Y and A Tutoring Paper 2 with Answers and Hints
20 questions · 75 min · Difficulty 51 · by Y and A Tutoring
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Questions in this paper
- Question 1Consider the statement: No positive integer N that is less than 20 can be written as the sum of two non-prime integers that are greater…
- Question 2Five sealed jars, labelled A, B, C, D and E, each contain the same (non-zero) number of £1 coins. The following statements are attached to…
- Question 3A child is chosen at random from a group. Each child is equally likely to be chosen. Which of the following conditions is/are necessary for…
- Question 4Consider the following incorrect attempt at a proof, given that a and b are real numbers such that a=b. On which line does the first…
- Question 5Consider the following two statements about the polynomial p(x) with exactly two stationary points at x=a and x=b where a<b. P: p(x) has a…
- Question 6Consider the following attempt at finding the number of solutions to the equation 6sin x=(7sin x)/(cos x) for 0≤ x≤360°. I 6=frac7cos x II…
- Question 7Consider the following two statements about the polynomial p(x): P: p(x) has at least one real root. Q: p(x) is a polynomial of order n…
- Question 8Consider the following statement about the polynomial p(x) where a and b are real numbers with a<b: (*) There exists a number c with a<c<b…
- Question 9The fact that 5×6=30, is a counter example to which of the following statements:
- Question 10A student attempts to answer the following question. What is the largest number of consecutive odd integers that are all prime? The…
- Question 11Consider the two statements: R: k is an integer multiple of π S: ∫_0^ksin2x d x=0 Which of the following statements is true?
- Question 12Consider the following equation where a is a real number and a>1: (*) a^x=x Which of the following equations must have the same number of…
- Question 13Consider the following statement about a pentagon P: (*) If at least one of the interior angles in P is 108°, then all the interior angles…
- Question 14Here is an attempt to solve the inequality x^4-2x^2-3<0 by completing the square: I if and only if x^4-2x^2+1<4 II if and only if…
- Question 15Consider the following theorem: If 2^k+1 is a prime, then k is a power of 2. (*) Which of the following statements, taken individually…
- Question 16Let x be a real number. Which one of the following statements is a sufficient condition for exactly three of the other four statements?
- Question 17The real numbers a,b,c and d satisfy 0 b-a III frac bc<frac da
- Question 18Let a,b,c>0. The equations: log_a b=c and a=b^c
- Question 19Which of the following statements are true? I There exists a real y such that for all real x, y>x II There exists a real x such that for…
- Question 20f is a function and a,b are real numbers. Given that exactly one of the following statements is true, which one is it?