tmua.fyi Paper 2 Challenge 1
20 questions · 75 min · Difficulty 17 · by tmua.fyi
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Questions in this paper
- Question 1For a real number x, consider the two statements x>2 and x^2>4. The condition x>2 is:
- Question 2Consider the statement “Every child in the class owns a bicycle.” Its negation is:
- Question 3Which statement is logically equivalent to “If it is raining then the ground is wet”?
- Question 4A proof that there is no largest prime begins: “Suppose, for contradiction, that p is the largest prime.” It then considers the number…
- Question 5It is known that any multiple of 12 is a multiple of 4. A particular integer n is not a multiple of 4. Which of the following can be…
- Question 6For how many of the first five prime numbers (p=2,3,5,7,11) is the number 2^p-1 also prime?
- Question 7Consider the argument: “All squares are rectangles. Some rectangles are not rhombuses. Therefore some squares are not rhombuses.” This…
- Question 8For a positive integer n, the statement “n is divisible by 6” is logically equivalent to:
- Question 9How many of the following statements are true for all real numbers x? I. x^2≥ x. II. If x>1 then x^2>x. III. If x^2>x then x>1. IV. x^2=x…
- Question 10The statement “For every real number x there is a real number y with y^2=x” is false. Its correct negation is:
- Question 11The implication “P⇒ Q” is false in exactly one of the following situations. Which one?
- Question 12Consider this “proof” that 2=1. Let a=b. Then a^2=ab, so a^2-b^2=ab-b^2, giving (a+b)(a-b)=b(a-b), hence a+b=b; with a=b this gives 2b=b…
- Question 13Which of the following is a correct necessary and sufficient condition for a parallelogram to be a rectangle?
- Question 14Let A and B be sets with A⊆ B. Which of the following must be true?
- Question 15Consider the statement: “For all integers a,b,c: if a divides bc then a divides b or a divides c.” This statement is:
- Question 16For which real values of x is the statement “x^2-x+1>0” true?
- Question 17The converse of the statement “If a function is differentiable at a point then it is continuous at that point” is:
- Question 18Three boxes are labelled “Apples”, “Oranges” and “Mixed”. You are told that every label is wrong. You may draw a single fruit from one box…
- Question 19The arithmetic-geometric mean inequality states that u+v≥2√(uv) for all positive reals u,v. Using only this fact, the minimum value of…
- Question 20Let n be an integer and consider the statement “if n is odd then n^2+n is even”. Which of the following are true? I. The statement is true…