These are original Marlbridge practice questions, not past exam questions. All scenarios are fictional. The code is Marlbridge’s rendering of the exam reference notation (← assignment, = equality test, lists start at index 1, DISPLAY shows a value). Mark points are a suggested Marlbridge rubric, not an official scoring guideline. No calculator is needed or allowed. Try each question before opening its answer.
Question 1 (multiple choice · foundation)
What is the value of 5 ≥ 5?
DISPLAY(5 ≥ 5)- (A) The expression produces an error.
- (B) 5
- (C) true
- (D) false
Answer and explanation
Answer: (C). ≥ means greater than or equal to, so equal values make it true.
- (A) Comparing equal numbers is valid.
- (B) A comparison produces a Boolean, never a number.
- (D) would be the answer for
5 > 5.
Question 2 (multiple choice · core)
The variables x and y hold 5 and 2. What is displayed?
x ← 5
y ← 2
DISPLAY(NOT(x > 3 AND y = 2))- (A) 2
- (B) 5
- (C) false
- (D) true
Answer and explanation
Answer: (C). x > 3 is true and y = 2 is true, so x > 3 AND y = 2 is true. NOT(true) is false.
- (A) and (B) are variable values; a Boolean expression produces true or false.
- (D) forgets the NOT.
Question 3 (multiple choice · core)
Which expression is true exactly when n is from 1 to 10, including both ends?
- (A)
n ≥ 1 AND n ≤ 10 - (B)
n ≥ 1 AND n ≥ 10 - (C)
n ≥ 1 OR n ≤ 10 - (D)
n > 1 AND n < 10
Answer and explanation
Answer: (A). Both bounds must hold, and ≥ and ≤ include the end values.
- (B) is true only for numbers that are at least 10.
- (C) is true for every number.
- (D) excludes 1 and 10.
Question 4 (multiple choice · core)
Which expression is equivalent to NOT(a OR b)?
- (A)
NOT a OR NOT b - (B)
a AND b - (C)
NOT(a AND b) - (D)
NOT a AND NOT b
Answer and explanation
Answer: (D). De Morgan: negating an OR gives the AND of the negations.
- (A) is the equivalent of
NOT(a AND b). - (B) is true for a different set of cases (when both are true, whereas
NOT(a OR b)is true only when both are false). - (C) differs when exactly one of a, b is true:
NOT(a AND b)is true there butNOT(a OR b)is false.
Question 5 (multiple choice · core)
What is displayed?
p ← true
q ← false
r ← true
DISPLAY((p OR q) AND NOT r)- (A) r
- (B) true
- (C) p
- (D) false
Answer and explanation
Answer: (D). p OR q is true; NOT r is NOT true, which is false; true AND false is false.
- (A) and (C) are variable names, not values.
- (B) ignores the NOT.
Question 6 (multiple choice · foundation)
The variable score holds 10. What does score ≠ 10 evaluate to?
score ← 10
DISPLAY(score ≠ 10)- (A) 10
- (B) true
- (C) false
- (D) 0
Answer and explanation
Answer: (C). ≠ means “not equal”, and 10 equals 10, so the comparison is false.
- (A) and (D) are numbers, not Booleans.
- (B) would be correct for
score = 10.
Question 7 (multiple select, choose two · stretch)
Which two expressions are equivalent to NOT(a ≥ b)?
- (A)
a < b - (B)
NOT(a > b) AND a ≠ b - (C)
a ≤ b - (D)
(a < b) OR (a = b) - (E)
a > b
Answer and explanation
Answers: (A) and (B). NOT(a ≥ b) means a is strictly smaller than b. a < b says that directly. NOT(a > b) means a ≤ b, and a ≠ b removes the equal case, leaving a < b.
- (C) includes a = b.
- (D) is the same as
a ≤ b. - (E) is the opposite direction.
Question 8 (constructed response · core)
A cinema gives a discount to a customer if (they are a student and under 26) or (they are a member and have been a member for at least 2 years). The variables are isStudent (Boolean), age, isMember (Boolean) and years. (a) Write a Boolean expression that is true exactly when the customer gets the discount. (b) State its value for a 24-year-old non-student who has been a member for 3 years. (c) State its value for a 30-year-old student with no membership.
Answer and explanation
(a) (isStudent AND age < 26) OR (isMember AND years ≥ 2)
(b) isStudent is false, so the first bracket is false. isMember is true and years ≥ 2 is true (3 ≥ 2), so the second bracket is true. false OR true is true: the customer gets the discount.
(c) The student is 30, so age < 26 is false and the first bracket is false. Not a member, so the second bracket is false. false OR false is false.
Suggested Marlbridge rubric (5 marks)
| Mark point | Marks |
|---|---|
(a) Correct AND grouping for the student condition (isStudent AND age < 26) |
1 |
(a) Correct AND grouping for the member condition with years ≥ 2 (not >) |
1 |
| (a) The two groups joined by OR, bracketed | 1 |
| (b) true with reasoning | 1 |
| (c) false with reasoning | 1 |
Question 9 (constructed response · core)
Complete a truth table for the expression p AND NOT q for all four combinations of p and q. State the single row in which it is true, and write one sentence in words describing when it is true.
Answer and explanation
| p | q | NOT q | p AND NOT q |
|---|---|---|---|
| true | true | false | false |
| true | false | true | true |
| false | true | false | false |
| false | false | true | false |
It is true only when p is true and q is false. In words: “p holds but q does not”.
Suggested Marlbridge rubric (4 marks)
| Mark point | Marks |
|---|---|
| Correct NOT q column | 1 |
| Correct p AND NOT q column (one true row) | 1 |
| Identifies the true row (p true, q false) | 1 |
| Correct description in words | 1 |
How did you do?
Count the questions you got right first time, then read the explanation for every one you missed, including the wrong options you rejected correctly, because the distractors show you the typical slips. Anything you missed twice goes onto your revision list for the revision notes; re-read the matching section of the study guide before trying again.