Official 2017 Paper 2
20 questions · 75 min · Difficulty 52
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Questions in this paper
- Question 1Given that y=dfrac(1-3x)^22x^(3/2), which one of the following is a correct expression for (d y)/(d x)?
- Question 2PQRS is a rectangle. The coordinates of P and Q are (0,6) and (1,8) respectively. The perpendicular to PQ at Q meets the x-axis at R. What…
- Question 3The first term of a geometric progression is 2√3 and the fourth term is frac94. What is the sum to infinity of this geometric progression?
- Question 4The following question appeared in an examination: > Given that tan x=√3, find the possible values of sin2x. A student gave the following…
- Question 5Consider the following three statements: - 1 10p^2+1 and 10p^2-1 are both prime when p is an odd prime. - 2 Every prime greater than 5 is…
- Question 6A sequence u_0, u_1, u_2, … is defined as follows: u_0=1 u_n=∫_0^1 4xu_(n-1) d x n≥1 What is the value of u_(1000)?
- Question 7The graphs of two functions are shown here: - y=a^x is shown with a solid line, where a is a positive real number - y=f(x) is shown with a…
- Question 8Which one of the following numbers is smallest in value?
- Question 9Consider the following attempt to prove this true theorem: > Theorem: a^3+b^3=c^3 has no solutions with a, b and c positive integers. > >…
- Question 10f(x) is a function defined for all real values of x. Which one of the following is a sufficient condition for ∫_1^3 f(x) d x=0?
- Question 11The function f(x) is increasing and f(0)=0. The positive constants a and b are such that a<b. The area of the region enclosed by the curve…
- Question 12The diagram shows the graphs of y=sin2x and y=cos2x for -fracπ2<x<fracπ2. Which one of the following is not true?
- Question 13The positive real numbers a×10^(-3), b×10^(-2) and c×10^(-1) are each in standard form, and (a×10^(-3))+(b×10^(-2))=(c×10^(-1)). Which of…
- Question 14The diagram below shows the graph of y=x^2-2bx+c. The vertex of this graph is at the point P. Which one of the following could be the graph…
- Question 15The function f is defined on the positive integers as follows: f(1)=5, and for n≥1: f(n+1)&=3f(n)+1&&if f(n) is odd f(n+1)&=tfrac12f(n)&&if…
- Question 16Consider the following statement: > (*) If f(x) is an integer for every integer x, then f'(x) is an integer for every integer x. Which one…
- Question 17A set S of whole numbers is called stapled if and only if for every whole number a which is in S there exists a prime factor of a which…
- Question 18Consider the following problem: > Solve the inequality (frac14)^n<(frac132)^(10), where n is a positive integer. A student produces the…
- Question 19Which one of the following is a sufficient condition for the equation x^3-3x^2+a=0, where a is a constant, to have exactly one real root?
- Question 20I have forgotten my 5-character computer password, but I know that it consists of the letters a, b, c, d, e in some order. When I enter a…