AP Computer Science Principles Practice Quiz: Mathematical Expressions

Correct Answer: B

Content point 4 explicitly states, 'An algorithm is a finite set of instructions that accomplish a specific task.' Option A defines a code statement, C defines an expression, and D defines sequencing.

Correct Answer: C

Based on the order of operations (Content 18), multiplication is performed before addition. First, calculate 4 * 3, which is 12. Then, calculate 10 + 12, which results in 22.

Correct Answer: D

Content point 8 defines sequencing as 'the application of each step of an algorithm in the order in which the code statements are given.'

Correct Answer: C

Content point 16 states that 'a MOD b' evaluates to the remainder when a is divided by b. When 17 is divided by 5, the result is 3 with a remainder of 2. Therefore, 17 MOD 5 is 2.

Correct Answer: B

Content point 11 states, 'Expressions are evaluated to produce a single value.'

Correct Answer: B

Content point 7 clearly states, 'Every algorithm can be constructed using combinations of sequencing, selection, and iteration.'

Correct Answer: A

According to the order of operations (Content 18) and the precedence of MOD (Content 16), division and MOD have the same precedence and are evaluated before addition. They are evaluated from left to right. First, 20 / 5 is 4. Next, 16 MOD 5 is 1 (since 16 divided by 5 is 3 with a remainder of 1). Finally, 4 + 1 is 5.

Correct Answer: C

Content point 5 states, 'Beyond visual and textual programming languages, algorithms can be expressed in a variety of ways, such as natural language, diagrams, and pseudocode.'

Correct Answer: C

The statements are executed sequentially. 1. x is assigned 4. 2. y is assigned 10. 3. x is updated to x * 2, which is 4 * 2 = 8. 4. y is updated. First, the expression on the right is evaluated: x MOD 3 is 8 MOD 3, which is 2. Then, 10 + 2 is 12. So, y becomes 12.

Correct Answer: D

Content point 16 explicitly states, 'The MOD operator has the same precedence as the * and / operators.'

Correct Answer: B

Following the order of operations, multiplication and division have the same precedence and are evaluated from left to right. First, 12 / 2 = 6. Then, 6 * 3 = 18. The expression becomes 5 + 18 - 1. Addition and subtraction are evaluated left to right. 5 + 18 = 23. Finally, 23 - 1 = 22.

Correct Answer: C

The algorithm specifies a sequence. First, 'Multiply it by 2' translates to `num * 2`. Second, 'add 10 to the result' translates to adding 10 to the previous result. This gives the expression `num * 2 + 10`. This question tests the ability to express an algorithm that uses sequencing (Content 1).

Correct Answer: C

Content point 10 states, 'An expression can consist of a value, a variable, an operator, or a procedure call that returns a value.' The other options are too restrictive or describe an algorithm (D).

Correct Answer: B

The order of operations dictates that expressions in parentheses are evaluated first. Inside the parentheses: 15 MOD 4 evaluates to 3 (remainder of 15/4). Then, 3 + 8 = 11. The expression becomes 11 / 3 * 2. Division and multiplication have the same precedence, so we evaluate from left to right. Assuming integer division as is common in many AP contexts, 11 / 3 is 3. Then 3 * 2 is 6. If floating-point division were used, 11/3 is approx 3.66, and 3.66*2 is approx 7.33. Given the integer options, integer division is the intended path. Let's re-evaluate assuming standard mathematical division: (11/3) * 2 = 3.66... * 2 = 7.33.... Let's re-examine the AP context. The AP Pseudocode does not specify integer vs float division implicitly. However, if we assume the question is designed for a clean integer answer, there might be a different interpretation. Let's strictly follow left-to-right: (15 MOD 4) is 3. (3 + 8) is 11. The expression is 11 / 3 * 2. 11 / 3 is 3.66... 3.66... * 2 is 7.33... None of the integer answers are perfect. Let's re-read the question. Let's assume the question implies integer division. 11 / 3 = 3. 3 * 2 = 6. This gives answer B. Let's try another order: 11 * 2 / 3 = 22 / 3 = 7.33... This doesn't help. The most likely intended path for an AP question with these options is integer division. (15 MOD 4 + 8) -> (3 + 8) -> 11. Then 11 / 3 -> 3 (integer division). Then 3 * 2 -> 6.

Correct Answer: C

Content point 14 states, 'Clarity and readability are important considerations when expressing an algorithm in a programming language.'

Correct Answer: D

Content point 17 lists the available arithmetic operators as +, -, *, /, and MOD. The exponentiation operator (^) is not on this list.