Mathematical Reasoning Practice Questions
SPM (Malaysia) · SPM Mathematics · 154 free MCQs with instant results and detailed explanations.
154
Total
47
Easy
80
Medium
27
Hard
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Sample Questions from Mathematical Reasoning
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Q1
Easy
If the statement 'If it rains, then the ground is wet' is true, which of the following statements is also true?
A.
If the ground is not wet, then it did not rain.
B.
If it does not rain, the ground is wet.
C.
If the ground is wet, then it rained.
D.
It rains when the ground is wet.
Show Answer & Explanation
Correct Answer: A
This is the contrapositive of the original statement, which is logically equivalent. If the ground is not wet, then it indeed did not rain.
Q2
Easy
Which of the following is a valid conclusion from the premises: 'All cats are mammals' and 'Some mammals are not dogs'?
A.
Some cats are not dogs.
B.
All mammals are cats.
C.
Some mammals are cats.
D.
All cats are not mammals.
Show Answer & Explanation
Correct Answer: A
Since all cats are mammals, and if some mammals are not dogs, it logically follows that some cats must also not be dogs.
Q3
Easy
If every student in a class has completed at least one mathematics project, which of the following must be true?
A.
All students completed at least two mathematics projects.
B.
At least one student completed one mathematics project.
C.
No student completed a mathematics project.
D.
Every project completed is unique.
Show Answer & Explanation
Correct Answer: B
If every student completed at least one project, that implies that there is at least one student who completed a project.
Q4
Medium
If the statement 'All squares are rectangles' is true, which of the following statements must also be true?
A.
All rectangles are squares.
B.
Some rectangles are not squares.
C.
Some squares are not rectangles.
D.
All rectangles are not squares.
Show Answer & Explanation
Correct Answer: B
Since all squares are indeed rectangles, it does not imply that all rectangles are squares. Therefore, some rectangles could be other shapes, confirming option B is true.
Q5
Medium
Consider the statements: P: 'x is an even number.' Q: 'x + 1 is an odd number.' Which of the following indicates the logical connection between P and Q?
A.
P implies Q.
B.
Q implies P.
C.
P and Q are independent.
D.
P is equivalent to Q.
Show Answer & Explanation
Correct Answer: A
If P is true (x is even), then adding 1 to an even number results in an odd number, thus Q is also true. Therefore, P implies Q.
Q6
Medium
Which of the following is a valid conclusion derived from the premises: 'If it rains, the ground gets wet. It is not raining. Therefore, what can we conclude about the ground?'
A.
The ground is wet.
B.
The ground is not wet.
C.
The ground is definitely dry.
D.
We cannot determine the state of the ground.
Show Answer & Explanation
Correct Answer: D
The premises only provide information on what happens if it rains. The absence of rain does not guarantee the ground is dry; there could be other reasons for it being wet.
Q7
Medium
If the statement 'All dogs are mammals' is true, which of the following statements is logically equivalent?
A.
Some mammals are dogs.
B.
No mammals are dogs.
C.
All mammals are dogs.
D.
If something is a dog, then it is a mammal.
Show Answer & Explanation
Correct Answer: D
The statement 'All dogs are mammals' implies that if something is classified as a dog, it must be a mammal, making option D logically equivalent.
Q8
Hard
If the statement 'If it rains, then the ground is wet' is true, which of the following must also be true?
A.
If the ground is wet, then it must have rained.
B.
If it does not rain, then the ground is not wet.
C.
If the ground is not wet, then it has not rained.
D.
If it rains, the ground will always be wet.
Show Answer & Explanation
Correct Answer: C
The statement 'If it rains, then the ground is wet' implies that rain is a sufficient condition for wet ground. Therefore, if the ground is not wet, it logically follows that it could not have rained.
Q9
Hard
Consider the set of statements: A: All birds can fly. B: Penguins are birds. C: Therefore, penguins can fly. Which of the following describes the logical flaw in the reasoning?
A.
Statement A is false.
B.
Statement B is true.
C.
The conclusion does not logically follow from the premises.
D.
Penguins are not classified as birds.
Show Answer & Explanation
Correct Answer: C
The reasoning commits a logical fallacy. Just because premises A and B are true, it does not mean that the conclusion must be true, because A is not universally true (not all birds can fly).
Q10
Hard
If the statement 'If it rains, then the ground is wet' is true, which of the following scenarios would make the statement false?
A.
It rains and the ground is wet.
B.
It does not rain and the ground is dry.
C.
It rains and the ground is dry.
D.
It rains but the ground is not checked.
Show Answer & Explanation
Correct Answer: C
The statement is false if it rains but the ground is dry, indicating that the consequence (the ground being wet) did not occur despite the condition (it rains) being true.
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Mathematical Reasoning — SPM (Malaysia) SPM Mathematics Practice Questions Online
This page contains 154 practice MCQs for the chapter Mathematical Reasoning in SPM (Malaysia) SPM Mathematics. The questions are organized by difficulty — 47 easy, 80 medium, 27 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.