Algebra 2 Problems of the Day

Daily Algebra 2 questions and answers.

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January 2017, Part I

All Questions in Part I are worth 2 credits. No work need be shown. No partial credit.


4. If sin²(32°) + cos²(M) = 1, then M equals

1) 32°
2) 58°
3) 68°
4) 72°

Answer: 1) 32°
The identify is: sin² x + cos² x = 1, so the two angles must be the same.

5. What is the solution to the system of equations y = 3x - 2 and y = g(x) where g(x) is defined by the function below?

1) {(0,-2)}
2) {(0,-2), (1,6)}
3) {(1,6)}
4) {(1,6), (6,16)}

Answer: 4) {(1,6), (6,16)}
First, notice that the graph of g(x) does not go through the point (0, -2), so choices (1) and (2) are incorrect.
Similarly, you can see that (1, 6) is not on the graph. So choice (3) is out.
Choice (4) is the only possible choice.
Point (1, 1) is part of g(x) and (1) = 3(1) - 2 is a true statement.
How do you know that (6, 16) is part of g(x)? You can tell from points (0, 4), (1, 1) and (2, 0) that g(x) is a quadratic function, which in vertex form is y = (x - 2)². Substitute 6 for x and you will get y = 16.

6. Which statement about statistical analysis is false?

1) Experiments can suggest patterns and relationships in data.
2) Experiments can determine cause and effect relationships.
3) Observational studies can determine cause and effect relationships.
4) Observational studies can suggest patterns and relationships in data.

Answer: 3) Observational studies can determine cause and effect relationships.
Observational studies can investigate an associations between two variables.
Experiment can determine cause and effect relationships.

Comments and questions welcome.

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