Free Printable M2 Math Core Final Exam

1.

Which of the following is NOT a type of polynomial?

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Algebra

2.

What is the degree of the polynomial $P(x)=4x^3+2x^2−5x+7$ ?

a)

3

b)

-2

c)

100

d)

0

3.

Which of these is a monomial?

a)

$2x^2+3x+1$

b)

$4x^3$

c)

x−5

d)

$\frac{1}{x}+3$

4.

Identify the polynomial NOT in standard form (descending order i.e. 4, 3, 2,1):

a)

$5x^4+3x^3−2x^2+x−6$

b)

$4x−x^2−7$

c)

$x^3−2x+1$

d)

$6x^5+x^4−3x+2$

5.

If $P(x)=x^3−2x^2+x−3$ , what is P(2)?

a)

7

b)

5

c)

−1

d)

−3

6.

What are the solutions (zeros) of P(x)=(x−2)(x+3)(x−4)?

a)

x={2,−4}

b)

x={2,3,6}

c)

x={2,−3,4}

d)

x={−1,5,−6}

7.

Add $P(x)=3x^2−x+4$ and $Q(x)=5x^2+2x−1$ :

a)

$8x^2+x+3$

b)

$8x^2+3x+3$

c)

$8x^2−3x+5$

d)

$8x^2−3x−5$

8.

Subtract $Q(x)=5x^2+2x−1$ and $P(x)=3x^2−x+4$ :

a)

$2x^2+3x−5$

b)

$−4x^2+6x−10$

c)

$−x^2+4x−9$

d)

$8x^2+2x−3$

9.

Multiply: (x+2)(x−3)

a)

$x^2+6x−36$

b)

$x^2+5x−10$

c)

$x^2−x−6$

d)

$x^2−7x−9$

10.

Factor: $(a^2−b^2)$

a)

$(a+b)^2$

b)

(a+b)

c)

$(a−b)^2$

d)

$(a+b)(a−b)$

11.

Factor: $2x^2−8x+6$

a)

(x−1)(2x−6)

b)

2(x−3)(x−1)

c)

(2x−3)(x−2)

d)

2(x+3)(x+1)

12.

Which of the following is a factor of $x^2+7x+10$ ?

a)

x+3

b)

x+5

c)

x−6

13.

Factor: $x^2−4x−12$

a)

(x+1)(x−3)

b)

(x+2)(x−4)

c)

(x−6)(x+2)

d)

(x+9)(x−8)

14.

Solve: $x^2+5x+6=0$

a)

$x=−2,x=−3$

b)

x=4

c)

x=6,x=−5

d)

x=1,x=−1

15.

Factor: $x^2−9$

a)

(x+3)(x+9)

b)

(x+3)(x−3)

c)

(x−3)(x−6)

d)

(x−9)(x+1)

16.

Simplify: $(2ab^2)(3a^2b^3)$

a)

$9a^2b^2$

b)

$8a^2b^2$

c)

$6a^3b^5$

d)

$3a^2b^6$

17.

Simplify: $a^5\times a^2$

a)

$a^3$

b)

5

c)

7a

d)

$a^7$

18.

Solve: $6^0$

a)

1

b)

0

c)

6

d)

36

19.

Rewrite: $x^{−1}$

a)

−1

b)

$\frac{1}{x}$

c)

0

d)

$\frac{−1}{x}$

20.

Simplify: $2a^{−2}$

a)

$\frac{a^2}{2}$

b)

2a

c)

$2a^2$

d)

$\frac{2}{a^2}$

21.

Express in standard notation: $5.2\times10^7$

a)

0.00000052

b)

0.0000052

c)

5,200,000

d)

52,000,000

22.

Express in scientific notation: 4,390,000,000,000

a)

$4.39\times10^{12}$

b)

4.39×10

c)

$4.99\times10^{10}$

d)

$4.33\times10^{−10}$

23.

Express the product in scientific notation: $3.6\times10^3$ and $4.8\times10^{−3}$

a)

17.28

b)

1.728×10

c)

1,728

d)

$1.728\times10^2$

24.

Express the quotient in standard notation: $6.0\times10^3$ and $3.0\times10^3$

a)

2

b)

3

c)

2,000

d)

3,000

25.

Simplify: $\frac{(3bc^2)^2}{(4c)^2}$

a)

$3b^2c^4$

b)

$\frac{9b^4}{16c}$

c)

$\frac{b^2}{16c}$

d)

$\frac{9b^2c^2}{16}$

26.

What is the degree of the polynomial: $x^2−y^4+xy−6$

a)

3

b)

4

c)

1

d)

6

27.

Which polynomial is in descending order (ex. 3, 2, 1)?

a)

$x^3+xy^2−7y^5$

b)

$a^4+ab^5−b^3$

c)

$d^5+6d^3−c^2$

d)

$4g+hg^3−h^2$

28.

Which polynomial is in descending order (ex. 3, 2, 1)?

a)

$x^3+xy^2−7y^5$

b)

$h^4+gh^5−g^3$

c)

$d^5+6f^3−z^2$

d)

$4c+ab^3−b^2$

29.

Which polynomial is in ascending order (ex. 1, 2, 3)?

a)

$a^3+ab^4−b^6$

b)

$3m^4+mn^2−n^2$

c)

$s^5+8r^6s^3−r^2$

d)

$gh+g^3−9ℎ^2$

30.

Simplify: $x^2(x+2)+3(x^3+4x^2)$

a)

$x^3+2x^2+x^3+x^2$

b)

$x^3−6x^2+3x^4+12x^5$

c)

$4x^3+14x^2$

d)

$2x^3+16x^2$

31.

Find the difference: $(7x^2+4)−(3x^2+2x−6)$

a)

$(3x^2+2x−6)$

b)

$(4x^2+2x+10)$

c)

$(−3x^2+2x−10)$

d)

$(−x^2−2x+2)$

32.

Find the Greatest Common Factor (GCF): $15c^2d$ and $45cd^2$

a)

15cd

b)

3∙3∙c∙d

c)

5c

d)

$45d^2$

33.

What are the prime factors of $18ab^3$ ?

a)

2∙3∙a∙b∙b

b)

2∙2∙3∙a∙b∙b∙b

c)

2∙3∙3∙a∙b∙b∙b

d)

3∙3∙a∙a∙a

34.

Find the prime factorization of −40

a)

4∙10

b)

−4∙10

c)

2∙2∙2∙5

d)

−1∙2∙2∙2∙5

35.

Find the Greatest Common Factor: 48 and 64

a)

$2^6$

b)

$2^4$

c)

$6^2$

d)

$8^2$

36.

Solve: $x^2−3x−4=0$

a)

$x(x−3)−4=0$

b)

$(x+1)(x−4)=0$

c)

x = −1, x = 4

d)

x = 1, x = −4

37.

Factor: $3x^3−75x$

a)

$3(x^2−25)$

b)

(x − 5)(x + 5)

c)

$(x−5)^2$

d)

$3x(x−5)(x+5)$

38.

Solve: $(x−4)^2=121$

a)

x = 15, x = −7

b)

(x − 4) = 11

c)

x = ±11

d)

x = 4

39.

Which is a prime number?

a)

4

b)

6

c)

9

d)

11

40.

What does “FOIL” stand for?

a)

Maths

b)

First, Outside, Inside, Last

c)

Distribution

d)

Fun over instruction level

41.

Which of the following is a rational expression?

a)

34x

b)

x + y

c)

$\frac{2x}{x^2}$

d)

0

42.

Which of the following is a rational equation?

a)

$\frac{5−2m}{6m−15}$

b)

3

c)

$\frac{5−2m}{6m}−15=m^2$

d)

None of the above

43.

Which of the following is a mixed expression?

a)

$4+\frac{2m}{15}$

b)

x + 3 = 9

c)

Polynomial

44.

Simplify: $\frac{10x-6}{10x-6}$

a)

x

b)

1

c)

10x= 6

d)

$\frac{10x-6}{10x-6}$

45.

Simplify: √20

a)

20

b)

5

c)

2√5

d)

√20

46.

Simplify: √2 * √8

a)

4

b)

0

c)

2

d)

3

47.

Simplify: −5√3 − 3√3

a)

−5√3

b)

3√3

c)

−8√3

d)

Does not exist

48.

Solve: x + 3 = 7

a)

0

b)

2

c)

4

d)

6

49.

Solve: $x^2=49$

a)

x = 7

b)

x = 5

c)

x = 18

d)

x = π

50.

Solve: √x = 5

a)

x

b)

5

c)

25

d)

100

51.

Factor: $9x^2+36x$

a)

$9x(x+4)$

b)

1 + x

c)

13

d)

$x^2+3$

52.

Solve: ℎ(ℎ + 5) = 0

a)

h = 10

b)

{0, -5}

c)

ℎ(ℎ + 5) = 0

d)

ℎ + 5 = 0

53.

Find the product: 6x(2x + 3)

a)

6x + 6

b)

18

c)

$12x^2+18x$

d)

$x^2$

54.

Rewrite: $\frac{\frac{a}{b}}{\frac{c}{d}}$

a)

$\frac{a}{b}\div\frac{c}{d}$

b)

$\frac{a}{b}=\frac{c}{d}$

c)

$a\times b\times c\times d$

d)

a = b

55.

Calculate the distance between point A (−4,−3) and point B (3,4) using the distance formula: $d=\sqrt{(x_2−x_1)^2+(y_2−y_1)^2}$

a)

0

b)

1

c)

√2

d)

√98

56.

Calculate the distance between points C (3,1) and D (3,−4).

a)

0

b)

1

c)

2

d)

5

57.

If x and y are inversely proportional, when x=21, y =11. Find x when y=33

a)

7

b)

63

c)

99

d)

0

58.

Solve for the hypotenuse using Pythagorean Theorem: $a^2+b^2=c^2$

a)

5

b)

10

c)

13

d)

20

59.

What type of triangle has a hypotenuse?

a)

Right Triangle

b)

Triangular Prism

c)

Spanish Triangle

d)

Circle

60.

Did you learn something during Math with Teacher Dana?

a)

Yes!

b)

Maybe...

c)

Absolutely nothing ☹

M2 Math Core Final Exam

Total questions: 60

Worksheet time: 30mins

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