Official 2022 Paper 2
20 questions · 75 min · Difficulty 48
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Questions in this paper
- Question 1Determine the number of stationary points on the curve with equation y=3x^4+4x^3+6x^2-5.
- Question 2Find the coefficient of the x^5 term in the expansion of (1+x)^5×Σ_(i=0)^5x^i.
- Question 3Consider the following statement about the positive integer n: > if n is prime, then n^2+2 is not prime Which of the following is a…
- Question 4The point P has coordinates (p,q), and the equation of a circle is x^2+2fx+y^2+2gy+h=0 where f, g, h, p and q are all real constants. Let L…
- Question 5A straight line L passes through (1,2). Let P be the statement > if the y-intercept of L is negative, then the x-intercept of L is…
- Question 6A list consists of n integers. Consider the following statements: - P: n is odd. - Q: The median of the list is one of the numbers in the…
- Question 7Consider the following claim: > The difference between two consecutive positive cube numbers is always prime. Here is an attempted proof of…
- Question 8A selection, S, of n terms is taken from the arithmetic sequence 1,4,7,10,…,70. Consider the following statement: > (*) There are two…
- Question 9Consider the following statement: > (*) For all real numbers x, if x<k then x^2<k. What is the complete set of values of k for which (*) is…
- Question 10Which of the following statements is/are true? - I. For all real numbers x and for all positive integers n, x<n. - II. For all real numbers…
- Question 11The diagram shows a kite PQRS whose diagonals meet at O. OP=x, OQ=y, OR=x, OS=z. Which of the following is necessary and sufficient for…
- Question 12Place the following integrals in order of size, starting with the smallest. P=∫_0^1 2^(√(x))d x Q=∫_0^1 2^xd x R=∫_0^1 (√2)^xd x
- Question 13Consider the statement (*) about a real number x: > (*) There exists a real number y such that x-xy+y is negative. For how many real values…
- Question 14Consider the two inequalities: |x+5|<|x+11| |x+11|<|x+1|. Which one of the following is correct?
- Question 15The real numbers x, y and z are all greater than 1, and satisfy the equations log_xy=z log_yz=x. Which one of the following equations for…
- Question 16In this question, a_1,…,a_(100) and b_1,…,b_(100) and c_1,…,c_(100) are three sequences of integers such that a_n≤ b_n+c_n for each n…
- Question 17A student answered the following question: > a and b are non-zero real numbers. > > Prove that the equation x^3+ax^2+b=0 has three distinct…
- Question 18P, Q, R and S show the graphs of y=(cos x)^(cos x), y=(sin x)^(sin x), y=(cos x)^(sin x) y=(sin x)^(cos x) for 0<x<dfracπ2 in some order…
- Question 19A polygon has n vertices, where n≥3. It has the following properties: - Every vertex of the polygon lies on the circumference of a circle…
- Question 20The functions f_1 to f_5 are defined on the real numbers by f_1(x)&=cos x f_2(x)&=sin(cos x) f_3(x)&=cos(sin(cos x)) f_4…