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Understanding Properties and Logical Reasoning in Mathematics for FTCE 5-9

Master key mathematical properties essential for the FTCE 5-9 exam, including reflexive, transitive, commutative, associative, and distributive properties. Explore logical reasoning by analyzing statements, converses, inverses, and contrapositives, such as for congruent angles. Engage with real-world scenarios and examples, such as relationships among athletes and shapes. Enhance your critical thinking skills and prepare effectively for your exam. Practice with various statements to solidify your understanding and application of these concepts.

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Understanding Properties and Logical Reasoning in Mathematics for FTCE 5-9

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  1. FTCE 5-9 Test Prep Center for Teaching and Learning

  2. Competency 3

  3. Competency 3 Properties Reflexive  a = a Transitive  is a = b, and b = c, then a = c Commutative  a + b, then b = a Associative  a + (b + c) = (a + b) + c Distributive  a (b + c) = ab + ac

  4. Competency 3 Name the property 5a + 4 = 4 + 5a (4x + 2x) + 7x = 4x + (2x + 7x) 2x(5 + y) = 10x + 2xy

  5. Competency 3 statement: if p then q converse: if q then p inverse: if not p then not q contrapositive: if not q then not p

  6. Competency 3 Write the inverse, converse and contrapositive. Statement: If two angles are congruent, then they have the same measure.

  7. Competency 3 Statement: If two angles are congruent, then they have the same measure. Converse: If two angles have the same measure, then they are congruent. Inverse: If two angles are not congruent, then they do not have the same measure. Contrapositive: If two angles do not have the same measure, then they are not congruent.

  8. Competency 3 Which statements are true? Converse: If two angles have the same measure, then they are congruent. Inverse: If two angles are not congruent, then they do not have the same measure. Contrapositive: If two angles do not have the same measure, then they are not congruent.

  9. Competency 3 Logical Conclusions If you are in Ft. Lauderdale, then you are in Broward County. True or false?

  10. Competency 3 Logical Conclusions All swimmers are athletes. All Athletes are scholars. Are all swimmers scholars?

  11. Competency 3 Logical Conclusions All swimmers are athletes. All wrestlers are athletes. Are all swimmers wrestlers?

  12. Competency 3 Logical Conclusions All rectangles are parallelograms. Quadrilateral ABCD is not a parallelogram. Is Quadrilateral ABCD a rectangle?

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