ALGEBRA CHAPTER 2 ALGEBRA 2 1 Real No
ALGEBRA CHAPTER 2
ALGEBRA 2. 1 Real No. , Sci. Notation & Order 2. 2 Real Number Properties 2. 3 2. 4 2. 5 2. 6 2. 7 Solving Equations & Ineq. Evaluating Formulas & Fctns. Solving Quadratic Equations Systems of Equations & Ineq. 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. 1 Scientific Notation (6. 1 x 1. 4) 8. 54 A. 854 B. 8540 C. 85. 4 D. -854
2. 1 Scientific Notation 8. 0. 000904 2, 260, 000 A. 4. 00 102 B. 4. 00 1010 C. 4. 00 109 D. 4. 00 10 -10 -4 – 6 = -10
2. 1 Order of Operations Please Excuse My Dear Parens. Expnts. Mult. Div. A. B. C. Aunt Sally Add Subt. D.
2. 2 Real Number Properties: Commutative, Assoc. , Distributive, Identity, Inverse 1. Choose the expression equivalent to the following: 15(13) + 15(10) A. 15(13+10) D. 30(13)(10) B. 15(15)+13(10) C. (15+15)(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: 4 x - 7 =3 x + 6 A. 7 x-7=6 C. 4 x-6=3 x+1 B. x-7=6 D. 4 x-1= 3 x+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: A. -2 x > 4 C. 2 x >4 4 - 2 x > 8 B. -2 x < 4 D. -2 x < -4
2. 3 Solving Linear Eqs. 1. If 7 x - 6 = 3 x + 20, then 4 x - 6 = 20 4 x = 26 Subtract 3 x Add 6 x = 26/4 Divide by 4 x = 13/2 Reduce
2. 3 Solving Inequalities 4. If 20 x 12 x + 20 > -x > x < A. x < 37 8 x + 20 > 6 x 6 x -1 (17 - 7 x) 6 x - 17 + 7 x 13 x - 17 -37 37 B. x > 2 (17 - 7 x), Comb. like Remove ( ) Comb. like Subtract 13 x Subtract 20 Divide by -1* C. x <-37/25 D. x > 37
2. 3 Checking Solutions 5. For each of the statements below, determine whether -1 is a solution: i. lx-1 l = 0 l-1 -1 l = l-2 l = 0 ii. (t-3)(t-6) < 6 (-1 -3)(-1 -6)=(-4)(-7) < 6 iii. y 2+3 y+17=15 (-1)2+3(-1)+17=1 -3+17 =15 A. i only B. ii and iii only C. iii only D. ii only
2. 4 Evaluating 3. The formula for finding simple interest (I) on a loan at rate r, after t years is I =Prt. Find the interest paid on a $10, 000, 4 year loan if the rate is 8%? =. 32 I = 10, 000 x 0. 08 x 4 A. $32, 000 B. $2000 C. $200 D. $3200
2. 4 Evaluating = (-3)2 - 4(-3) + 3 = 9 + 12 + 3 A. 9 B. 6 C. 24 D. 6
2. 5 Quadratic Expressions A. Factoring Quadratic Expressions Difference of Squares 1. Which is a linear factor of 4 x 2 - 9 ? A=2 x, B=3 4 x 2 -9=(2 x+3) (2 x-3) A. 2 x+9 B. 2 x-9 C. 2 x-3 D. 3 x-2
2. 5 Quadratic Expressions A. Factoring Quadratic Expressions Trinomial Forms: Key number ac=-12 Factors of -12 that add to b=-11 : -12, 1 Rewrite: 3 x 2 -12 x +x -4 = 3 x(x-4)+1(x-4) =(3 x+1)(x-4) A. x+4 B. 3 x-4 C. 3 x+1 D. 3 x+2
2. 5 Quadratic Equations Factoring: Set=0 Factors=0 (3 x-5) (x+1) = 0 3 x-5 = 0 or x+1 = 0 x = 5/3 or x = -1
2. 5 Quadratic Formula Solutions to ax 2+bx+c=0 Are given by: a= 3, b= -6, c= 1 A. B. C. D.
2. 6 Solving Systems System of Equations: 2 eq. and 2 var. Solution to System: ordered pairs (x, y) that solve both equations Possible Solutions: one ordered pair (intersecting lines) no ordered pair (parallel lines) many ordered pair (same line) (x, y) 2=0 empty set
2. 6 Solving Inequalities 4. Which shaded region identifies the portion of the plane which corresponds to x<0 and y>2? 5 A. -5 5 B. 5 -5 -5 C. Is x<0? D. 5 -5 In A and B we will try (4, -2) -5 5 We can pick a point from each shaded region and see if it satisfies the given conditions 5 -5 In C we will try (-4, -2) 5 -5 No! Is y>2? No!
2. 6 System Example 1. Choose the correct solution set x + 4 y = -1 for the system 4 x + y = 11 Multiply by -4 -16 x - 4 y = -44 x + 4 y = -1 Recopy Eq. 1 Add -15 x = -45 x=3 Divide 3 +4 y = -1, 4 y = -4 y = -1 A. {(3, -1)} B. {(3, 1)} C. D. {(x, y)|y=-4 x+11}
2. 7 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. For 2 machines A. B. C. D.
2. 7 Variation 3 Types: direct: y = kx invs: y = k/x joint: y = kxz Directly proprtional to Varies directly as <-This one Inversely proportional to Varies inversely as 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 Direct Variation: y = kx P=k. T 8 = k (480) 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? k =8/480=1/60 P=k. T P = (1/60)(120)=2 A. 32 lb per in 2 B. 4 lb per in 2 C. 2 lb per in 2 D. 16 lb per in 2
REMEMBER MATH IS FUN AND … YOU CAN DO IT
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