TExES Exam Mathematics 7-12 3 — Questions and Answers
Question 1: A high school teacher wants students to discover the formula for the area of a circle. Which approach BEST promotes conceptual understanding?
- State the formula and have students memorize it
- Have students rearrange sectors of a circle to approximate a parallelogram (Correct answer)
- Assign textbook problems using the formula
- Show a video explaining the formula
Correct answer: Have students rearrange sectors of a circle to approximate a parallelogram
Rearranging sectors to form a near-parallelogram is a discovery activity that builds conceptual understanding of why A = πr².
Question 2: Which number is irrational?
- 0.75
- √9
- √2 (Correct answer)
- 1/3
Correct answer: √2
√2 is irrational because it cannot be expressed as a ratio of two integers and its decimal expansion is non-terminating and non-repeating.
Question 3: In probability, which term describes events where the outcome of one does NOT affect the other?
- Mutually exclusive events
- Dependent events
- Independent events (Correct answer)
- Complementary events
Correct answer: Independent events
Independent events are those where the probability of one event occurring is not affected by whether the other event has occurred.
Question 4: Which property allows you to rewrite 3(x + 4) as 3x + 12?
- Commutative property
- Associative property
- Distributive property (Correct answer)
- Identity property
Correct answer: Distributive property
The distributive property states that a(b + c) = ab + ac, allowing multiplication to be distributed over addition.
Question 5: A TExES Mathematics 7-12 candidate should know that the sum of interior angles of a triangle is:
- 90°
- 180° (Correct answer)
- 270°
- 360°
Correct answer: 180°
The interior angles of any triangle always sum to 180°, a fundamental theorem of Euclidean geometry.
Question 6: Which instructional approach allows students to explore multiple solution strategies before the teacher formalizes a concept?
- Direct instruction
- Lecture-based teaching
- Problem-based learning (Correct answer)
- Rote memorization
Correct answer: Problem-based learning
Problem-based learning engages students in solving open-ended problems first, allowing diverse strategies before the teacher consolidates learning.
TExES Exam Mathematics 7-12 3
A high school teacher wants students to discover the formula for the area of a circle.
Which approach BEST promotes conceptual understanding?