Quarter 1 Exam Review Sheet:
Memorize your formula sheet!!!
Sets of Numbers:
1) Which number is not an integer?
a) -10
b) -2/3
c) 0
d) 5
2) Give an example of a number which is whole but not natural. _____________
3) Which of the following is a natural number?
a) -6
b) 16
c) 0
d) 3.14
4) Is 3.6352152512... rational or irrational? _________________
5) Is 4.975975975975975975975... rational or irrational? _______________
Properties:
___ 1) 7 · 1 = 7
___ 2) If 2 + 3 = 5, and 51 = 5, then 2 + 3 = 51.
___ 3) 5(x + 4) = 5x + 20
___ 4) (6 · 3) · 4 = 6 · (3 · 4)
___ 5) 4 · 0 = 0
___ 6) 6 + 3 = 6 + 3
___ 7) If 6 + 8 = 14, then 7 · 2 = 14.
___ 8) 9 + 6 = 6 + 9
___ 9) 9 + 0 = 9
___ 10) (7 + 5) + 4 = 7 + (5 + 4)
Simplify each of the following:
1) 1.5m - 4.2m - 12.5v + 4.2m
4) -(12k + 5m - 62)
A) Reflexive
B) Additive Identity
C) Mult. Identity
D) Assoc. Prop. of Mult.
E) Transitive
F) Assoc. Prop. of Addition
G) Symmetric
H) Comm. Prop. of Multiplication
I) Mult. Prop. of Zero
J) Distributive
2) 3.3t2 + 8.7t - 9.4t2 + 5t
5) 9(4x + 1.2y - 8.1) 6) 9(5 + t) - 6(t + 3)
8) -(m + 3) - 2(m + 3)
9) _a6_
a14
13) (2p6)0
15) x6 · x2 · x4
3) 1.4b - 3b2 + 4c - 2b2 + c
7) 4(r + 8) - 5(2r + 1)
10) _a2b4z10_
a4b9z5
11) (1/x)3
Factor each of the following:
1) x2 - 64
2) x2 - 100
3) x2 - 81
4) r2 + 4r + 3
5)q2 - 18q + 45
6) d2 + 21d + 38
8) 2y2 + 5y + 2
9) 20x2 + 80x + 35
10) 6x - 4
14) (6y2)2
7) 6x2 + 23x + 7
11) 10x3 - 25x2 + 20
12) 2t2 - 10t4
12) (6/n6)2
Solve the following using factoring:
1) x2 - 8x - 48 = 0
2) x2 + x = 12
3) t2 - 3t = 28
4) x2 = -8x - 15
Solve the following using the quadratic formula:
1) x2 + 6 = 5x
2) 2x2 + 4x - 7 = 0
Simplify:
1) _m - 2_ · _ 2m + 6_
3m + 9
2m - 4
2) _x2 + 6x + 2_ ÷ _x + 4_
x2 + x - 2
2x + 4
3) _t2 + 5t + 6_ · _t2 - 2t - 3_
t-3
t2 + 3t + 2
4) _c2 + 3c + 2_ ÷ _c + 2_
c2 - 4c + 3
c-3
Venn Diagrams:
1) At a school of 1,450 students, 674 buy lunch, 233 bring their own, and 154 do both. How
many of the students do not but lunch or bring their own?
Logic:
1) Write a statement that is logically equivalent to "If I did not eat, then I am hungry."
2) The expression "if p then q is written as __________.
3) Let p represent "Ann can climb Mount Everest" and q represent "The weather is clear." In
symbolic form, write "If the weather is clear, then Ann can climb Mount Everest."
4) The converse of - m → p is ______________.
5) The contrapositive of m → - r is _____________.
6) The logical equivalent of - y → - k is ______________.
Math Systems:
Name the identity element and inverse elements of the following system:
Adjacent Angles:
1) In the accompanying diagram, the measure of angle FBC = 20, what is the measure of angle
EBD?
2) In the accompanying diagram, find the measure of angle ABD.
Complementary and Supplementary:
1) Two complementary angles are in a ratio of 8:1. What is the measure of the larger angle?
2) Two supplementary angles are in a ratio of 2:4. What is the measure of the smaller angle?
3) Find x, angle AOD, and angle DOB.
4) Find x, angle AOC, angle COD, and angle DOB.