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Unit 4: Algebra Review
Pre-Algebra
Place each list of numbers in order from least to greatest. (Use of the number line is optional,
but suggested.)
a) –8, 6, 0, 3, -4, 4, 7
b) -⅓, ⅔, ⅛, -⅜, -⅝, ⅞, -½
Simplify each of the following completely. (Remember to double-check your answer from your
calculator based on the rules you know for operations with signed numbers.)
b) 3⅝ - 8⅞
a) (4 x 3)² + 4 x 3²
c)
e)
 Round to the
nearest thousand
 Round to the nearest
thousandth
d)
Round to the
nearest whole number
f)
m) Use the formula ºF = 9/5(ºC) + 32 to convert –8 ºC to ºF. Round to the nearest degree.
Basic Algebra
Simplify Completely:
a) 3⅜x – 2¼y + 4⅛x + 6y
b) 3(x + y) + 6(x – y)
c) 3xy(6x² + 4xy²)
d) x²
x9
e) 3x5 – 9x7 + 3x
3x
Evaluate for the indicated values:
a) M=3x – 5y + 4z for x=-7, y=6, z=2
b)V=LWH for L=3½, W=2¼, H=5⅜
Solve the equations. Round to three significant digits:
a) 5x – 2(x – 1) = 11
b) 12 – 7y = y – 18
c) 12 = 4 – x
Rewrite in Scientific Notation:
a) 0.00000482
b) 2,127,000
Rewrite as a number in standard form:
a) 5.146 x 10-7
b) 9.071 x 104
Solve the following word problems:
Electronics. Assuming that there is no mutual coupling, the total inductance in this circuit can be calculated
from the following formula: LT =
L1L2 . Calculate LT for L1 = 200 mH and L2 = 50 mH.
L1 + L2
Advanced Algebra
SYSTEMS of EQUATIONS: simultaneous equations that share a common solution consisting of a coordinate
pair (i.e. an (x,y) value for a solution)
Steps for the Substitution Method:
Steps for the Elimination Method:
1. Solve each equation for y
1. Make sure both equations are in the same format
2. Set the two equations equal to one
2. Multiply both equations to make x- or y-values
another have the same coefficient
3. Solve for the x-value
3. Add/subtract so that only one variable remains
4. Plug the x-value into either equation
4. Solve for that variable
5. Solve for the y-value
5. Plug the solution into the equation
6. Write the solution as (x,y)
6. Solve for the other x- or y-value
7. Write the solution as (x,y)
Examples: Solve the following systems using the method of your choice.
1.
2.
SYSTEM WORD PROBLEMS: Write the equation then solve the same as above.
5. Pam is playing with red and black marbles. The number of red marbles she has is three more than twice the
number of black marbles she has. She has 42 marbles in all. How many red marbles does Pam have?
6. Josh and Mae work at a concession stand. They each earn $8 per hour. Josh worked three hours more than
Mae. If Josh and Mae earned a total of $120, how many hours did Josh work?
QUADRATIC EQUATIONS: equations in the format of y = ax² + bx + c where a, b, and c are integer values
Methods to Solve a Quadratic:
Factor Completely
1. Take out a GCF (greatest common factor)
2. Difference of Perfect Squares
3. Factor the Trinomial
Examples: Follow the directions stated in each problem below.
7. When 36 is subtracted from the square of a number, the result is five times the number. What is the positive
solution?
8. Johanna has two sisters. One of the sisters is 7 years older than Johanna. The other sister is 3 years younger
than Johanna. The product of Johanna’s sisters' ages is 24. How old is Johanna?
9. Factor
completely
11. Factor completely:
10. Factor completely:
13. Factor
completely.