Question 1

Click the the given picture.

Question 2

On average, approximately how many millions kilometres from the Sun is the planet Neptune?

Accepted Answer

4500 million km

Answer

5 million km

Answer

30 million km

Answer

180 million km

Question 3

What percentage of the triangles in the first four rows of Alex's pattern are blue?

Accepted Answer

37.5%

Answer

50.0%

Answer

62.5%

Answer

60.0%

Question 4

If Alex were to extend the pattern to a fifth row , what would be the percentage of blue triangles in all five rows of the pattern?

Accepted Answer

40.0%

Answer

50.0%

Answer

66.7%

Answer

60.0%

Question 5

Alex is going to add more rows to this pattern. He claims that the percentage of blue triangles in the pattern will always be less than 50%. Is Alex is correct? Explain your answer.

Accepted Answer

The correct selection is “Yes,” that the claim is true, and an acceptable explanation recognises that the number of red triangles in each row will always be greater than the number of blue triangles in each row.

Question 6

Given the average margin of victory for the season, is it possible that the team never actually won a game by 19 points? Explain your answer.

Accepted Answer

The correct selection is “Yes” that it is possible that the team never actually won a game by 19 points, even though 19 is the average margin of victory. Students can respond by recognizing that the mean does not have to be a member of the data set, or they can provide an example data set that has a mean of 19 but which does not contain 19 in the data set. Note that for this latter approach, students can also provide a counterexample based on a value other than 19 because it still represents an appropriate line of reasoning in this context. For example, the arithmetic mean of the data set 6, 9, and 15 is 10, even though 10 is not a member of the data set. Partial-credit responses address the idea that some values in the data set must be greater and some values in the data set must be less than the mean, but do not explicitly mention that the mean does not have to be a member of the data set.

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