Official 2019 Paper 2
20 questions · 75 min · Difficulty 46
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Questions in this paper
- Question 1Find the coefficient of the x^4 term in the expansion of x^2(2x+frac1x)^6
- Question 2(2x+1) and (x-2) are factors of 2x^3+px^2+q. What is the value of 2p+q?
- Question 3a, b and c are real numbers. Given that ab=ac, which of the following statements must be true? - I a=0 - II b=0 or c=0 - III b=c
- Question 4Consider the following conjecture: > If N is a positive integer that consists of the digit 1 followed by an odd number of 0 digits and then…
- Question 5Consider the following statement about the positive integers a, b and n: > (*): ab is divisible by n The condition either a or b is…
- Question 6A student attempts to solve the equation cos x+sin xtan x=2sin x-1 in the range 0≤ x≤2π. The student's attempt is as follows: cos x+sin…
- Question 7For which one of the following statements can the fact that 12^2+16^2=20^2 be used to produce a counterexample?
- Question 8a, b and c are real numbers with a 0 - III dfrac cb>dfrac ab
- Question 9A large circular table has 40 chairs round it. What is the smallest number of people who can be sitting at the table already such that the…
- Question 10PQRS is a quadrilateral, labelled anticlockwise. Which one of the following is a necessary but not sufficient condition for PQRS to be a…
- Question 11An arithmetic series has n terms, all of which are integers. The sum of the series is 20. Which of the following statements must be true? -…
- Question 12Most students in a large college study Mathematics. A teacher chooses three different students at random, one after the other. Consider…
- Question 13A student approximates the integral ∫_a^bsin^2 x d x using the trapezium rule with 4 strips. The resulting approximation is an…
- Question 14Consider the following statements about the polynomial p(x), where a<b: - I p(a)≤ p(b) - II p'(a)≤ p'(b) - III p"(a)≤ p"(b) Which of these…
- Question 15The numbers a, b and c are each greater than 1. The following logarithms are all to the same base: log(ab^2c)=7 log(a^2bc^2)=11…
- Question 16The graph of the quadratic y=px^2+qx+p where p>0, intersects the x-axis at two distinct points. In which one of the following graphs does…
- Question 17A multiple-choice test question offered the following four options relating to a certain statement: Given that exactly one of these options…
- Question 18Consider the following inequality: (*): a|x|+1≤|x-2| where a is a real constant. Which one of the following describes the complete set of…
- Question 19Find the value of the expression √(8-4√2+1)+√(9-12√2+8)
- Question 20When the graph of the function y=f(x), defined on the real numbers, is reflected in the y-axis and then translated by 2 units in the…