Official 2016 Paper 2
20 questions · 75 min · Difficulty 52
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Questions in this paper
- Question 1Find the value of ∫_1^2(x^2-(4)/(x^2))^2d x
- Question 2f(x)=frac(x^2+5)(2x)√[4]x^3, x>0 Which one of the following is equal to f'(x)?
- Question 3What is the value, in radians, of the largest angle x in the range 0≤ x≤2π that satisfies the equation 8sin^2x+4cos^2x=7?
- Question 4Five sealed urns, labelled P, Q, R, S, and T, each contain the same (non-zero) number of balls. The following statements are attached to…
- Question 5Consider the statement: > (*) A whole number n is prime if it is 1 less or 5 less than a multiple of 6. How many counterexamples to (*) are…
- Question 6The sequence of functions f_1(x),f_2(x),f_3(x),… is defined as follows: f_1(x)=x^(10) f_(n+1)(x)=xf_n'(x) n≥1 where f_n'(x)=(d f_n(x))/(d…
- Question 7The four real numbers a,b,c, and d are all greater than 1. Suppose that they satisfy the equation log_c d=(log_a b)^2. Use some of the…
- Question 8A region is defined by the inequalities x+y>6 and x-y>-4 Consider the three statements: - 1 x>1 - 2 y>5 - 3 (x+y)(x-y)>-24 Which of the…
- Question 9Triangles ABC and XYZ have the same area. Which of these extra conditions, taken independently, would imply that they are congruent? - (1)…
- Question 10In this question x and y are non-zero real numbers. Which one of the following is sufficient to conclude that x<y?
- Question 11f(x) is a polynomial with real coefficients. The equation f(x)=0 has exactly two real roots, x=-p and x=p, where p>0. Consider the…
- Question 12The first term of an arithmetic progression is a and the common difference is d. The sum of the first n terms is S_n. If S_8>3S_6, what can…
- Question 13In this question, a, b, and c are positive integers. The following is an attempted proof of the false statement: > If a divides bc, then a…
- Question 14Let f(x)=ax^4+bx^3+cx^2+dx+e, where a, b, c, d, and e are real numbers. The equation f(x)=1 has p distinct real solutions, the equation…
- Question 15Consider the quadratic f(x)=x^2-2px+q and the statement: > (*) f(x)=0 has two real roots whose difference is greater than 2 and less than…
- Question 16In the figure, PQRS is a trapezium with PQ parallel to SR. The diagonals of the trapezium meet at X. U lies on SP and T lies on RQ such…
- Question 17Consider these simultaneous equations, where c is a constant: y=3sin x+2 y=x+c Which of the following statements is/are true? - 1 For some…
- Question 18Consider this statement about a function f(x): (*) If (f(x))^2≤1 for all -1≤ x≤1 then ∫_(-1)^1(f(x))^2 d x≤∫_(-1)^1f(x) d x Which one of…
- Question 19Some identical unit cubes are used to construct a three-dimensional object by gluing them together face to face. Sketches of this object…
- Question 20Each interior angle of a regular polygon with n sides is frac34 of each interior angle of a second regular polygon with m sides. How many…