AFDA Final Exam
Review Packet
Block __ – Mrs. Hanby
Name:____________________
Due: Day of Exam – no exceptions:___________
Date Submitted:_______________
Work hard on completing this packet. Remember to bring this to class on
the day of the final exam for Bonus Points!!!!!!!!
Algebra Postulates
Here are the basic postulates of equality, inequality, and operations. Dave didn't get a chance to write them,
and I needed them for my section on the basic postulates of Geometry (review is always good). Have a
blast!
Postulates of Equality
Reflexive Property of Equality: a = a
Symmetric Property of Equality: if a = b, then b = a
Transitive Property of Equality: if a = b and b = c, then a = c
.
Postulates of Equality and Operations
Addition Property of Equality: if a = b, then a + c = b + c
Multiplication Property of Equality: if a = b, then a * c = b * c
Substitution Property of Equality: if a = b, then a can be substituted for b in any equation or inequality
Subtraction Property of Equality: if a = b, then a - c = b - c
.
Postulates of Inequality and Operations
Addition Property of Inequality: if a < > b, then a + c < > b + c
Multiplication Property of Inequality: if a < b and c > 0, then a * c < b * c
if a < b and c < 0, then a * c > b * c
Equation to Inequality Property: if a and b are positive, and a + b = c, then c > a and c > b
if a and b are negative, and a + b = c, then c < a and c < b
Subtraction Property of Inequality: if a < > b, then a - c < > b - c
Transitive Property of Inequality: if a < b and b < c, then a < c .
Postulates of Operation
Commutative Property of Addition: a + b = b + a
Commutative Property of Multiplication: a * b = b * a
Distributive Property: a * (b + c) = a * b + a * c and vice versa
Solve each system of equations graphically. Describe as consistent or inconsistent.
What is consistent?__________________ What is inconsistent?_______________
1.
3y = x - 6
y = -4x – 2
3.
2x – y = -4
x = -3
Solve each of the equations.
4.
4(x + 3) = x + 6
6.
-4(3 – x) + 5x = 8x + 10 – 3x
2.
y = 0.5x + 3
y = 0.5x – 1
5.
5(2x – 1) -2(x – 8) = 9x – 14
7.
7(3x – 4) – (8x – 12) = 3(2x + 4)
Solve each system of equations algebraically using the substitution method.
8.
y = 5x + 2
9.
3w + z = 8
4y = 5x – 7
w – 4z = 7
Solve each system of equations algebraically using the combination/elimination method.
10. x + 7y = 13
11. 5x – 8y = -4
x + 4y = 10
3x + 2y = -3
12. You are thinking of starting a small business baking cakes for people in your
neighborhood. Suppose that the cost, C(n), of producing n cakes is C(n) = 5n + 30. If
you plan on selling each cake for $10, how many cakes do you need to sell to break
even?
Solve each system of equations using any of the methods from above.
13. x – 4y = 11
14. 5x + 4y = 32
3x + 4y = -15
2x + 4y = 14
15.
16. You took your two little cousins to the movies last week and spent $18.50 on a
regular priced ticket and two child priced tickets. The person behind you in line spent
$31.50 on two regular priced tickets and three child priced tickets. How much does the
movie theater charge for each regular priced and each child priced ticket?
Solve each of the inequalities.
17. 3x + 7 > 6x + 16
19.
18 < 3(x – 2) < 27
18.
6(3 – 2x) + 2x < 4(3x – 6) – 2
20.
21. Solve each system of linear inequalities graphically.
a. 3x + y < -2
b.
4x – 2y > 6
0.5x + y < 4
y > -4x – 6
y – x > -6
22.
23.
You have your own floral shop, and you rely greatly on the sale of centerpieces for the
business’s income. Your fixed costs (i.e. rent, utilities, & insurance) average $2000 each month. You
pay your employees about $6 for each centerpiece and the flowers (& other decorations) cost about
$21. You sell each centerpiece for an average of $45. Let x be the number of centerpieces made in
one month.
Dollars (1 tick = $500)
What is the equation for the total cost of making x centerpieces in one month?
A. C(x) = 27x
B. C(x) = 27x + 2000
C. C(x) = 45x
D. C(x) = 45x + 2000
Number of Centerpieces (1 tick = 10 centerpieces)
Which is an equation that describes the revenue from selling x centerpieces in one month?
A.
B.
C.
D.
R(x) = 27x
R(x) = 27x + 2000
R(x) = 45x
R(x) = 45x + 2000
What is the cost of making exactly 80 centerpieces in one month?
A. $4169
B. $3600
C. $2240
D. $4160
Which statement describes the profit if you sold exactly 500 centerpieces in one month?
A. You would make $22,500 of profit.
B. You would lose $7,000.
C. You would make $7,000 of profit.
D. You would lose $22,500.
24.
FACTORING NOTES:
Always check for the Greatest common factor (GCF)!!
Look for perfect Squares
Reverse Foil (product/sum table – “a * c gives you b”)
Group
If SOLVING - must be set equal to zero!!!
25.
26. Solve by factoring:
a. x(x + 7) = 0
b. x2 + 16 = 8x
c. 8x2 + 6x – 4 = 2x2 – 5x – 7
27. Find the discriminate. How many solutions will there be?
a. 3x2 + 11x – 4 = 0
b. x2 – 7x = 18
28.
a.
29.
Solve using the quadratic formula.
2x2 + 7x – 15 = 0
b. x2 – 48 = 2
30.
31.
32.
Find the vertex, axis of symmetry, and y-intercept of the graph of the parabola defined
by the equations:
a.
y = -2x2 + 3x + 25
b.
y = x2 – 4x + 4
33.
34. Chap 5 Review: