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Intermediate Algebra Final Exam Name ___________________
- Express the set in roster form.
} 3
{ x | x I and x
- Consider the following set of numbers.
a. List the rational numbers.
b. List the irrational numbers.
- Arrange the numbers from smallest to biggest.
( 9 )^3 9 ( 32 )
- Simplify:
- Simplify:
2 2 2 5 3 ( 2 7 5 )
- Simplify:
3 [( 144 6 ) ( 28 )]
[( 4 ( 3 5 )) 7 ]
2
2
8.^ Simplify:
- Evaluate for x = 25 and y = 36 :
( x y )^2
- Simplify. 3 2 2
3 2 3 3
1 2
- Multiply.
( 2 x^7^ yz^5 )^3 ( 4 x^6 y^4 z )
- Simplify. 3 4 5
4 3 8
16
a bc
ab c
Convert the following to standard form.
698 104
Simplify.
9
6 7
^
- Simplify. 4 x 7 ( 9 y 3 ) 2 ( y 3 x ) 4 y
- Simplify.
^
x x
- Solve for x. 3 ( 6 4 x ) 4 { 5 x [ 6 x ( 4 x ( 3 x 2 ))]}
- Solve for x.
x x
- Solve for y.
2 ) 6
7 ( y y
- Solve ( )
for .
- A yield sign on a particular road has an area of 150 in². What is the length of the base if the height is 12 inches? Remember: A bh 2
- You are choosing between two long-distance telephone plans. One plan has a monthly fee of $25 with a charge of 2 5 ¢ per minute. The other plan has a monthly fee of $10 with a charge of 30¢ per minute. For how many minutes of long-distance calls will the costs for the two plans be the same?
- If French roast coffee sells for $8.50 per pound and vanilla hazelnut coffee sells for $12.50 per pound, how many pounds of vanilla hazelnut should you mix with 9 pounds of French roast to get a blend that is sold for $11 per pound?
- Determine if the following graphs represent a function. It does represent a function, then state the domain.
- Graph.
2 x 5 y 10
- Write the equation of the line.
- Write an equation of the line that goes through the point (4, -1) and perpendicular to the line 2 x 3 y 9.
x
y
- The population of the United States, in millions, in 1980 was 226.5 million, and in 1990 was 250 million. This information is shown in the following graph.
a. Determine a linear function that can be used to estimate the population of the United States, P , in millions, in terms of t years after 1960.
b. Use the function determined in part a) to determine the population of the United States in
c. Use the function determined in part a) to estimate the year at which the population of the United States will be 500 million.
- Let 3 2
f ( x ) x^2 x and g ( x ) 2 x 5
a. Find ( f g )( x )
b. Find ( f g )( 3 )
c. Find ( f g )( 4 )
- Graph 4 x 2 y 2
x
y
- Jesse, Maria and Charles went to the local craft store to purchase supplies for making decorations for the upcoming dance at the high school. Jesse purchased three sheets of craft paper, four boxes of markers and five glue sticks. His bill, before taxes was $24.40. Maria spent $30.40 when she bought six sheets of craft paper, five boxes of markers and two glue sticks. Charles, purchases totaled $13. when he bought three sheets of craft paper, two boxes of markers and one glue stick. Determine the unit cost of each item? Let ______ = _______________________________________ Let ______ = _______________________________________ Let ______ = _______________________________________
Equations:
Solve the following system of linear inequalities by graphing.
2
2 3
x y
x
- Indicate whether monomial, binomial, or trinomial, and state the degree:
xy z xyz
Type of polynomial _________
Degree of polynomial ________
- Subtract: ) 3
( 6 x^2 x x^2 x
- Multiply:
( 2 x^2 3 y )( 4 x^4 6 x^2 y 9 y^2 )
- Divide:
3 2
4 3 3 2 2 4 3
8
xy z
xyz xyz x yz
x
y
- Divide using long division: 47. Divide using synthetic division:
x
x x x x
- Factor.
a^2 b^2 4 b 4
- Factor.
2 ( x 2 )^2 7 ( x 2 ) 3
- Factor.
81 x^4 ( x 5 )( x 5 )
- Factor. 1 27 x^3 y^3
- Solve for r.
5 r 2 14 r 3
- Solve for k.
( k 7 )^2 k^2 ( k 2 )^2
(4 x^4^ 6 x^3^ 3 x 2) (2 x^2 1)
- You throw a ball straight up from a rooftop 160 feet high with an initial speed of 48 feet per second.
The function h ( t ) 16 t^2 48 t 160 describes the ball’s height above the ground, h ( t ), in feet, t seconds after you threw it. a. Find the time it takes for the ball to hit the ground.
b. Find the time it takes the ball to be at a height of 192 feet.
- A 15-ft ladder is leaning against a building. The ladder reaches up the wall 3 feet more than the distance of the ground between the base of the ladder to the building. Find the length the ladder reaches up the wall and the distance of the ground between the base of the ladder to the building.
15 feet
Answers:
a.
, 6 , 0 , 0. 7 , 4. 9 , 12 3
b. , 8
32 x^27 y^7 z^16
24
9 15 8 c
ab
10 x 65 y 21
x
x 2
x 26
No Solution
b 25 inches
300 minutes
15 lbs of Vanilla Hazelnut
½ hour
(3, 5]
( , 5 ][ 3 ,)
y 1 , y 2
a. function { x | x } b. function { x | x } c. not a function
y x
y x
