Official 2021 Paper 2
20 questions · 75 min · Difficulty 45
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Questions in this paper
- Question 1Find the value of ∫_1^4(3√(x)+(4)/(x^2))d x.
- Question 2A(0,2) and C(4,0) are opposite vertices of the square ABCD. What is the equation of the straight line through B and D?
- Question 3A student is chosen at random from a class. Each student is equally likely to be chosen. Which of the following conditions is/are necessary…
- Question 4Consider the following claim about positive integers a, b and c: > if a is a factor of bc, then a is a factor of b or a is a factor of c…
- Question 5On which line is the first error in the following argument?
- Question 6Consider the following two statements about the polynomial f(x): - P: f(x)=0 for exactly three real values of x - Q: f'(x)=0 for exactly…
- Question 7A circle has equation (x-9)^2+(y+2)^2=4. A square has vertices at (1,0), (1,2), (-1,2) and (-1,0). A straight line bisects both the area of…
- Question 8Consider the following statement about the polynomial p(x), where a and b are real numbers with a (*) There exists a number c with a<c<b…
- Question 9Consider the following statements about a polynomial f(x): - I. f(x)=px^3+qx^2+rx+s, where p≠0. - II. There is a real number t for which…
- Question 10The first seven terms of a sequence of positive integers are: u_1&=15 u_2&=21 u_3&=30 u_4&=37 u_5&=44 u_6&=51 u_7&=59 Consider the…
- Question 11A student attempts to solve the following problem, where a and b are non-zero real numbers: > Show that if a^2-4b^3≥0 then there exist real…
- Question 12Which of the following statements about polynomials f and g is/are true? - I. If f(x)≥ g(x) for all x≥0, then ∫_0^x f(t)d t≥∫_0^x g(t)d t…
- Question 13A region R in the (x,y)-plane is defined by the simultaneous inequalities y-x&<3 y-x^2&<1. Which of the following statements is/are true…
- Question 14Consider the following simultaneous equations, where p is a real number: p2^x+log_2y&=2 2^x+log_2y&=1. What is the complete range of p for…
- Question 15A circle has equation x^2+ax+y^2+by+c=0 where a, b and c are non-zero real constants. Which one of the following is a necessary and…
- Question 16p and q are real numbers, and the equation x|x|=px+q has exactly k distinct real solutions for x. Which one of the following is the…
- Question 17Consider the following functions defined for x>1: f(x)=log_2(log_2√(x)) g(x)=log_2(√(log_2x)). Which one of the following is true for all…
- Question 18A student chooses two distinct real numbers x and y with 0<x<y<1. The student then attempts to draw a triangle ABC with: AB&=1 sin A&=x sin…
- Question 19The angle θ can take any of the values 1°,2°,3°,…,359°,360°. For how many of these values of θ is it true that sinθ√(1+s…
- Question 20A sequence of functions f_1,f_2,f_3,… is defined by f_1(x)=|x| f_(n+1)(x)=|f_n(x)+x| n≥1. Find the value of ∫_(-1)^1f_(99)(x)d x.