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Math 097 Final Exam Review Questions

Operations on Real Numbers, Order of Operations (Lessons 1-2)
1. Evaluate:
a) | 8
c) 5 4
2 |
3
b) | 6|
3 2
2. Evaluate 5
3
2√3
4
if
1,
| 4|
2.
3. State the property of real numbers being used.
3∙4 ∙5
3∙ 4∙5
4. Perform the indicated operations and simplify.
a) 5 3
b)
4
6
2
5
3
2
4
3

Linear Equations and Inequalities (Lessons 3-5)
5. Solve algebraically.
a) 2
b) 2
3
c) 3 4
5
3
d)

and
10
2 6
5
8
7
1
Equations of Lines and Systems of Equations (Lesson 6-7)
6. Find an equation of the line that is perpendicular to 4
2
6
0 and passes through the
point (-2, 5).
7. Find the slope of the line containing the points (2, -5) and (-1, 7).
8. Find an equation of the horizontal line that passes through the point (4,-3)
9. Solve the system of equations.
2

3
5
4
2
Exponents and Scientific Notation (Lesson 8)
10. Write in scientific notation to 3 decimal place accuracy.
b) 0.000008971254
a) 56432189
c) -31415×10-4
11. Simplify. Only positive exponents should appear in your final answer.
a) 2
c)
16
b) 2
d)
3

Polynomials (Lessons 9-11,19-20)
12. Perform the indicated operations and simplify.
a) (3x  4) 2
b) (t  5) 2  2(t  3)(8t  1)
c) (1  x  x 2 )(1  x  x 2 )
13. Factor completely.
a) y 3  y 2  y  1
b) 3 x 3  27 x
c) z 2  6 z  16
d) 8 x 4  10 x 2  3
e) 4r 2  12 rs  9 s 2
f) 8 x 2  22 xy  12 y 2
h) 36 x 2  60 xy  25 y 2
g) 8 x 3  27
14. Solve for x algebraically.
a) x (6 x  8)  8
c) x 4 x 2 4  2
15. Solve by completing the square.
2
3
6
16. Solve using the quadratic formula.
2
3
6
b) x 4  16  0
d) 3 20
1
11 20
1
6 20
1
0

Rational Expressions (Lessons 12-15)
17. Perform the indicated operation and simplify.
a)
x 2  x  6 x3  x2

x 2  2x x 2  2x  3
b)
4y2  9
2y2  y  3

2 y 2  9 y  18 y 2  5 y  6
c)
3
x

x4 x6
d)
2
3
4

 2
2
ab b
a
e)
1
x
 2
x  x  2 x  5x  4
f)
1
2
3

 2
2
x  1 ( x  1)
x 1
2
x 1  y 1
g)
( x  y ) 1
5

1
x

h)
x

x 1
2
x 1
1
x 1
18. Solve algebraically.
a) x  3 
 2x 2  7x  3
x3
b)
60
60 2


x5 x
x

Rational Exponents and Radical Expressions (Lessons 16-19)
19. Simplify:
a)
c)
 x  x 
3
2
5
6
2 1
5 2 3
b)
4
2 3
d) 18 
14
2
 6 72
20. Solve algebraically.
a) x  2 x  8  0

b)
x  20  7  x
Distance, Midpoint, Circles (Lesson 21)
21. Determine an equation of a circle with centre (2, -3) and radius 4.
22. Determine the centre and radius of the circle given by the equation
x 2  y 2  6x  5 y  5  0 .

Application Problems
23. A rectangular room is 1.5 times as long as it is wide. Its perimeter is 40 m. How wide is the
room?
24. A public swimming pool is going to be constructed on a lot that is 180 feet by 240 feet. The
local building code specifies that a lawn of uniform width and equal in area to the pool
must surround the pool. Find the required width of the lawn.
25. Kelly leaves for school at 8 am and travels eastbound at 50 km/hr. At 8:15 am, her
roommate Tara realizes that Kelly left her term-paper behind and leaves the house to
catch up to Kelly travelling in the same direction at 60 km/hr. At what time will Tara
catch up to Kelly?
26. At 4 pm a man 180 cm tall casts a shadow 144 cm long. At the same time, a tall building
nearby casts a shadow 160 m long. How tall is the building?
27. Billy has $1.45 in pennies, nickels and dimes in his piggy bank. He has three times as
many nickels as dimes. The number of pennies is five more than the number of nickels.
How many nickels does Billy have?