 5 + 7(n − 1)

15.

Using your formula for 5, 12, 19, …, what is the 30th term a_30?

a)

a_30 = 225

b)

a_30 = 212

c)

a_30 = 216

d)

a_30 = 208

16.

Manny’s Pizza has monthly net profit following 4000, 1000, −2000, −5000, … . What is the common difference d?

a)

d = −3000

b)

d = −1000

c)

d = −2000

d)

d = −4000

17.

Find the explicit formula: $a_n=a_1+d\left(n-1\right)$
-23, -16, -9, -2, ...

a)

a_n = -23 + 7(n -1)

b)

a_n = -23 - 7(n -1)

c)

a_n = 7 - 23(n -1)

d)

a_n = 7 + 23(n -1)

18.

Using the pictured graph, what is y, when x= -3?

a)

-3

b)

-1

c)

1

d)

3

19.

What is the value of y when x = -2?

a)

4

b)

2

c)

-3

d)

-4

20.

The graph represents a piecewise function. How many pieces make up the function?

a)

1

b)

2

c)

3

d)

4

21.

The solution to this system of equations is:

a)

(4, 3)

b)

(3, 4)

c)

(-4, 3)

d)

No solution

22.

When you graph the exact same equation twice,

a)

you will have no solution.

b)

you will have one solution.

c)

you will have infinite solutions.

d)

you will graph a giraffe.

23.

When graphing a system of linear equations, what does the point where the two lines intersect represent?

a)

The slope of the steeper line

b)

The midpoint of each line

c)

The y-intercept of both lines

d)

The solution to the system

24.

Solve the system of equations.

a)

(11, 21)

b)

(3, 11)

c)

(11, -67)

d)

No solution

e)

Infinite solutions

25.

Solve the system of equations by graphing.

a)

(-1, 4)

b)

(1, 0)

c)

No Solution

d)

(0, 2)

26.

This system has _____ solutions

a)

0

b)

1

c)

2

d)

Infinitely many

27.

What is the solution to this system of equations?
$y=x-2$
$y=-2x+1$

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

28.

Is (-1,0) a solution to the system?

a)

Solution

b)

Not a solution

c)

Solution only for the red

d)

Solution only for the blue

29.

Given the system, determine a solution.

a)

No solution

b)

Infinite solutions

c)

(-5, 5)

d)

(5, -5)

30.

Is (-2,4) a solution to the system?

a)

Solution

b)

Not a solution

31.

Given f(x) = $−(x − 3)^2 + 2$ , which transformation from y = $x^2$ occurred?

a)

Left 3, up 2, no reflection

b)

Right 3, down 2, reflection over y-axis

c)

Left 3, down 2, vertical stretch by 2

d)

Right 3, up 2, reflection over x-axis

32.

For f(x) = $x^2 + 2x - 5$ , what is the x-coordinate of the vertex?

a)

x = −1

b)

x = −2

c)

x = 1

d)

x = 2

33.

For f(x) = $x^2 + 2x - 5$ , what is the y-coordinate of the vertex?

a)

y = −4

b)

y = −7

c)

y = −5

d)

y = −6

34.

Which statement describes how a changes in $f(x) = a(x − h)^2 + k$ affect the graph?

a)

a < 0 opens down

b)

a < 0 shifts right

c)

a = 0 reflects over y-axis only

d)

a > 0 shifts up by a units

35.

For y = $x^2 + 3x + 2$ , what is the y-intercept?

a)

(0, 2)

b)

(0, 3)

c)

(0, 1)

d)

(0, 0)

36.

Which statement about the graph of $f(x) = -2x^2 - 4x + 6$ is true?

a)

It is linear and has no vertex

b)

It opens downward and has a minimum

c)

It opens upward and has a maximum

d)

It opens downward and has a maximum

37.

A parabola has vertex (1, 2) and passes through (2, −5). What is its equation in vertex form?

$y=a\left(x-h\right)^2+k$

a)

y = $−7(x + 1)^2 − 2$

b)

$y = 7(x − 1)^2 + 2$

c)

$y = −7(x − 1)^2 + 2$

d)

$y = 7(x − 2)^2 − 5$

38.

Write the vertex form of a parabola with vertex (1, 3) passing through (2, −6).

$Formula:f(x)=a(x-h)^2+k$

a)

$y = −3(x − 1)^2 + 9$

b)

$y = −9(x + 1)^2 + 3$

c)

$y = −9(x − 1)^2 + 3$

d)

$y = 9(x − 1)^2 − 3$

39.

Using the points (2, −8), (3, −8), and (6, 4), which equation matches the parabola in standard form $y = ax^2 + bx + c$ ?

a)

$y = x^2 - 6x + 8$

b)

$y=x^2−5x-2$

c)

$y = x^2 - 8x + 8$

d)

$y=x^2-5x+4$

40.

Given y = $ax^2 + bx + c$ and points (2, −8), (3, −8), and (6, 4), which value of c is correct?

a)

c = 10

b)

c = 8

c)

c = 6

d)

c = -2

41.

For y = $x^2 + 4x + 3$ , identify the vertex.

a)

(-2, -1)

b)

(2, 7)

c)

(-4, 3)

d)

(0, 3)

42.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

43.

Factor
x²+12x+35

a)

(x+5)(x+7)

b)

(x+4)(x+3)

c)

(x+7)(x-5)

d)

Prime

44.

Factor
12x + 9

a)

3(4x + 3)

b)

x(12+9)

c)

3(4x - 3)

d)

not factorable

45.

Factor
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

$\left(x-25\right)\left(x+25\right)$

46.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

47.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

48.

(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

49.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

50.

Simplify.

a)

-5i

b)

5

c)

5i

d)

-5

51.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

52.

√-81

a)

9i

b)

-9i

c)

-9

d)

9

53.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

54.

4+5i+6+6i

a)

21i

b)

20i+36

c)

24+30i

d)

10+11i

55.

Find the value of "c" that completes the square.

x_{ }^2+8x+c

a)

-4

b)

4

c)

8

d)

16

56.

Find the value of "c" that completes the square.

x^2+28x+c

a)

28

b)

14

c)

196

d)

56

57.

$x^2+12x+$ ___

Complete the square!

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x2 + 12x - 144

58.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

59.

Identify a, b and c when y = x² +5x +7,

Quadratic formula

$x=\frac{-b\pm\sqrt[]{b^2+-4ac}}{2a}$

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

60.

Solve Using the Quadratic Formula
2x² + 7x - 15 = 0

$x=\frac{-b\pm\sqrt[]{b^2+-4ac}}{2a}$

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

61.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

62.

Solve by the Quadratic Formula:

$9u^2-11u+7=0$

a)

$\frac{-11\pm\sqrt{131}}{18}$

b)

$\frac{11\pm\sqrt{131}}{18}$

c)

$\frac{11\pm\sqrt{131}}{-18}$

d)

$\frac{11\pm i\sqrt{373}}{18}$

63.

Identify a, b and c in the quadratic equation: $2x^2-3x-5=0$

a)

a = 2 , b = 3, c = -5

b)

a = 2, b = -3, c = 5

c)

a = 2, b = -3, c = -5

d)

a = -2, b = 3, c = 5

64.

$x^2+4x+3=0$ $x=\frac{-b\pm\sqrt[]{b^2+-4ac}}{2a}$

a)

x = 1 and -3

b)

x = -1 and -3

c)

x = -1 and 3

d)

x = 1 and 3

65.

Find the solution(s).

a)

(3,18) and (-4, 15)

b)

(5,2) and (5,-9)

c)

(-4,-4)

d)

(-4,2)

66.

Simplify into Standard Form:

$4x^2-5x+10+2x^2\ +12x\ -3$

a)

$6x^2+7x\ +8$

b)

$6x^2+7x\ +7$

c)

$11x^2+7$

d)

$7$

67.

Rewrite f(x) = $−3x^3 + 2x^5 + x + 8x^3 − 6 + x^4 − 3x^2$ in standard form.

a)

$2x^5 + x^4 + 5x^3 + 3x^2 + x - 6$

b)

$2x^5 + x^4 - 5x^3 - 3x^2 + x - 6$

c)

$2x^5 + x^4 + 5x^3 - 3x^2 + x - 6$

d)

$2x^5 + x^4 + 5x^3 - 3x^2 - x - 6$

68.

What is the degree of f(x) = $2x^5 + x^4 + 5x^3 - 3x^2 + x - 6$ ?

a)

Degree 3

b)

Degree 4

c)

Degree 5

d)

Degree 6

69.

Add the polynomials: $(4x^3 + 2x + 2x^2 − 8) + (2x^3 + x^2 + 9)$ .

a)

$6x^3 + 3x^2 + 2x - 1$

b)

$6x^3 + 3x^2 + 2x + 1$

c)

$6x^3 + x^2 + 2x + 1$

d)

$6x^3 + 3x^2 - 2x + 1$

70.

Subtract the polynomials: $(9a^3 − 6a − 4) − (3a^3 − 2a + 1)$ .

a)

$6a^3 - 8a - 5$

b)

$6a^3 - 4a + 5$

c)

$6a^3 - 4a - 5$

d)

$12a^3 - 4a - 3$

71.

For g(x) with leading term $2x^5$ , what is the end behavior of g(x) as x → −∞?

a)

y constant

b)

y → 0

c)

y → ∞

d)

y → −∞

72.

What is the end behavior as x → -∞ f(x)→ ?

a)

-∞

b)

∞

c)

0

d)

constant

73.

Multiply the monomial and polynomial: $4x(5x^2 − 3x + 1)$ . What is the simplified result?

a)

$20x^3 - 12x^2 + 4x$

b)

$20x^3 - 12x + 4x^2$

c)

$20x^3 − 12x^2 − 4x$

d)

$20x^2 − 12x^3 + 4x$

74.

Apply the distributive property to multiply (3x − 2)(6x + 2). What is the simplified expression?

a)

$18x^2 + 12x - 4$

b)

$18x^2 - 12x + 4$

c)

$18x^2 + 10x - 4$

d)

$18x^2−6x−4$

75.

When expanding $\left(a+b\right)^5$ with Pascal’s Triangle, which set of coefficients is used?

a)

1, 2, 1

b)

1, 4, 6, 4, 1

c)

1, 3, 3, 1

d)

1, 5, 10, 10, 5, 1

76.

Expand: $\left(a+b\right)^2$

a)

$a^2+ab+b^2$

b)

$a^2+2ab+b^2$

c)

$a^2-ab+b^2$

d)

$a^2-2ab+b^2$

77.

Factor completely: $4x^2 - 144y^6$

a)

$4(x - 3y^3)(x + 3y^3)$

b)

$4(x - 6y^3)(x + 6y^3)$

c)

$(2x - 12y^3)(2x + 12y^3)$

d)

$(x - 12y^3)(x + 12y^3)$

78.

Factor completely: $216 + 343y^3$

a)

$(6 + 7y)(36 − 42y + 49y^2)$

b)

$(6 + 7y)(36 + 42y + 49y^2)$

c)

$(6 − 7y)(36 − 42y + 49y^2)$

d)

$(6 − 7y)(36 + 42y + 49y^2)$

79.

9x²- 49y⁶

a)

( 3x + 7y³) (3x + 7y³)

b)

( 3x - 7y³) (3x + 7y³)

c)

( 3x - 7y³) (3x - 7y³)

d)

Unfactorable

80.

Using synthetic division, which number is used in the box to divide by (x − 4)?

a)

1

b)

−4

c)

4

d)

0

81.

Using synthetic division for divisor (x + 2), what number goes in the box?

a)

1

b)

0

c)

2

d)

−2

82.

Perform the division: $(2x^4+x^3+0x^2-10x−1)\div(x+2)$ . What is the remainder?

a)

Remainder −1

b)

Remainder 1

c)

Remainder 43

d)

Remainder 17

83.

Perform the division: $(x^4 − 25x^2 + 144) ÷ (x − 4)$ . What is the remainder?

a)

Remainder 144

b)

Remainder −80

c)

Remainder 80

d)

Remainder 0

84.

Evaluate P(5) for P(x) = $−x^3 + 12x^2 + 6x + 80$ .

a)

285

b)

155

c)

130

d)

80

85.

Evaluate $Evaluate\ P\left(3\right)when\ \ \ P\left(x\right)=-1x^3+12x^2+6x+80$

a)

125

b)

179

c)

95

d)

80

86.

What are the zeros of f(x) = x(3x + 2)(x − 8)(x + 5)?

a)

x = 0, 3/2, −8, 5

b)

x = 0, −2/3, 8, −5

c)

x = 0, −2, 8, −5

d)

x = 0, 2/3, −8, 5

87.

Find the real and complex solutions to $f(x)=x^3+8x^2+19x+12$

a)

x = −4, x = −3, x = −i

b)

x = −2, x = −3, x = 4

c)

x = −7, x = 4, x = 1

d)

x = −4, x = −3, x = −1

88.

Which factorization correctly rewrites $4x^3 + 4x^2 - 8x$ for solving the inequality $4x^3 + 4x^2 - 8x < 0$ ?

a)

$2x(2x^2 + x - 4)$

b)

$4x(x^2 + x − 2)$

c)

$x(4x^2 + 4x - 8)$

d)

$4(x^3 + x^2 − 2x)$

89.

For the cubic inequality $4x(x^2 + x - 2)$ $< 0$ , which interval represents the solution set?

a)

(−2, 1)

b)

(−2, 0) ∪ (1, ∞)

c)

(−∞, −2) ∪ (0, 1)

d)

(−∞, 0) ∪ (1, ∞)

90.

List all the possible rational solutions: $4x^3 + 8x^2 - x - 2 = 0$

a)

±1, ±2, ±4, ±8

b)

±1, ±2, ±1/2

c)

±1, ±2, ±1/2, ±1/4, ±4

d)

±1, ±2, ±1/2, ±1/4

91.

List the possible rational zeros of

f(x) = x³ - 4x² -4x + 16

a)

1, 2, 4, 8, 16

b)

$\pm1,\pm2,\pm4,\pm8,\pm16$

c)

$\pm1,\pm4,\pm\frac{1}{4}$

d)

-2 and-4

92.

Write a polynomial equation with roots of −6 and 2 and 0

a)

(x − 6)(x − 2)x = 0

b)

(x + 6)(x + 2)x = 0

c)

(x − 6)(x + 2)x = 0

d)

(x + 6)(x − 2)x = 0

93.

What are the other roots if two roots are 8 − √6 and 7

a)

8 + √6 and 7

b)

8 − √6 and −7

c)

8 + √6 and −7

d)

−8 + √6 and 7

94.

Simplify √-4

a)

$\pm$ 2i

b)

-2i

c)

2

d)

4i

Q1: Semester Exam Ch 1-3

Total questions: 94

Worksheet time: 3hrs 12mins

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