Free Printable Third Quarter PRACTICE EXAM

1.

In the equation

y = x² +5x +7, match each leading coefficient with its correct letter

a)

a=0, b=5, c=7

b)

a=1, b=5, c=7

c)

a=7, b=5, c=1

2.

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

a)

-4.9 and -0.1

b)

-8.54 and 8.54

c)

-0.45 and 3.55

d)

-6.77 and 1.77

3.

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.

4.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

5.

Identify the 'b' value: y = 16x² -8x -24

a)

16

b)

-8

c)

8

d)

-24

6.

What is the discriminant?

a)

b² - 4ac

b)

b²/ 2a

c)

4ac

d)

b²± 4ac

7.

If the discriminant equals 0, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

8.

If the discriminant is negative, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solutions

9.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

10.

b² - 4ac would equal: y = 2x² -x -3

a)

25

b)

-23

c)

-25

d)

0

11.

The quadratic formula can be used to solve quadratic equations that cannot be factored.

a)

True

b)

False

12.

Which expression gives the solutions of -5+2x²=-6x?

a)

A

b)

B

c)

C

d)

D

13.

When a quadratic equation is graphed, it creates a

a)

Square

b)

Circle

c)

Parabola

d)

Line

14.

Solve using the quadratic formula.

2x^2\ -\ 9x\ -35\ =\ 0

a)

$x\ =\ \frac{7}{2}\$ and $-6$

b)

$x\ =\ -\frac{5}{2}\$ and $5$

c)

$x\ =\ \frac{3}{7}\$ and $6$

d)

$x\ =\ -\frac{5}{2}\$ and $7$

15.

Solve the following equation:

x^2\ -\ 5x\ +\ 10\ =\ 0

a)

$\frac{\left(5\ -\ \sqrt{15}\ i\right)}{2}\ \ ,\ \frac{\left(5\ +\ \sqrt{15}\ i\right)}{2}$

b)

$\frac{\left(5\ -\ \sqrt{15}\right)}{2}\ ,\ \frac{\left(5\ +\ \sqrt{15}\right)}{2}$

c)

$\frac{\left(5\ -\ \sqrt{65}\ i\right)}{2}\ ,\ \frac{\left(5\ +\ \sqrt{65}\ i\right)}{2}$

d)

$\frac{\left(5\ -\ \sqrt{65}\right)}{2}\ ,\frac{\left(5\ +\ \sqrt{65}\right)}{2}$

16.

$x^2\ +\ 25\ =\ 10x$

Solve the following quadratic equation:

a)

$x\ =\ 5,\ -5$

b)

$x\ =\ -5$

c)

$x\ =\ 5$

d)

$x\ =\ 5\ +\ 5\sqrt{2\ }\ ,\ 5\ -\ 5\sqrt{2}$

17.

Competitors in the 10-meter platform diving competition jump upward and outward before diving into the pool below. The height (h) of a diver in meters above the pool after (t) seconds can be approximated by the equation

h=-4.9t^2+3t+10.

When will the diver hit the water?

a)

10 seconds

b)

1.77 Seconds

c)

3 seconds

d)

2.44 seconds

18.

Solve by using the quadratic formula:

3x^2-4x-8=-6

a)

$\frac{6\pm\sqrt{7}}{3}$

b)

$\frac{4\pm\sqrt{20}}{6}$

c)

$\frac{2\pm\sqrt{10}}{3}$

d)

$\frac{4\pm i\sqrt{40}}{3}$

19.

If the answer to a quadratic formula has an imaginary number in the solution, then that means . . .

a)

The discriminant is zero

b)

The discriminant is negative

c)

The discriminant is positive

d)

There is only one real root

20.

Solve the following equation using the quadratic formula:

m^2-8m=-14

a)

$m=4\pm\sqrt{2}$

b)

m = 6, m = -6

c)

$m=4\pm i\sqrt{2}$

d)

$m=4\pm2\sqrt{2}$

21.

Simplify.
$\frac{-7x^5y^5z^4}{21x^7y^5z^2}$

a)

$\frac{-x^{-2}z^2}{3}$

b)

$\frac{-3z^2}{x^2}$

c)

$\frac{-z^2}{3x^2}$

d)

$\frac{x^{-2}z^2}{-3}$

22.

Simplify.

4\left(a^2+5a-6\right)-3\left(2a^3+4a-5\right)

a)

$-6a^3+4a^2+8a-9$

b)

$-6a^3+4a^2+32a-9$

c)

$6a^3+4a^2+9a-9$

d)

$-6a^3+4a^2+9a-9$

23.

$\left(\frac{5a^{-7}b^2}{ab^{-6}}\right)^{-3}$

a)

$\frac{a^{24}}{125b^{24}}$

b)

$125a^{24}b^{24}$

c)

$\frac{125b^8}{a^8}$

d)

$\frac{5^{-3}a^{21}b^{-6}}{a^{-3}b^{18}}$

24.

Which expression is equivalent to

\left(m^2-m+1\right)\left(m+1\right)?

a)

$m^3+1$

b)

$m^3-m^2+1$

c)

$m^3+2m^2+1$

d)

$m^3+m^2-m+1$

25.

The U.S. Department of Transportation limits the time a truck driver can work each day to eleven hours. For the first part of his trip, Tom drives at a speed of 60 miles per hour, and for the second part of the trip, he drives at a speed of 70 miles per hour. Write a simplified polynomial to represent the distance driven. Type your answer simplified with no spaces.

(a)

26.

Find the product:
$\frac{4}{3}x^2\left(6x^2+9x-12\right)$

a)

$8x^2+12x^3-4x$

b)

$8x^4+12x^3-16x^2$

c)

$8x^4+12x^2-16x$

d)

$8x^2+12x^3-16x^2$

27.

Coefficient of x³y in the expansion of (2x+y)⁴

(a)

28.

Convert 15 miles per hour to inches per second. Type the number only.

(a)

29.

Consider the expansion of $\left(x+3y\right)^4$ starting with the term $x^4$ . Which option shows the correct fifth term?

a)

$108x^4y$

b)

$81xy^4$

c)

$54x^2y^2$

d)

$81y^4$

30.

Simplify.

$\left(x^4+x^3-6x^2-4x+14\right)\left(x^2+x-2\right)^{-1}$

a)

$x-4+\frac{6}{x^2+x-2}$

b)

$x^2-4\ remainder\ 6$

c)

$x^2-4+\frac{6}{x^2+x-2}$

d)

$x^2+4+\frac{6}{x^2+x-2}$

31.

What is the Binomial expansion of (x + 1)⁵ ?

a)

x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

b)

x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

c)

x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

d)

x⁵ + 1

32.

Which row of Pascal's Triangle would you use to expand (x+y)³?

a)

1

b)

1 1

c)

1 2 1

d)

1 3 3 1

33.

Choose the right Pascal's triangle

a)

b)

c)

d)

34.

Convert 62 miles/hour to feet/second. (5,280 ft = 1 mi)

a)

5,456 ft/s

b)

.003 ft/s

c)

91 ft/s

d)

909 ft/s

35.

Gas costs $3.05 a gallon, and your car travels at 27 miles for each gallon of gas. How far can you travel in your car with $95 in your pocket?

a)

11 miles

b)

840 miles

c)

7800 miles

d)

870 miles

36.

Which expression is equivalent to

\left(2y^3-5y^2-4\right)-\left(4y^3+11y^2-3y+5\right)?

a)

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

b)

$-2y^3-16y^2+3y-9$

c)

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

d)

$2y^3+16y^2-3y+9$

37.

Which expression is equivalent to

\frac{16m^4n^9+36m^8n^6+8m^6n^{12}}{4m^2n^3}

?

a)

$4m^2n^3+9m^4n^2+2m^2n^4$

b)

$4m^2n^6+9m^6n^3+2m^4n^9$

c)

$12m^2n^3+32m^4n^2+4m^2n^4$

d)

$12m^2n^6+32m^6n^3+4m^4n^9$

38.

What is the remainder when you divide

\frac{x^4+3x^2+x+6}{x+3}

?

a)

111

b)

$\frac{111}{x+3}$

c)

$\frac{111}{x-3}$

d)

$\frac{105}{x+3}$

39.

Consider the expression

\frac{x^3-4x+2}{x+3}

. What do you need to do differently when rewriting the numerator

x^3-4x+2

before you can divide the expression by x+3 using long division?

a)

Change the order of the terms

b)

Insert $0x^4$ .

c)

Insert $0x^2$ .

d)

Add a number corresponding to the remainder.

40.

Divide $4x^3$ by x+2. Which terms are part of the quotient? Choose all that apply.

a)

$4x^2$

b)

$2x^2$

c)

-8x

d)

4x

e)

0x

41.

Match the equation above with the graph below

a)

b)

c)

d)

42.

a)

b)

c)

d)

43.

Which graph represents an odd-degree function with a negative leading coefficient and zeros at x = -2 and x = 3?

a)

b)

c)

d)

44.

The table describes the values of g(x). Which statement describes the relative maxima of g(x)?

a)

A relative maximum occurs between x = -7 and x = -6

b)

A relative maximum occurs between x = -6 and x = -4

c)

A relative maximum occurs between x = -4 and x = -2

d)

A relative maximum occurs between x = -2 and x = -1.

45.

What should be the order of the polynomial coefficients if

(3x - 4x³+ 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

46.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

-2

47.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

48.

What is the degree of the polynomial function

P(x)=3x⁴-7x²-2x⁷-x+4?

a)

4

b)

7

c)

2

d)

1

49.

The function shown in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

50.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

51.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

52.

Factor completely. If the polynomial is not factorable, write prime.

$8c^3-27d^3$

a)

Prime

b)

$\left(2c-3d\right)\left(4c^2+6cd+9d^2\right)$

c)

$\left(2c+3d\right)\left(4c^2-6cd+9d^2\right)$

d)

$\left(2c-3d\right)\left(4c^6+6c^3d^3+9d^6\right)$

53.

Write in quadratic form, if possible.

$9x^8-21x^4+12$

a)

Not possible

b)

$\left(3x^4\right)^2-7\left(3x^4\right)+12$

c)

$3\left(3x^8-7x^4+4\right)$

d)

$3\left(x^4\right)^2-21\left(x^4\right)+12$

54.

Write in quadratic form, if possible.

$9x^8-21x^4+12$

a)

Not possible

b)

$\left(3x^4\right)^2-7\left(3x^4\right)+12$

c)

$3\left(3x^8-7x^4+4\right)$

d)

$3\left(x^4\right)^2-21\left(x^4\right)+12$

55.

Which choice is one of the zeros of the following equation?

$y^4-18y^2+72=0$

a)

$-2\sqrt{3}$

b)

6

c)

$\sqrt{-6}$

d)

$-2i\sqrt{3}$

56.

Which choice is one of the factors after you factor the following expression?

$x^5-16x$

a)

$\left(x^2+4\right)$

b)

$\left(x+4\right)$

c)

$\left(x^2-2\right)$

d)

Prime

57.

Which choice is one of the solutions to the following equation?

$x^6+7x^3-8=0$

a)

$1\pm i\sqrt{3}$

b)

2

c)

-1

d)

$\frac{1\pm i\sqrt{3}}{2}$

58.

Factor by grouping:

5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

59.

Factor the GCF

4b⁵+4b³+16b²

a)

4b³(b⁴+b²+4b)

b)

4b³(b⁴+4b+5)

c)

4(b⁵+b³+4b²)

d)

4b²(b³+b+4)

60.

Factor

k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

61.

125x³ - 64

a)

(5x - 4)(25x² + 20x + 16)

b)

(5x + 2)(25x² - 10x + 4)

c)

(3x - 1)(9x² + 3x + 1)

d)

(4x - 3)(16x² + 12x + 9)

62.

What is this called?

$b^2-4ac$

a)

Discriminant

b)

Denominator

c)

Derogatory

d)

Disinfectant

63.

The function

C\left(x\right)\ =\ 2.46x^3-22.37x^2+53.81x+548.24

can be used to approximate the number, in thousands, of international college students studying in the United States x years since 2010. How many international college students can be expected to study in the U.S. in 2025?

a)

4624.24 students

b)

2286.04 students

c)

4,624,640 students

d)

2,286,040 students

64.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

65.

True or false:

The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

66.

Given the polynomial and one of its factors, find the remaining factors of the polynomial. Check all that apply:

2x^3+17x^2+23x-42;\ x-1

a)

(x+12)

b)

(x+7)

c)

(x+6)

d)

(2x+7)

e)

(x+1)

67.

State the possible number of positive real zeros, and negative real zeros of the function:

f\left(x\right)=3x^5-8x^3+2x-4

a)

3 or 1 positive, 2 or 0 negative

b)

2 or 0 positive, 3 or 1 negative

c)

2 or 0 positive, 2 or 0 negative

d)

3 or 1 positive, 3 or 1 negative

68.

Solve the equation. Choose all solutions that apply.

x^3+1=0

a)

x = -1

b)

x = $\frac{1\pm i\sqrt{3}}{2}$

c)

x = $\frac{1\pm3i}{2}$

d)

x = 1

e)

x = 0

69.

How many of each type of root does this equation have? Check all that apply.

$16x^4-625=0$

a)

1 negative

b)

1 positive

c)

2 imaginary

d)

3 imaginary

e)

2 negative

70.

What is the remainder when you use synthetic substitution to find f(-5)?

$f\left(x\right)=x^3+2x^2-3x+1$

(a)

71.

Using Descartes' Rule of Signs, how many possible NEGATIVE roots are there for the polynomial f(x) = x⁴+x³+x²+x+5. Select all that apply.

a)

0

b)

1

c)

2

d)

3

e)

4

72.

Determine the roots of the polynomial.

f(x) = -x(x+1)(x-3)

a)

-1, 3

b)

0, -1, 3

c)

1, -3

d)

0, -3, 1

73.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

Third Quarter PRACTICE EXAM

Total questions: 73

Worksheet time: 6hrs 5mins

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