Reasoning and Proof: math test, Grade 10 – download the PDF

1 Conditional statements / 4 pts

Consider: “If a quadrilateral is a rectangle, then it has four right angles.”

1. Write the converse, inverse and contrapositive, and give the truth value of each.
2. Write the statement as a biconditional if possible.

2 Reasoning and counterexamples / 3 pts

1. You compute \(3\cdot 1=3\), \(3\cdot 3=9\), \(3\cdot 5=15\), \(3\cdot 7=21\) and conjecture that 3 times an odd number is odd. What type of reasoning is this?
2. Disprove: “If a number is a multiple of 5, then it is odd.”
3. Disprove: “The sum of two prime numbers is prime.”

3 Algebra proof / 4 pts

Given: \(4(x+3)=2x+30\). Prove: \(x=9\). Write a two-column proof.

4 Angle addition / 4 pts

Ray \(BD\) lies inside \(\angle ABC\), \(m\angle ABC=108^\circ\), \(m\angle ABD=(4x-6)^\circ\), \(m\angle DBC=(2x+12)^\circ\). Find \(x\), \(m\angle ABD\) and \(m\angle DBC\), naming the postulate used.

5 Paragraph and flow proof / 5 pts

Given: \(\angle 1\) and \(\angle 3\) are complementary, and \(\angle 2\) and \(\angle 3\) are complementary. Prove: \(\angle 1\cong\angle 2\).

1. Write a paragraph proof.
2. List the boxes of a flow proof with the reason under each.