Download Review for MAT111 Final

Review for MAT007 Final
Know how to do all of the following problems.
Evaluate the following expressions
4  25   5  2
4  2  3  8
43  2   3 2
2
82  62
Find P (3) if P( x)  3x 2  4 x  10 .
Simplify the following expressions (answer with positive exponents only)
2x
3
y
4
6x
5
y
7
 6 x 2 y 2

 3 xy

2 y  13 y  7

3xy 2 5 x 3  2 xy 4  4 y 5



2
4x
3
 
2a  3b  2   a  5b  9


 4x 2  2x  2x 2  9x  1
2 x  5 y 2
2 x  32 x 2  3x  5
2 x 3 y 2  8 x 2 y 3  12 xy 4
8 xy3
Write the final answer in Scientific Notation
8.0  10 3
4.0  10 6
8.0 10 3.110 
359,800,000
5 x 3  35 x 2  20 x
x 2  5xy  6 y 2
6 x 2  21x  15
6 p 2  5 p  25
2a 2  4ab  3ab  6b 2
2ax  10bx  3 ya  15 yb
3
4
Factor completely
Solve the following equations
x x
 2
5 7
x  53x  10  0
xx  3  2x  4  2
x 2  64  0
x 2  6 x  11  0
x 2  4 x  12
2 x 2  6 x  20  0
5 x  3  2 x  7  3( x  2)
2  3r 2  4r
Solve the system of equations
2x  3y  4
9 x  5 y  45
5 x  6 y  13
5 x  y  25
3x  y  8
6 y  18 x  12
Graph the following equations in two variables (graph the solution set)
y
4
x4
5
3x  2 y  6
y  2 x
Find the slope of the line through the points (1, –4) and (–2,0)
Find the slope of the line through the points (2, –3) and (3,–1)
Find the x-intercept and the y-intercept for the equation –4x + 5y = –20
Solve the following word problems
Suppose Thomas has 26 coins totaling $1.90. If he has only dimes and nickels, how many each
type does he have?
Mary Jo spends $1,320 to buy stock in two companies. She pays $14 a share to one of the
companies and $20 a share to the other. If she ends up with a total of 75 shares, how many
shares did she buy at $14 a share and how many did she buy at $20 a share?
Two positive numbers have a difference of 12. The larger number is twice the smaller decreased
by 2. Find the two numbers.
The product of two consecutive odd integers is 1 less than 4 times their sum. Find the two
integers.
The hypotenuse of a right triangle is 15 yards. One of the legs is 3 yards more than the other.
Find the lengths of the two legs.
The base of a triangle is 4 times the height. The Area is 18 square inches. Find the base.
One number is 4 times another. Their product is 4 times their sum. Find the numbers.