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ALGEBRA

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ALGEBRA

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  1. ALGEBRA CHAPTER 2

  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.

  3. 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.

  4. 2.1 Examples - Radicals

  5. 2.1 Scientific Notation (6.1 x 1.4) 8.54 A. 854 B. 8540 C. 85.4 D. -854

  6. 2.1 Scientific Notation 8. 0.000904  2,260,000 -4 – 6 = -10 A. 4.00102 B. 4.001010 C. 4.00109 D. 4.0010-10

  7. A. B. C. D. 2.1 Order of Operations Please Excuse My Dear Aunt Sally Parens. Expnts. Mult. Div. Add Subt.

  8. 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)

  9. 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

  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 symbol 5. Choose the equiv. to: 4 - 2x > 8 A. -2x > 4 B. -2x < 4 C. 2x >4 D. -2x < -4

  11. 2.3 Solving Linear Eqs. 1. If 7x - 6 = 3x + 20, then 4x - 6 = 20 Subtract 3x Add 6 4x = 26 x = 26/4 Divide by 4 x = 13/2 Reduce

  12. 2.3 Solving Inequalities 4. If 20x - 8x + 20 > 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 Subtract 20 -x > -37 Divide by -1* x < 37 A. x < 37 B. x > 2 C. x <-37/25 D. x > 37

  13. 2.3 Checking Solutions 5. For each of the statements below, determine whether -1 is a solution: i. lx-1l = 0 ii. (t-3)(t-6) < 6 iii. y2+3y+17=15 l-1-1l = l-2l = 0 (-1-3)(-1-6)=(-4)(-7) < 6 (-1)2+3(-1)+17=1-3+17 =15  A. i only B. ii and iii only C. iii only D. ii only

  14. 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

  15. 2.4 Evaluating = (-3)2 - 4(-3) + 3 = 9 + 12 + 3 A. 9 B. 6 C. 24 D. 6

  16. 2.5 Quadratic Expressions A. Factoring Quadratic Expressions Difference of Squares 1. Which is a linear factor of 4x2 - 9 ? A=2x, B=3 4x2-9=(2x+3) (2x-3) A. 2x+9 B. 2x-9 C. 2x-3 D. 3x-2

  17. 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: 3x2-12x +x -4 = 3x(x-4)+1(x-4) =(3x+1)(x-4) A. x+4 B. 3x-4 C. 3x+1 D. 3x+2

  18. 2.5 Quadratic Equations Factoring: Set=0 Factor (3x-5) (x+1) = 0 Factors=0 3x-5 = 0 or x+1 = 0 x = 5/3 or x = -1

  19. A. B. C. D. 2.5 Quadratic Formula Solutions to ax2+bx+c=0 Are given by: a= 3, b= -6, c= 1

  20. 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: (x,y) one ordered pair (intersecting lines) 2=0 no ordered pair (parallel lines) empty set many ordered pair (same line)

  21. 5 5 5 5 -5 -5 -5 -5 5 5 5 5 -5 -5 -5 -5 2.6 Solving Inequalities 4. Which shaded region identifies the portion of the plane which corresponds to x<0 and y>2? B. A. We can pick a point from each shaded region and see if it satisfies the given conditions In A and B we will try (4,-2) Is x<0? No! C. D. In C we will try (-4,-2) Is y>2? No!

  22. 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 x + 4y = -1 Recopy Eq. 1 Add -15x = -45 x = 3 Divide 3 +4y = -1, 4y = -4 y = -1 A. {(3,-1)} B. {(3,1)} D. {(x,y)|y=-4x+11} C. 

  23. A. B. C. D. 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. For 2 machines

  24. 2.7 Variation 3 Types: direct: y = kx Directly proprtional to Varies directly as invs: y = k/x Inversely proportional to Varies inversely as joint: y = kxz Varies jointly as <-This one 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?

  25. 2.7 Variation 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? Direct Variation: y = kx P = k T 8 = k (480) A. 32 lb per in2 k =8/480=1/60 B. 4 lb per in2 P = k T P = (1/60)(120)=2 C. 2 lb per in2 D. 16 lb per in2

  26. REMEMBER MATH IS FUN AND … YOU CAN DO IT