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DVMT 108 Testing Enhancement Workshop

This workshop, hosted by the Department of Mathematics and Computer Science at Coppin State University in September 2009, focuses on signed numbers and basic operations. Participants will learn to evaluate signed number expressions, understand addition and subtraction rules based on signs, and apply techniques for multiplication and division of both same and different signs. Additionally, the workshop covers essential concepts like the distributive property, evaluating polynomials, and solving equations to build a strong mathematical foundation.

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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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