Official 2023 Paper 2
20 questions · 75 min · Difficulty 55
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Questions in this paper
- Question 1Given that frac1√(x)-6-frac1√(x)+6=frac311 what is the value of x?
- Question 2Evaluate ∫_9^(16)(frac1√(x)+√(x))^2d x-∫_9^(16)(frac1√(x)-√(x))^2d x.
- Question 3Consider the claim: > For all positive real numbers x and y, > > √(x^y)=x^(√(y)). Which of the following is/are a counterexample to the…
- Question 4A student attempts to answer the following question. > What is the largest number of consecutive odd integers that are all prime? The…
- Question 5Consider the two statements - R: k is an integer multiple of π - S: ∫_0^ksin2xd x=0 Which of the following statements is true?
- Question 6Consider 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 7The graph of the line ax+by=c is drawn, where a, b and c are real non-zero constants. Which one of the following is a necessary but not…
- Question 8A student draws a triangle that is acute-angled or obtuse-angled but not right-angled. The student counts the number of straight lines that…
- Question 9Consider the following statement about a pentagon P: > (*) If at least one of the interior angles in P is 108°, then all the interior…
- Question 10Here is an attempt to solve the inequality x^4-2x^2-3<0 by completing the square: x^4-2x^2-3<0 - I. if and only if x^4-2x^2+1<4 - II. if…
- Question 11In this question, k is a positive integer. Consider the following theorem: > If 2^k+1 is a prime, then k is a power of 2. (*) Which of the…
- Question 12In this question, p is a real constant. The equation sin xcos^2x=p^2sin x has n distinct solutions in the range 0≤ x≤2π. Which of the…
- Question 13Let x be a real number. Which one of the following statements is a sufficient condition for exactly three of the other four statements?
- Question 14Three lines are given by the equations: ax+by+c&=0 bx+cy+a&=0 cx+ay+b&=0 where a, b and c are non-zero real numbers. Which one of the…
- Question 15The base 10 number 0.03841 has the value 0×10^(-1)+3×10^(-2)+8×10^(-3)+4×10^(-4)+1×10^(-5)=0.03841. Similarly, the base 2 number 0.01101…
- Question 16A sequence is defined by: u_1&=a u_2&=b u_(n+2)&=u_n+u_(n+1) n≥1 where a and b are positive integers. The highest common factor of a and b…
- Question 17The ceiling of x, written lceil xrceil, is defined to be the value of x rounded up to the nearest integer. For example: lceilπrceil=4…
- Question 18The equation x^4+bx^2+c=0 has four distinct real roots if and only if which of the following conditions is satisfied?
- Question 19In this question, f(x) is a non-constant polynomial, and g(x)=xf'(x). f(x)=0 for exactly M real values of x. g(x)=0 for exactly N real…
- Question 20Let f be a polynomial with real coefficients. The integral I_(p,q) where p 0 only if p<0.