Sometimes, a question is labeled "Mark ALL that apply", which means that there might be more than one mark in the correct answer. It is really a set of True/False or Yes/No questions. You mark the bubble if the answer is True or Yes, and you leave it blank if the answer is False or No. We call these questions "Multiple Decision" (MD) questions.

The basic MD question consists of 5 decisions and is worth a maximum of 5 points.

M1. (5pts) A block is sitting on a wedge being pulled at constant speed as shown below. Which of the following forces would be in a valid free-body diagram for the block? (Mark ALL that apply.) (A) Gravitation due to the Earth (B) Normal force due to the wedge (C) Tension force due to the string (D) Static friction due to the wedge (E) Kinetic friction due to the wedge

The correct answer contains three marks, A, B, and D. Answering this question is like answering 5 Yes/No questions: (A) Is the gravitational force due to the Earth on a free-body diagram for the block? Yes or No. (B) Is the normal force due to the wedge...? Yes or No...

Points are earned for each correct decision, not for each correct mark. Marking A, B, and D earns only 3 points. The other 2 points are earned for not marking C and E. Therefore, if you mark A and B (only), you would earn 4 points, because you have made 4 correct decisions. Marking C (only) would earn only 1 point, because you did not mark E (the only correct decision).

Another type of MD question has only 4 decisions. Choice (E) is used for you to indicate that none of the 4 choices applies.

M2. (4pts) A block is sitting on a wedge being pulled at constant speed as shown below. Which of the following forces are vertical? (Mark ALL that apply.) (A) Gravitation due to the Earth (B) Normal force due to the wedge (C) Tension force due to the string (D) Static friction due to the wedge (E) None of these forces is vertical.

The correct answer is A, but this does not mean the question is a "standard" question (with exactly one correct answer), because you do not know beforehand that there is only one mark in the correct answer. Like M1, it is really a series of Yes/No questions.

If you mark A (only), you would earn 4 points, because you have made 4 correct decisions. If you mark AB, you would earn 3 points. If you mark B (only), you would earn 2 points, because you have not marked C or D, which is 2 correct decisions. Marking E earns 3 points; the only incorrect decision is not marking A. Marking AE earns 3.5 points, i.e., the average of marking A and marking E. Marking BE earns 2.5 points.

A third type of MD question is shown below.

M3. (4pts) A ball of mass m is thrown straight up into the air. Which of the following statements about the ball at its maximum height are true? (Mark ALL that apply.) (A) The speed is zero. (B) The acceleration is zero. (C) The net force is zero. (D) The gravitational force is mg. (E) None of these statements is true.

The correct answer is AD. This question is really 4 True/False questions. If the statement is true, you mark the appropriate bubble. If false, you leave it blank. Choice E is used for you to indicate that all 4 statements are false.

A fourth style of MD question is shown below.

For the next 3 questions, use the 4 situations shown below, labeled A, B, C, and D. In each case, mark ALL that apply, or choose: (E) None of the situations applies. M4. (4pts) For which situations is the object accelerating at the instant shown? M5. (4pts) For which situations is the acceleration of the object to the right at the instant shown? M6. (4pts) For which situations is the net force on the object horizontal at the instant shown?

The correct answers are M4: ABCD; M5: AD; M6: ACD.

There is always at least one mark in the correct answer to a Multiple Decision question. If you leave your answer blank, you earn 0 points.

There are at most 4 marks in the correct answer to a Multiple Decision question. If you mark all 5, this is interpreted as "just guessing", and you earn 2 points.

If you are just guessing, the average score on a Multiple Decision question is 50%, because you have a 50/50 chance of guessing correctly for each decision. If you fill in all 5 bubbles, you will earn a score of 2 points (out of 4 or 5). Typical scores are 3, 4, or 5, and averages on MD questions tend to be a little higher than the averages on standard questions.

There are other types of Multiple Decision questions, but these are the most common. For more information about Multiple Decision questions, please contact Bill Leonard at wjleonard@physics.umass.edu.