Official 2018 Paper 2
20 questions · 75 min · Difficulty 51
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Questions in this paper
- Question 1The function f is given, for x>0, by f(x)=(x^3-4x)/(2√ x) Find the value of f'(4).
- Question 2Find the value of the constant term in the expansion of (x^6-frac1x^2)^(12)
- Question 3Consider the following statement: > A car journey consists of two parts. In the first part, the average speed is u km/h. In the second…
- Question 4The non-zero real number c is such that the equation cos x=c has two solutions for 0<x<frac32π. How many solutions of the equation cos^2…
- Question 5The two diagonals of the quadrilateral Q are perpendicular. Consider the following statements: - I One of the diagonals of Q is a line of…
- Question 6Which one of the following functions provides a counterexample to the statement: > if f'(x)>0 for all real x, then f(x)>0 for all real x.
- Question 7Sequence 1 is an arithmetic progression with first term 11 and common difference 3. Sequence 2 is an arithmetic progression with first term…
- Question 8The diagram shows an example of a *mountain profile*. This consists of *upstrokes* which go upwards from left to right, and *downstrokes*…
- Question 9Consider the following attempt to solve the equation 4x√(2x-1)=10x-5: 4x√(2x-1)=10x-5 [2pt] (I) [2pt] 4x√(2x-1)=5(2x-1) [2pt] (II) [2pt]…
- Question 10The function f(x) is defined for all real numbers. Consider the following three conditions, where a is a real constant: - I f(a-x)=f(a+x)…
- Question 11Consider the equation 2^x=mx+c, where m and c are real constants. Which of the following statements is/are true? - I The equation has a…
- Question 12Consider the following statement: > For any positive integer N there is a positive integer K such that N(Km+1)-1 is not prime for any…
- Question 13The following is an attempted proof of the conjecture: > if tanθ>0, then sinθ+cosθ>1. Suppose tanθ>0, so in particular cosθ≠0. - (I) Since…
- Question 14In the triangle PQR, PR=2, QR=p and ∠ RPQ=30°. What is the set of all the values of p for which this information uniquely determines the…
- Question 15It is given that f(x)=x^3+3qx^2+2, where q is a real constant. The equation f(x)=0 has 3 distinct real roots. Which of the following…
- Question 16In this question, x_1, x_2, x_3, … is an arithmetic progression, all of whose terms are integers. Let n be a positive integer. If the…
- Question 17A positive integer is called a squaresum if and only if it can be written as the sum of the squares of two integers. For example, 61 and 9…
- Question 18f(x) is a polynomial function defined for all real x. Which of the following is a necessary condition for the inequality fracf(a)+f(b)2≥…
- Question 19Three real numbers x, y and z satisfy x>y>z>1. Which one of the following statements must be true?
- Question 20It is given that the equation √(x+p)+√ x=p has at least one real solution for x, where p is a real constant. What is the complete set of…