Free Printable PCM review Day 3

1.

Simplify

a)

(x-9)/(x+9)

b)

1/(x-9)

c)

(x+9)

d)

1/(x+9)

2.

Which factor cancels out when you simplify this rational expression.

a)

x + 2

b)

x - 2

c)

x + 6

d)

Nothing cancels out

3.

Simplify as much as possible.

a)

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

b)

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

c)

$-\frac{1}{3}$

d)

Cannot simplify

4.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

5.

Factor the expression: 21z² - 70z + 49

a)

7(3z - 7)(z - 1)

b)

7(3z + 7)(z + 1)

c)

7(3z - 7)(z + 1)

d)

7(3z + 7)(z - 1)

6.

Factor the expression: 10v² + 11v - 8

a)

(5v + 8)(2v + 1)

b)

(v + 8)(v - 1)

c)

(5v + 8)(2v - 1)

d)

(10v - 8)(v + 1)

7.

x² - 16

a)

(x + 4) (x - 4)

b)

(x + 8) (x - 2)

c)

(x + 4)²

d)

x + 4(x - 4)

8.

$b^2+8b-33=0$

a)

$\left\{8,-33\right\}$

b)

$\left\{3,-11\right\}$

c)

$\left\{3,11\right\}$

d)

$\left\{-11,-3\right\}$

9.

$x^2-100=0$

a)

$\left\{25,4\right\}$

b)

$\left\{-50,2\right\}$

c)

$\left\{-10,10\right\}$

d)

$\left\{0,100\right\}$

10.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

11.

Which graph is not a function?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

12.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D:{0, 1, 2, -4}
R:{1, -3, -4}

c)

D:{0, 1, 2, 3, 4}
R:{1, -3, -4}

13.

What is the RANGE?

a)

[4, ∞)

b)

(-∞, 4]

c)

$\left(-\infty,\infty\right)$

d)

[-1, 5]

14.

What is the DOMAIN?

a)

[4, ∞)

b)

(-∞, 4)

c)

$\left(-\infty,\infty\right)$

d)

[-1, 5]

15.

What is/ are the x-intercepts?

a)

x=1

b)

x=1, x=-3

c)

x=-3

d)

x=3

16.

What is/ are the y-intercepts?

a)

y=1

b)

y=1, -3

c)

y=-3

d)

y=3

17.

$Find\ \left(f+g\right)\left(n\right)$

$f\left(n\right)=x^2+1$
$g\left(n\right)=2x-5$

a)

x²-2x+6

b)

-x²+2x+4

c)

-x²-2x-6

d)

x²-2x-4

18.

Given
f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

a)

11x² - 1

b)

5x⁴ + 6x² - 1

c)

5x² + 6x - 1

d)

5x² + 8x - 1

19.

What is f(2)?

a)

-4

b)

8

c)

0

d)

5

20.

What is the value of f(-5)?

a)

-2

b)

2

c)

4

d)

0

21.

$Find\ \left(\frac{f}{g}\right)\left(n\right)$

$f\left(n\right)=x^2+1$
$g\left(n\right)=2x-5$

a)

$\frac{x^2+1}{2x-5}$

b)

$\frac{2x-5}{x^2+1}$

c)

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

d)

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

22.

$Find\ \left(\frac{f}{g}\right)\left(-2\right)$

$f\left(n\right)=x^2+1$
$g\left(n\right)=2x-5$

a)

$\frac{1}{3}$

b)

$-4$

c)

$-\frac{5}{9}$

d)

$undefined$

23.

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

$g\left(x\right)=x+5$

Evaluate\ \left(\frac{g}{f}\right)\left(-2\right)

a)

$\frac{11}{3}$

b)

$\frac{3}{11}$

c)

1

d)

$\frac{7}{3}$

24.

2√18a⁶b²

a)

3a³b√2

b)

6a³b²√2

c)

6a³b√2

d)

2a³b√2

25.

$\left(10-3\sqrt{2}\right)\left(10+3\sqrt{2}\right)$

a)

$82-\sqrt{2}$

b)

$20-6\sqrt{2}$

c)

$100-60\sqrt{2}$

d)

82

26.

Simplify.

a)

y²z¹⁰√xy

b)

20yz√xy

c)

xy²z¹⁰√y

d)

yz⁶√xy²z²

27.

Simplify:

2\sqrt{6}\cdot\sqrt{12}\cdot4\sqrt{10}

a)

$48\sqrt{20}$

b)

$16\sqrt{360}$

c)

$8\sqrt{720}$

d)

$96\sqrt{5}$

28.

Simplify:

\sqrt{72a^5b^8}

a)

$6ab\sqrt{2ab}$

b)

$6a^2b^4\sqrt{2a}$

c)

$3a^2b^4\sqrt{8a}$

d)

$6a^4b^8\sqrt{2a}$

29.

$\left(3-4\sqrt{10}\right)\left(\sqrt{5}+2\sqrt{3}\right)$

a)

$3\sqrt{5}+6\sqrt{3}-20\sqrt{2}-8\sqrt{30}$

b)

$\sqrt{15}+18-4\sqrt{50}-8\sqrt{30}$

c)

$-3\sqrt{88}$

d)

$3\sqrt{5}+6\sqrt{3}-4\sqrt{50}-8\sqrt{30}$

30.

a)

1

b)

43

c)

8

d)

55

31.

Solve using the square root property:
$\left(x+5\right)^2=18$

a)

$\left\{-5\pm3\sqrt{2}\right\}$

b)

$\left\{-5\pm3\sqrt{6}\right\}$

c)

$\left\{3\sqrt{2}\pm5\right\}$

d)

$\pm3\sqrt{2}$

32.

Solve using the quadratic formula
$x^2-4x-20=0$

a)

$x=\left\{-2\pm6\sqrt{2}\right\}$

b)

$x=\left\{2\pm6\sqrt{2}\right\}$

c)

$x=\left\{2\pm2\sqrt{6}\right\}$

d)

$x=\left\{-2\pm2\sqrt{6}\right\}$

33.

Solve using the quadratic formula.
$x^2-8x-14=0$

a)

$x=\left\{4\pm\sqrt{30}\right\}$

b)

$x=\left\{30\pm\sqrt{4}\right\}$

c)

$x=\left\{4+\sqrt{30}\right\}$

d)

$x=\left\{-4+\sqrt{30}\right\}$

34.

Rewrite in exponential form:

log₃(9)=2.

a)

3⁹=2

b)

3²=9

c)

x²=9

d)

3^x=2

35.

Write in logarithm form
$6^{-3}=\frac{1}{216}$

a)

$\log_6\ -3=\frac{1}{216}$

b)

$\log_{-3}\ 6=\frac{1}{216}$

c)

$\log_6\ \frac{1}{216}=-3$

d)

$\log_{\frac{1}{216}}\ 6=-3$

36.

Rewrite in exponential form: $\log_4\ \frac{1}{64}=-3$

a)

$\left(\frac{1}{64}\right)^{-3}=4$

b)

$4^{\frac{1}{64}}=-3$

c)

$\left(-3\right)^4=\frac{1}{64}$

d)

$4^{-3}=\frac{1}{64}$

37.

Rewrite in log form: $8^{-3}=\frac{1}{512}$

a)

$\log_8\left(-3\right)=\frac{1}{512}$

b)

$\log_8\ \frac{1}{512}=-3$

c)

$\log_{-3}8=\frac{1}{512}$

d)

$\log_{\frac{1}{512}}8=-3$

38.

Solve for x using the same base method.
3^x-20= 27

a)

17

b)

27

c)

-7

d)

23

39.

Solve: 2^x = 4^x+1

a)

-2

b)

2

c)

-3

d)

3

40.

Write the equation of the graph.

a)

f(x) = 5^x+ 2

b)

f(x) = 3^x - 2

c)

f(x) = 3^x + 2

d)

f(x) = -3^x +2

41.

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

a)

1 foot

b)

5 feet

c)

7 feet

d)

8 feet

e)

12 feet

42.

The number of bacteria in a refrigerated food is given by $N\left(T\right)=.1T^2-.4T+6$ where T is the temperature of the food in Celsius. At what temperature will the number of bacteria be minimal?

a)

$2.2$

b)

0

c)

.4

d)

2

PCM review Day 3

Total questions: 42

Worksheet time: 4hrs 30mins

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