Olympic College Math 94 Final Exam Practice
Math 94 Final Exam Practice
1.
Evaluate the following. Reduce any fractions in your answers to lowest terms.
Show all relevant working to get full credit.
(a)
144 20

15 48
(b)
7 3

4 10
(c)
– 40 – (– 25) + 17
(d)
(2)4(– 5)2
(e)  5
(f)

10
3
 12  16
3( 2)  8
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Olympic College Math 94 Final Exam Practice
2. Evaluate each expression for the given value of the variable or variables:
2
(a) 2 x  x , for x  5
(b) x 2  y 2 , for x  3, y  2
3.
Solve the following equations.
(a)
14x + 7 = 3x - 4
(b)
8x
 12
3
(c)
2x – 5(x+3) = 3x – 6
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Olympic College Math 94 Final Exam Practice
4.
In a scale drawing, a building 80 feet tall is drawn 4 inches high. The building next to it is
drawn 2. 5 inches high. How tall is the second building?
5.
A Geology book costs $14 more than a Math book. If the two books together cost $96, how
much does each book cost?
6.
The length of a rectangle is 1 foot less than twice its width. If its perimeter is 70 feet, find its
dimensions.
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Olympic College Math 94 Final Exam Practice
7.
A rocket is launched at noon and travels at 12,000 miles per hour. One hour later, a second
rocket is launched in the same direction, traveling at 14,400 miles per hour. How long after
the first rocket is launched will the rockets be the same distance from Earth?
8.
Change the subject to the indicated variable.
(a)
(b)
8y – 3x = 6
y  5hx 3
Solve for y.
Solve for h.
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Olympic College Math 94 Final Exam Practice
9. Find the value of y that makes each ordered pair a solution to the equation: y = 4x – 3
 1 
(a)   , y
 2 
(b) (1,y)
y
10.
Graph the line y = 3x + 1
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
-3
-4
-5
11. Find the slope and y-intercept of the line 4x – 2y = 8
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Olympic College Math 94 Final Exam Practice
12. Write the equation of the line shown in the graph below.
y
5
4
3
2
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
-3
-4
-5
13. Find the equation of each line with a Slope = 
1
, passing through the point (5,3)
5
14. Find the equation of each line passing through the points (–1,2) and (1,4)
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Olympic College Math 94 Final Exam Practice
15.
A person purchased a house for $250,000, and expect its value to appreciate by $2,500
per year. Write an equation for the value of the house, V, in terms of years, t.
Problems 16 & 17, refer to this illustration
of the cost of building a certain type of
patio, in terms of its area.
$2,000
16. What the cost of building a 300
Square foot patio?
Cost
$1,500
$1,000
$500
$0
0
100
200
300
400
500
Area (square feet)
17 Write an equation for the cost, C, in terms of area, a.
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Olympic College Math 94 Final Exam Practice
18.
Simplify the following expressions (The answers are to have only positive exponents.):
 3x 
(a) 

 4x2 
(b)
(c)
19.
2
y 2
y3
x 1
x 2
Simplify the following expressions (The answers are to have only positive exponents.):
(a)  3x 4 y 3
(b)
10 x 2
5x  3 y
 4 x 3 y 109 z 34
(c) 
7
9
 245 x y12 z
20




0
(a) Write the following in scientific notation: 108,000
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Olympic College Math 94 Final Exam Practice
(b) Write the following in standard notation: 6.4 X 10-2
21. Express each polynomial in descending order. Give the degree of each polynomial:
(a) 6x – 5 – 2x3
(b) 8 – y3
22. Simplify: (a)
(b)
23.
(6x3 – 5x) + (3x3 – 4x2)
(6x2 - 5x + 3) – (x2 + 8x – 1)
Find the products:
(a)
–2x2(3x2 – 4x + 2)
(b)
(4x + 3)(3x – 5)
(c)
(3x – 2y)(2x + y)
24. Simplify:
6 x 4  12 x3  15 x 2
3x 2
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Olympic College Math 94 Final Exam Practice
Solutions
1.
Evaluate the following. Reduce any fractions in your answers to lowest terms.
Show all relevant working to get full credit.
(a)
(b)
48 5
240
144 20

= 
=
15 48
5 12
60
7 3

=
4 10
35
6
+
20
20
(d) – 40 – (– 25) + 17 =
(d) (2)4(– 5)2
(e)  5
(f)
2.

=
4
=
41
1
= 2
20
20
– 40 + 25 + 17 =
(16)(25) =
4
68
=
(various ways to get this answer)
2
400
5 3
15

=
1 10
10
10
=
3
 12  16
=
3( 2)  8
=
4
=
2
=
3
2
=
1
1
2
2
Evaluate each expression for the given value of the variable or variables:
(b) 2 x  x 2 , for x  5
2x  x 2 =
2(–5) + (–5)2 = – 10 + 25 = 15
(b) x 2  y 2 , for x  3, y  2
x 2  y 2 = (3) 2  2 2 = 9 – 4
3.
= 5
Solve the following equations.
(a)
14x + 7
14x
11x
=
=
=
3x – 4
3x – 11
– 11
subtract 7 from both sides
subtract 3x from both sides
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Olympic College Math 94 Final Exam Practice
3.(b)
(c)
4.
x
=
8x
3
=
12
8x
=
36
x
=
x
=
–1
divide both sides by 11
multiply both sides by 3
36
8
1
4
2
2x – 5(x+3)
2x – 5x – 15
– 3x – 15
– 15
–9
9
6
1
1
2
divide both sides by 8
simplify
1
36 9
= =4
2
2
8
=
=
=
=
=
3x – 6
3x – 6
3x – 6
6x – 6
6x
multiply out the brackets – 5(x+3) = – 5x – 15
collect like terms 2x – 5x = – 3x
add 3x to both sides
add 6 to both sides
=
x
divide both sides by 6
=
x
simplify
3
1
9
=
= 1
2
2
6
In a scale drawing, a building 80 feet tall is drawn 4 inches high. The building next to it is
drawn 2.5 inches high. How tall is the second building?
4 in
80 ft
2.5 in
4
80
=
2 .5
x
4x
=
200
x
=
50 ft
x ft
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Olympic College Math 94 Final Exam Practice
5.
A Geology book costs $14 more than a Math book. If the two books together cost $96, how
much does each book cost?
Math book
=
Geology book =
total cost
x + x +14
2x + 14
2x
x
=
=
=
=
=
x
x + 14
96
96
96
82
41
subtract 14 from both sides
divide both sides by 2
Math book cost = x = $41
6.
the Geology book cost = x + 14 = 41 + 14 = $55
The length of a rectangle is 1 foot less than twice its width. If its perimeter is 70 feet, find its
dimensions.
Width =
w and Length=
2w – 1
Perimeter =
70
2w
+
2(2w
–
1)
=
70
w
2w + 4w – 2 =
70
6w – 2 =
70
6w
=
72
add 2 to both sides
2w – 1
w
=
12
divide both sides by 4
Width of rectangle = w = 12 feet and length of rectangle = 2w – 1 = 2(12) – 1= 23 feet
7.
A rocket is launched at noon and travels at 12,000 miles per hour. One hour later, a second
rocket is launched in the same direction, traveling at 14,400 miles per hour. How long after the
first rocket is launched will the rockets be the same distance from Earth?
First rockets speed
=
12000 mph
First rockets time
=
x hours
Distance traveled by first rocket
=
Speed  time =
12000x
Second rockets speed =
second rockets time =
14400 mph
(x – 1) hours …….. since it left one hour after the first
Distance traveled by second rocket
= Speed  time =
Both rockets will meet when
Distance traveled by first rocket
12000x
–2400x
=
=
=
14400(x – 1) = 14400x – 14400
Distance traveled by second rocket
14400x – 14400
– 14400
subtract 14400x from both sides
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Olympic College Math 94 Final Exam Practice
8.
(a)
(b)
x
=
6
divide both sides by – 2400
So it will take 6 hours before the rockets catch up with each other.
Change the subject to the indicated variable.
8y – 3x
8y
=
=
6
6 + 3x
6  3x
8
Solve for y.
add 3x to both sides
y
=
y
=
5hx3
Solve for h.
=
h
Divide both sides by 5x3
y
5x 3
divide both sides by 8
9. Find the value of y that makes each ordered pair a solution to the equation: y = 4x – 3
10.
 1 
(a)   , y
 2 
y =
4x – 3 = 4( 
(b) (1,y)
y=
4x – 3 = 4(1) – 3 = 4 – 3
1
)–3 =–2–3=–5
2
= 1
y
Graph the line y = 3x + 1
5
For x = 0
y = 3(0) + 1 = 1 point(0,1)
4
3
For x = 1
For x = 2
2
y = 3(1) + 1 = 4 point(1,4)
y = 3(2) + 1 = 1 point(2,7)
1
-5 -4 -3 -2 -1 0
-1
x
1
2
3
4
5
-2
-3
-4
-5
11. Find the slope and y-intercept of the line 4x – 2y = 8
4x – 2y
– 2y =
y=
y=
=
8
– 4x + 8
 4x  8
2
2x – 4
subtract 4x from both sides
divide both sides by – 2
divide – 4x by – 2 and divide +8 by – 2
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Olympic College Math 94 Final Exam Practice
The slope of this line is 2 and the y-intercept is at (0, – 4)
12. Write the equation of the line shown in the graph below.
y
5
Slope =
rise
run
=
4
3
2
3
2
1
y-intercept = (0,– 3)
Equation of this line is
y=
-5 -4 -3 -2 -1 0
-1
3
x–3
2
x
1
2
3
4
5
-2
-3
-4
-5
1
13. Find the equation of each line with a Slope =  , passing through the point (5,3)
5
1
The slope = m = 
the point (5,3) = (x1 , y1 )
5
Use the equation y – y1 =
m(x – x1)
1
 (x – 5)
y–3 =
5
1
 x+1
y–3 =
5
1
 x+4
y
=
add 3 to both sides
5
14. Find the equation of each line passing through the points (–1,2) and (1,4)
the point (–1,2) = (x1 , y1 ) and the point (1,4) = (x2 , y2 )
Slope =
y 2  y1
=
x 2  x1
42
=
1  ( 1)
2
=
2
1
The slope = m = 1
and the point (–1,2) = (x1 , y1 )
Use the equation
y – y1
y–2
y–2
y–2
=
=
=
=
m(x – x1)
1 (x – (–1))
1(x + 1)
x+1
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Olympic College Math 94 Final Exam Practice
y
=
x+3
add 2 to both sides
15. A person purchased a house for $250,000, and expect its value to appreciate by $2,500
per year. Write an equation for the value of the house, V, in terms of years, t.
Value of house
V
=
=
250,000 + 2500  number of years
250,000 + 2500t
Problems 16 & 17, refer to this illustration
of the cost of building a certain type of
patio, in terms of its area.
$2,000
Cost
$1,500
16. What the cost of building a 300
Square foot patio?
$1,000
$500
About $12,500
$0
0
100
200
300
400
500
Area (square feet)
17 Write an equation for the cost, C, in terms of area, a.
Slope of line =
rise
run
=
1000
=
400
Cost =
5
a + 500
2
5
2
y-intercept = (0,500)
Equation of this line is
18.
Simplify the following expressions (The answers are to have only positive exponents.):
 3x 
(a) 

 4x2 
(b)
(c)
y 2
y
3
x 1
x 2
2
=
9x 2
=
16 x 4
9 x 2 4
=
16
=
y– 2 – 3 =
y–5
=
=
x– 1 – (-2)=
x1
=
9 x 2
16
=
9
16 x 2
1
y5
x
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Olympic College Math 94 Final Exam Practice
19.
Simplify the following expressions (The answers are to have only positive exponents.):
 3y 3
x4
(a)  3x 4 y 3 =
(b)
10 x 2
5x  3 y
 4 x 3 y 109 z 34
(c) 
7
9
 245 x y12 z
20
2 x 2 ( 3)
y
=
=
2x 5
y
0

 =


1
(a) Write the following in scientific notation: 108,000
=
1.8 x 105
(b) Write the following in standard notation: 6.4 x 10-2
=
0.064
21. Express each polynomial in descending order. Give the degree of each polynomial:
(a) 6x – 5 – 2x3
=
– 2x3 + 6x – 5
Degree = 3
(b) 8 – y3 = – y3 + 8
22. Simplify: (a)
Degree = 3
(6x3 – 5x) + (3x3 – 4x2) =
=
=
(b) (6x2 - 5x + 3) – (x2 + 8x – 1)
23.
6x3 – 5x + 3x3 – 4x2
6x3 + 3x3 – 4x2 – 5x
9x3 – 4x2 – 5x
=
=
=
6x2 – 5x + 3 – x2 – 8x + 1
6x2 – x2 – 5x – 8x + 3 + 1
5x2 – 13x + 4
Find the products:
(a)
–2x2(3x2 – 4x + 2)
=
– 6x4 + 8x3 – 4x2
(b)
(4x + 3)(3x – 5)
=
12x2 – 20x + 9x – 15 =
12x2 – 11x – 15
(c)
(3x – 2y)(2x + y)
6x2 + 3xy – 4xy – 2y2 =
6x2 – xy – 2y2
=
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Olympic College Math 94 Final Exam Practice
24.
Simplify:
6 x 4  12 x3  15 x 2
=
3x 2
6 x 4 12 x 3 15 x 2


= 2x2 – 4x + 5
2
2
2
3x
3x
3x
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