Free Printable M3 Sem1 Review

1.

Describe the transformation: (choose all correct answers)

$h\left(x\right)=3\left(x-1\right)^2+5$

a)

Shift 1 unit left

b)

Shift 1 unit right

c)

Shift 5 units up

d)

Shift 5 units down

e)

Stretch by a factor of 3

2.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

3.

What is the degree of this polynomial?

a)

14

b)

5

c)

3

d)

6

4.

What is the name of a polynomial with three terms?

a)

monomial

b)

binomial

c)

trinomial

d)

cubic

5.

Which polynomial expression is written in standard form?

a)

$4x^4-16x^2+12-5x$

b)

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

c)

$7x^5+4x^3-2x^2+18$

6.

What is the leading coefficient of this polynomial?

a)

14

b)

5

c)

3

d)

6

7.

Divide using syntheic division? (x³-3x²-10x+24) ÷ (x+3)

a)

2x²-6x-2

b)

3x²-4x+8

c)

x²+6x+9

d)

x²-6x+8

8.

Divide using syntheic division? (x³-4x²-63x+28) ÷ (x-10)

a)

4x²-6x+28

b)

$1x^2+6x-3-\frac{2}{x-10}$

c)

$x^2-5x+4+\frac{21}{x-10}$

d)

i do not know

9.

4a² - 25

a)

(2a + 5) (2a - 5)

b)

(2a - 5) (2a - 5)

c)

(x + 5) (x - 5)

d)

Can't factor using Diff. of Squares

10.

Factor.
$12x^3+16x^2+21x+28$

a)

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

b)

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

c)

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

d)

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

11.

Factor
64a⁴b + 96ab³ - 8a

a)

8a(8a³b + 12b³ - a)

b)

8ab(8a³ - 12b² - 1)

c)

8a(8a³b - 12b² + 1)

d)

8a(8a³b + 12b³ - 1)

12.

Subtract these polynomials:

(x⁵ + x³) - (6x - x³ + 6x⁵)

a)

-5x⁵ + 2x³ - 6x

b)

7x⁵ - 6x

c)

-5x³ + 2x² - 6x

d)

-5x⁵ - 6x

13.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

14.

Find the product.

(5x + 2) (x²- 3x +6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

15.

Factor:

2x²+ x - 15

a)

(2x-15)(x+1)

b)

2(x-5)(x+3)

c)

(2x-3)(x+5)

d)

(2x-5)(x+3)

16.

Determine the end behavior of the graph of
f(x) = 3x³ + 2x - 5

a)

As x →∞, f(x) →∞.
As x→-∞, f(x) →-∞.

b)

As x →∞, f(x) →∞.
As x→-∞, f(x) →∞.

c)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →∞.

d)

As x →∞, f(x) →-∞.
As x→-∞, f(x) →-∞.

17.

What transformations has the function undergone?

a)

reflect over the y-axis, vertical compression by a factor of 2, vertical down right 5, horizontal shift right 1

b)

reflect over the x-axis, horizontal compression by a factor of 2, left 5, up 1

c)

reflect over the x-axis, vertical stretch by 2, horizontal shift right 5, vertical shift up 1

d)

reflect over the y-axis, horizontal stretch by a factor of -2, horizontal shift right 5, and vertical shift up 1

18.

What are the real and complex zeros of the function?

a)

5,-3i,3i

b)

-5,-3i, 3i

c)

-5,-3,3

d)

-3,20

19.

What are the x-intercepts and y-intercepts of g(x) = x² - 25?

a)

x-intercepts: $\pm13.5$

y-intercept: 25

b)

x-intercepts: $\pm5$

y-intercept: -25

c)

x-intercepts: $\pm5$

y-intercept: 25

d)

x-intercepts: $\pm25$

y-intercept: -25

20.

Is the degree even or odd?

a)

even

b)

odd

21.

Identify the zeros and match the function to the correct graph.

$y=x\left(x-2\right)\left(x+7\right)$

a)

b)

c)

d)

22.

What is the degree of the function graphed?

a)

1

b)

2

c)

3

d)

4

23.

Which equation best matches the graph?

a)

y = (x+2)(x+1)(x-1)(x-3)

b)

y = x(x+2)(x+1)(x-1)(x-3)

c)

y = (x-2)(x-1)(x+1)(x+3)

d)

y = x⁴ - 2x³ - 1x² + 1x + 3

24.

Multiply:

(1 − 2i)(6 + 5i)

a)

16 − 7i

b)

-16 + 7i

c)

-16 − 7i

d)

16 + 7i

25.

Simplify:
(10+ 15i) - (48 - 30i) + 3

a)

61 - 45i

b)

61 - 15i

c)

-35 - 15i

d)

-35 + 45i

26.

Solve: $\frac{x+9}{x-10}=\frac{4}{8}$

a)

-9

b)

-28

c)

9

d)

4

27.

a)

A

b)

B

c)

C

d)

D

28.

Simplify: $\frac{x^2-25}{5x^3}\div\frac{5-x}{15x^5}$

a)

$3x^2\left(x+5\right)$

b)

$-3x^2\left(x+5\right)$

c)

$\frac{\left(x^2-25\right)\left(5-x\right)}{75x^8}$

d)

$\frac{3x^2\left(x+5\right)\left(x-5\right)}{5-x}$

29.

Multiply and Simplify:

$\frac{x+2}{4}\cdot\frac{4x-8}{x-2}$

a)

$-1$

b)

$x+2$

c)

$-\left(x-8\right)$

d)

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

30.

Find the horizontal asymptote.

a)

y = 1

b)

none

c)

y = 0

d)

y = 1/2

31.

Which of the following below would be an extraneous solution to the equation?

a)

$x\ =\ 3$

b)

$x\ =\ 5$

c)

$x\ =\ 1$

d)

$x\ =\ -5$

32.

Perform the indicated operation and simplify: $\frac{x^2+5x-34}{x^2-9x+8}-\frac{10}{x-8}$

a)

$\frac{x^2-5x-44}{\left(x-8\right)\left(x-1\right)}$

b)

$\frac{x^2-5x-24}{\left(x-8\right)\left(x-1\right)}$

c)

$\frac{x+6}{x-1}$

d)

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

33.

Simplify and state the domain:

$\frac{x^2+3x-18}{2x^2+28x+96}$

a)

A $\frac{x-3}{x+8};\ x\ne3,-8$

b)

B $\frac{x-3}{x+8};\ x\ne-6,-8$

c)

$\frac{x-3}{2\left(x+8\right)};\ x\ne3,-8$

d)

$\frac{x-3}{2\left(x+8\right)};\ x\ne-6,-8$

34.

Find the x-value of the hole

$y=\frac{x^2+3x-10}{x^2+11x+30}\$

a)

x=5

b)

x=-5

c)

x=-5,-6

d)

x=-6

35.

What are the x-intercept(s)?

a)

(2/3,0)

b)

(4,0), (-2,0)

c)

(-8,0), (1,0)

d)

(-4,0), (2,0)

36.

What is the vertical asymptote(s)?

a)

x = 2 and x = 5

b)

x = - 2 and x = - 5

c)

x = 3 and x = - 3

d)

x = 0

37.

What are the asymptotes?

a)

x=-2 and y=-1

b)

x=-2 and y=1

c)

x=2 and y=1

d)

x=2 and y = -1

38.

Which of the following has a horizontal asymptote of y = 0?

a)

$y=\frac{2x^3+7x^2+3x}{x^2+4x+4}$

b)

$y=\frac{3}{x^2+x-12}$

c)

$y=\frac{x-4}{2-x}$

d)

they all have a horizontal asymptote y=0

39.

Simplify. Your answer should contain only positive exponents.

$\frac{\left(yx^{\frac{3}{2}}\right)^3}{x^{\frac{5}{6}}y^{\frac{1}{2}}}$

a)

$\frac{x^{\frac{5}{3}}y^{\frac{31}{36}}}{y^2}$

b)

$\frac{y^{\frac{3}{2}}}{x^{\frac{5}{4}}}$

c)

$\frac{x^{\frac{1}{2}}}{y^{\frac{5}{16}}}$

d)

$x^{\frac{11}{3}}y^{\frac{5}{2}}$

40.

Simplify: $\sqrt[3]{250x^5y^2}$

a)

$2xy^2\sqrt[3]{3y^2}$

b)

$5x\sqrt[3]{2x^2y^2}$

c)

$-4x^2\sqrt[3]{6xy}$

d)

$3x^2y\sqrt[3]{4}$

41.

Solve and check your solution(s).

a)

x = 2, 3

b)

x = -2, -3

c)

x = -1, -6

d)

No solution

42.

Rationalize the denominator. Simplify the expression. $\frac{2\ -\sqrt{3}}{4\ +\sqrt{3}}$

a)

$\frac{11\ +6\sqrt{3}}{13}$

b)

$\frac{11\ -6\sqrt{3}}{13}$

c)

$\frac{-11\ +\sqrt{3}}{13}$

d)

$\frac{-11\ +2\sqrt{3}}{13}$

M3 Sem1 Review

Total questions: 42

Worksheet time: 3hrs 42mins

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