ALGEBRA
CHAPTER 2
ALGEBRA
2.1 Real No., Sci. Notation & Order
2.2 Real Number Properties
2.3 Solving Equations & Ineq.
2.4 Evaluating Formulas & Fctns.
2.5 Solving Quadratic Equations
2.6 Systems of Equations & Ineq.
2.7 Proportion, Variation, Word Prob.
2.1 Operations-Irrationals
Expression - collection of numbers & letters
with operation signs
Like terms - have exactly the same letters
and exponents
Like radicals - have exactly same “inside”
Multiply radicals - keep the radical sign &
multiply the radicand
Divide radicals - keep the radical sign & div.
2.1 Examples - Radicals
2. 75 - 3 5 3 1 3
25 3 5 3
A. 5 B. 66 C. 4 3 D. 72
40
5. 20 4 5 2 5
2
A. 40 B. 2 10 C. 4 5 D. 2 5
2.1 Scientific Notation
n
M x 10 M is between1 and 10
n is an integer
16
7. (6.1 x 10 ) x (1.4 x 10 -14
)
(6.1 x 1.4) x (10 16 x 10 -14 )
2
8.54 x 10
A. 854 B. 8540 C. 85.4 D. -854
2.1 Scientific Notation
n
M x 10 M is between1 and 10
n is an integer
8. 0.000904 2,260,000 -4 – 6 = -10
A. 4.00102 9.04 x 10 -4
B. 4.001010 6
C. 4.00109 2.26 x 10
D. 4.0010-10
2.1 Order of Operations
Please Excuse My Dear Aunt Sally
Parens. Expnts. Mult. Div. Add Subt.
10. 10t t x 2 14t 7 x 5
2
10t 2t 2t 2 x 5
12t 10t 2
A. B. C. D.
2.2 Real Number Properties
Properties: Commutative, Assoc.,
Distributive, Identity, Inverse
1. Choose the expression equivalent
to the following: 15(13) + 15(10)
A. 15(13+10) B. 15(15)+13(10)
C. (15+15)(13+10) D. 30(13)(10)
2.2 Properties for Solving
To get an equivalent eq. or ineq.:
Add, Subtract, Mult., or * Div. both
sides by the same non-zero number.
*When Div. or Mult. an Ineq. by a
negative, reverse the symbol
4. Choose the equiv. to: 4x - 7 =3x + 6
A. 7x-7=6 B. x-7=6
C. 4x-6=3x+1 D. 4x-1= 3x+6
2.2 Properties for Solving
To get an equivalent eq. or ineq.:
Add, Subtract, Mult., or * Div. both
sides by the same non-zero number.
*When Div. or Mult. an Ineq. by a
negative, reverse symbol
5. Choose the equiv. to: 4 - 2x > 8
A. -2x > 4 B. -2x 4 D. -2x 6x - (17 - 7x),
12x + 20 > 6x -1 (17 - 7x) Comb. like
12x + 20 > 6x - 17 + 7x Remove ( )
12x + 20 > 13x - 17 Comb. like
-x + 20 > -17 Subtract 13x
-x > -37 Subtract 20
x 2 C. x 37
2.3 Checking Solutions
5. For each of the statements below,
determine whether -1 is a solution:
i. lx-1l = 0 l-1-1l = l-2l = 0
ii. (t-3)(t-6) 2?
A. 5 B. 5
We can pick a point from each
shaded region and see if it
-5 5 -5 5 satisfies the given conditions
-5 -5 In A and B we will try (4,-2)
Is x2? No!
-5 5
-5 -5
2.6 System Example
1. Choose the correct solution set
for the system x + 4y = -1
4x + y = 11
Multiply by -4 -16x - 4y = -44
Recopy Eq. 1 x + 4y = -1
Add -15x = -45
Divide x=3
3 +4y = -1, 4y = -4 y = -1
A. {(3,-1)} B. {(3,1)} C. D. {(x,y)|y=-4x+11}
2.7 Proportions
Proportions:
1. Two machines can complete 5 tasks every 3
days. Let t represent the number of tasks these
machines can complete in a 30-day month. Select
the correct relationship.
tasks 5 t
For 2 machines
days 3 30
A. B. C. D.
2.7 Variation
3 Types:
direct: y = kx Directly proprtional to
Varies directly as <-This one
invs: y = k/x Inversely proportional to
Varies inversely as
joint: y = kxz Varies jointly as
2. The pressure is directly proportional to
the temp. If the pressure is 8 lb/sq.in. when
temp. is 480 F, what is the pressure when
temp. is 120 F?
2.7 Variation
2. The pressure is directly
Direct Variation: proportional to the temp. If
y = kx the pressure is 8 lb/sq.in.
when temp. is 480 F, what is
the pressure when temp. is
P=kT 120 F?
8 = k (480)
A. 32 lb per in2
k =8/480=1/60 B. 4 lb per in2
P=kT C. 2 lb per in2
P = (1/60)(120)=2 D. 16 lb per in2
REMEMBER
MATH IS FUN
AND …
YOU CAN DO IT