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DVMT 108 Testing Enhancement Workshop

DVMT 108 Testing Enhancement Workshop. Department of Mathematics and Computer Science Coppin State University September 2009. Outline. Signed numbers ~Basic operations ~Evaluate signed number expressions Special equations Quadrants. Addition and Subtraction. Same sign:

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DVMT 108 Testing Enhancement Workshop

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  1. DVMT 108Testing Enhancement Workshop Department of Mathematics and Computer Science Coppin State University September 2009

  2. Outline • Signed numbers ~Basic operations ~Evaluate signed number expressions • Special equations • Quadrants

  3. Addition and Subtraction • Same sign: Ex: 1+3 = 4 −1 − 3 = − 4 Keep sign and add the absolute values. • Different signs: Ex: − 1 + 20 = +19 = 19 11 − 29 = − 18 Give the sign of the number having the larger absolute value and subtract absolute values.

  4. Multiplication and Division • Same sign: positive Ex: − 1 (− 3) = +3 = 3 − 18 ÷(− 3) = +6 • Different signs: negative Ex: − 1 (20) = − 20

  5. Textbook Page 80 When dividing fractions, multiplying by the reciprocal of the divisor. A 5)

  6. Select the lesser of two numbers |2| = |2| = 2 − |2| = − 1∙|2| = − 1 ∙2= − 2 − | − 2| = − 1 ∙ | − 2| = − 1 ∙2 = − 2 A2) − | − 2| and − | − 20| − | − 20| = − 20 − | − 20| is the lesser; B6) | − 19| and | − 23| | − 19|=19; | − 23|=23; | − 19| is the lesser.

  7. Evaluate sighed number expressions A7) evaluate (− 6x − 3y)(− 2a) given x= − 2, y=3 and a= − 4. Substitute x, y and a by the given numbers. (− 6x − 3y)(− 2a) = [− 6(− 2) − 3(3)][− 2(− 4)] = (12 − 9)(8) =3(8) =24 Always use parenthesis around the negative numbers.

  8. Perform the indicated operations A8)

  9. The difference • A4) After one round in a card game, your score was 44 points. After the second round, your score was −42 points. How many points did you lose in the second game? Gain +/ Lose − − 42 − 44 = −(44+42)= − 86

  10. The difference of signed numbers • B9)The stock market gained 15 points on Tuesday and lost 11 points on Wednesday. Find the difference between these changes. 15 −(− 11) = 15+11 =26

  11. Distributive Property • -2(5) = -10 • -2(5+x) = -2(5) + (-2)x=-10-2x • A10) Use the distributive property to rewrite the expression. −8(3x) − 8(−5y) = −8(3x) + (−8)(−5y) = −8(3x − 5y)

  12. Exponents • Question: (−2)2 = −22? (−2)2 = (−2)(−2) = 4 • Answer: NO. −22 = −1(2 · 2) = −1(4) = −4 (−2)3 = (−2)(−2)(−2) = −8

  13. Evaluate the polynomial • A27)Evaluate 2x3 − 6x2 − x + 10 for x = −2. • Substitute x by (−2). • 2(−2)3 − 6(−2)2 − (−2) + 10 (use parentheses around the numbers) = 2(−8) − 6(4) + 2 + 10 = −16 − 24 + 12 = −40 + 12 = −28

  14. Equations • A12) Solve 3x − 4x = 7 −x = 7(combine like terms) x = −7(divide both sides by −1)

  15. Special Equations • A13) Solve 24(x − 2) = 6(4x + 3) − 66 24x − 48 = 24x + 18 − 66 24x − 48 = 24x − 48 −24x −24x − 48 = − 48 True statement. Solution: all the real numbers.

  16. Special Equations • Solve −2(3y − 5) = −6y + 1 −6y + 10 = −6y + 1 (add 6y both sides) 10 = 1 False statement. No solution.

  17. Quadrants

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