Free Printable Alg. 2: Semester 1 Practice Final Exam

1.

Determine the solution to the following inequality:
$7<2x+3\le9$

a)

$2<x\le3$

b)

$5\le x<6$

c)

$2<x\le6$

d)

$3\le x<2$

2.

Determine which compound inequality is shown by the following graph:

a)

$-5<x\le2$

b)

$x>-5\ \ or\ x\le2$

c)

$-5\le x\le2$

d)

$-5\le x<2$

3.

Determine which inequality represents the solution to the following:

$7x+2\le-x+18$

a)

$x\le2$

b)

$x\le-2$

c)

$x\ge3$

d)

$x\le3$

4.

Solve! $\left|2x+3\right|+8=23$

a)

$x=-9\ \ \&\ x=6$

b)

$x=6$

c)

$x=9\ \&\ x=6$

d)

$x=-9\ \&\ x=-6$

5.

Solve! $2\left(x-4\right)+3\left(x+5\right)=2x-2$

a)

-3

b)

2

c)

5

d)

-4

6.

Solve for y! $3x-2y=16$

a)

$y=\frac{3}{2}x-8$

b)

$y=-\frac{3}{2}x-8$

c)

$y=\frac{3}{2}x+8$

d)

$y=-3x+8$

7.

Solve! $\left|3n-6\right|+8\le17$

a)

$-1\le n\le5$

b)

$n\le-1\ \ or\ \ n\ge5$

c)

$n\le5$

d)

$-\frac{19}{3}\le n\le5$

8.

Line 1 passes through the points (1, 4) and (-2, 5). Line 2 passes through the points (4, 3) and (5, 6). After calculating the slopes, what can be said is true about lines 1 and 2?

a)

They are perpendicular

b)

They are parallel

c)

They both have negative slopes

d)

They both have positive slopes

9.

What is the vertex?

$y=3\left|x-2\right|+4$

a)

(2, 4)

b)

(-6, 0)

c)

(-2, 4)

d)

(-2, -4)

10.

Which set of points would produce a line with the slope of $-\frac{3}{2}$ ?

a)

(5, 7) and (7,4)

b)

(3,2) and (1,-3)

c)

(-3,0) and (0,-2)

d)

(5,2) and (8,0)

11.

Determine the equation of a line that passes through the point (-3,6) and is PERPENDICULAR to $y=\frac{1}{3}x+\frac{4}{3}$ .

a)

$y=-\frac{1}{3}x-\frac{4}{3}$

b)

$y=-3x+\frac{4}{3}$

c)

$y=-3x-3$

d)

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

12.

Write the equation.

a)

f\left(x\right)=\left|x+3\right|-4

b)

$f\left(x\right)=\left|x+4\right|-3$

c)

$f\left(x\right)=-\left|x-3\right|-4$

d)

$f\left(x\right)=-\left|x-4\right|+3$

13.

Determine the x-intercept, the y-intercept, and the slope of the given equation:

$9x-6y=18$

a)

x-intercept: (2, 0), y-intercept: (0, -3), slope : $\frac{3}{2}$

b)

x-intercept: (-2, 0), y-intercept: (0, 3), slope : $-\frac{2}{3}$

c)

x-intercept: (-3, 0), y-intercept: (0, 2), slope : $-\frac{3}{2}$

d)

x-intercept: (3, 0), y-intercept: (0, -2), slope : $\frac{2}{3}$

14.

Write the equation of the line that passes through the point (4, -7) and is parallel to $y=-3x+9$ .

a)

$y=-3x+5$

b)

$y=\frac{1}{3}x-\frac{25}{3}$

c)

$y=-3x-5$

d)

$y=\frac{1}{3}x+\frac{25}{3}$

15.

If elimination is used to solve this system of equations, what is the result after the first step?
$x+y=6$

x-y=2

a)

$2x=8$

b)

$2y=8$

c)

$x=8$

d)

$x-y=8$

16.

Determine the solution of the following system of equations; then calculate the value of x + y:
$3x+2y=-13$

3x+4y=1

a)

-2

b)

-6

c)

2

d)

4

17.

Determine the solution for the following system of equations:
$y=-\frac{3}{2}x-1$

y=-\frac{1}{2}x+1

a)

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

b)

$\left(-2,-4\right)$

c)

$\left(2,5\right)$

d)

$\left(-3,2\right)$

18.

Determine the solution of the following system of equations; then calculate the value of x ⋅ y:
$2x+3y=-12$

x=-3y-18

a)

-48

b)

14

c)

-12

d)

9

19.

At an NFL football game, four hot dogs and two sodas cost $22.50, while three hot dogs and four sodas cost $25.00. Find the price of a hot dog and the price of a soda at the game. Then determine the total cost if a spectator purchases 2 hot dogs and 2 sodas.

a)

$14.50

b)

$13.25

c)

$16.50

d)

$15.75

20.

For which equation is the axis of symmetry x = 5?

a)

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

b)

$f\left(x\right)=x^2-10x+7$

c)

$f\left(x\right)=x^2+10x-3$

d)

$f\left(x\right)=x^2+5x+2$

21.

Identify the vertex.

$y=2\left(x-4\right)^2+6$

a)

(4,6)

b)

(6,4)

c)

(-4,-6)

d)

(-4,6)

22.

$Y=x^2-5x-24$

a)

{-3,8}

b)

{-8, 3}

c)

{5, 24}

d)

{-6, 4}

23.

Find the x-value of the function where the minimum value occurs.
$y=x^2+5x+6$
Hint: Find the axis of symmetry.

a)

$-\frac{5}{2}$

b)

$-5$

c)

$-3$

d)

$-2$

24.

Factor completely! $8x^2+28x+12$

a)

$4\left(x+3\right)\left(2x+1\right)$

b)

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

c)

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

d)

$4\left(x+1\right)\left(x+6\right)$

25.

Solve! $w^2+9w=0$

a)

w={-9, 0}

b)

w = {-9, 3}

c)

w = {0, 9}

d)

w = {1, 9}

26.

Solve! $y^2+3=-24$

a)

$\pm3\sqrt{3}$

b)

$\pm3i\sqrt{3}$

c)

$\pm6i\sqrt{3}$

d)

$\pm9i\sqrt{3}$

27.

Determine the y-intercept & the x-intercepts:
$f\left(x\right)=2x^2+x-6$

a)

y-intercept: -6, x-intercept: $\frac{3}{2}$ & -2

b)

y-intercept: -6, x-intercept: $-\frac{3}{2}$ & 2

c)

y-intercept: -6, x-intercept: $\frac{3}{2}$ & 2

d)

y-intercept: -6, x-intercept: $-\frac{3}{2}$ & -2

28.

Multiply! $\left(7-i\right)\left(2+3i\right)$

a)

$17+19i$

b)

$11+23i$

c)

$24-16i$

d)

$14-24i$

29.

A normal distribution of data has a mean of 85 and a standard deviation of 4, determine P(x < 89)

a)

84%

b)

34%

c)

16%

d)

95.5%

30.

In a certain region in California, the average backyard swimming pool has about 540 gallons. The amount varies and is normally distributed with a standard deviation of 35 gallons. Determine the z-score for a pool with 550 gallons and the probability that a pool will have fewer than 550 gallons.

a)

z-score = .29; probability = .6141

b)

z-score = .29; probability = .6347

c)

z-score = .58; probability = .5824

d)

z-score = .37; probability = .4291

31.

In a certain region in California, the average backyard swimming pool has about 540 gallons. The amount varies and is normally distributed with a standard deviation of 35 gallons. If a real estate company is evaluating at 1,500 homes, about how many of those homes would have a pool with fewer than 550 gallons? Round your answer to the nearest whole number.

a)

921

b)

837

c)

542

d)

952

32.

Find the value of

f\left(-2\right)

.

a)

2

b)

-7

c)

6

d)

-3

33.

Find the value of $f\left(3\right)$

a)

2

b)

7

c)

-2

d)

-3

34.

Find the value of $f\left(8\right)$

a)

3

b)

2

c)

12

d)

-3

35.

Match the graph with the equation:

$y=3x+3$

a)

b)

c)

36.

Match the graph with the equation:

$5x+2y+6=0$

a)

b)

c)

37.

Match the graph with the equation:

$12x-8y=-24$

a)

b)

c)

38.

Match.

a)

b)

c)

39.

Match.

a)

b)

c)

40.

Match.

a)

b)

c)

41.

Match:

$y=\left|x+3\right|$

a)

b)

c)

d)

42.

Match:

$y=\left|x-3\right|$

a)

b)

c)

d)

43.

Match:

$y=\left|x\right|+3$

a)

b)

c)

d)

44.

Match:

$y=\left|x\right|-3$

a)

b)

c)

d)

45.

Match!

a)

b)

c)

46.

Match!

a)

b)

c)

47.

Match!

a)

b)

c)

48.

Match:

$f\left(x\right)=2x^2+8x-2$

a)

b)

c)

49.

Match:

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

a)

b)

c)

50.

Match:

$f\left(x\right)=\left(x-2\right)\left(x+4\right)$

a)

b)

c)

Alg. 2: Semester 1 Practice Final Exam

Total questions: 50

Worksheet time: 25mins

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