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It’s the Final Countdown
1. Express in simplest form:
x2  4 x  3
a. 2
x  11x  24
x x
b. (7 x 3 ) 2  
2 8
2
ab
c.
 ab2
c
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2. Find LCD, and express each fraction with the LCD
a.
2a  3b a  2b 1
,
,
3a 2b 4ab 2 6ab
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3. Simplify
a.
x 2 x 2  10 x  25

x 5
3x 2
b. a 
c.
2
6
a 1
x2  x  2 x2  4

x
2x
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4. Divide and write your answer as a polynomial or mixed expression.
a.
x 2  15 x  56
x7
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5. Write each ratio in simplest form using common units.
a. 2 ft: 8 in
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6. Solve and check.
a.
y 5 7
5


2 y 3 y 12
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b.
v 1 v  3

v3
v
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7. Percentages – find each number.
a. 20% of 75 is what number?
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b. 66 is 55% of what number?
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c. 48 is what percent of 150?
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8. Word problems – solve.
a. Two printing presses can turn out one day’s newspapers in 6 hours. The faster press
can do the job, operating alone, in 10 hours. How long would it take the slower press,
operating alone, to do the job?
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b. Two numbers are in the ratio 7:8, and their sum is 135. What are the numbers?
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9. Give answers in terms of positive exponents
a. a 6  a 3
b.
 6a
b c
2 3
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3
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c. a 0
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d. 5 2
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102
e.
105
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10. Scientific Notation
a. 3.75 105 (Write without scientific notation.)
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b. .00000047 (Write with scientific notation.)
32 105
c.
16 104
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11. Find the slope and y – intercept of the line determined by the given condition.
a. Equation 3x  6 y  2
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b. Containing the points (2, 4) and (3, 5)
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12. Graph the following lines in parts a - f on the axes on the following page.
a. x = 7 (Is this line horizontal or vertical? What is the slope?)
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b. y = - 2 (Is this line horizontal or vertical? What is the slope?)
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c. 3 x  4 y  12 (What is the slope? What is the y – intercept? Is (3, 5) on this line? Is
this line parallel to y  3x  12 ?)
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d. The line passing through (1, 3) and (-2, 9) (What is the equation? What is the y –
intercept? What is the slope?)
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e. Find the equation of a line in slope-intercept form that is parallel to the line
y = 2x + 8 and which goes through the point (3, -5)
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f. Graph 2 x  y  2
3
10
9
8
7
6
5
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
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9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
For a, b, e
-10
10
9
8
7
6
5
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
For c, d
-10
10
9
8
7
6
5
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
For f
4
4
3
2
1
-2
-1
1
2
-1
-2
13. Find the equation of this line.
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14. Hooke’s Law states that the distance d that a spring is stretched by a hanging
object varies directly as the weight W of the object. If a 6 – kg weight stretches a
particular spring 72 cm, how far will the spring stretch when W = 4 kg?
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15. Find all of the solutions to the following sets of equations.
a.
y  3x  2
9x  3y  6
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c.
2y  x  2
b.
1
x3
2
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y
2 x  5 y  1
3x  y  5
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15.3. Word problem – solve.
a. Pat biked 1 miles in 3 minutes with the wind at his back, and then he returned in 4
minutes riding against the wind. What was the speed of the wind?
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b. Cullen is 20 years younger than Mr. Schlegel. In three years, Mr. Schlegel will be
twice as old as Cullen will be. How old is each now?
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c. How much water must be added to 3 quarts of a 30% acid solution to form a 20%
acid solution?
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16. Express as a fraction in the simplest form
a. 3.27
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17. Find the indicated roots.
a.
484
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b.
169
441
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c.
425m6 n10
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18. Solve:
a. 12 x 2  27  0
b.
2x  3  7
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c. 5 4 x  3  15
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d. 16 x 2  100
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19. Simplify
5 3

8 2
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a.
3
2
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c.
e.
6
 5
ab 2
  3 a 
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g.
3  2 
6 3
12
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b.
d.
5  20  45
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f.
2

3 5 2 3 3

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2
h.
3

12  3

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i. a 7
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j. 4 2  2 5
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20. Rationalize the denominator
5
2 3 1
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a.
8
13
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b.
21. Solve with both the quadratic formula and completing the squares. You will
need to know both methods for the test.
a. y 2  4 y  3  0
b. 2 y 2  12 y  18
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

c. Is 2  3, 2  3 a solution set for x 2  4 x  1 ? (True or False)
22. Simplify completely
a.  168
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23. Consider the parabola f ( x)  2 x 2  4 x  5
a. Find the vertex
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b. Find f (-2)
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10
9
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7
6
5
4
3
2
1
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
-2
-3
-4
-5
-6
-7
-8
-9
c. Graph the parabola.
-10
24. The point (-2, 8) is in which quadrant? (I, II, III, IV)? _________
25. Solve and graph
a. 12  t  4  20
b. 2 4 x  3  3  10
26. Simplify leaving as a single fraction with no negative exponents.
1 1
a.   
x y
3
2
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 4x 2 
b.  3  = __________________
 y 
27. Simplify, leaving in radical form.
2
128x5 y 2  3 = _____________________
Have Fun. Good Luck!
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