Official 2020 Paper 2
20 questions · 75 min · Difficulty 50
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Questions in this paper
- Question 1Find the complete set of values of k for which the line y=x-2 crosses or touches the curve y=x^2+kx+2.
- Question 2Given that tanθ=2 and 180°<θ<360°, find the value of cosθ.
- Question 3A student makes the following claim: > For all integers n, the expression 4(dfrac9n+12-dfrac3n-12) is divisible by 3. Here is the student's…
- Question 4Consider the following statement: > Every positive integer N that is greater than 6 can be written as the sum of two non-prime integers…
- Question 5Which one of the following shows the graph of y=(2^x)/(1+2^x) (Dotted lines indicate asymptotes.)
- Question 6The function f(x) is defined for all real values of x. Which of the following conditions on f(x) is/are necessary to ensure that ∫_(-5)^0…
- Question 7Consider the following conditions on a parallelogram PQRS, labelled anticlockwise: - I length of PQ= length of QR - II The diagonal PR…
- Question 8A student is asked to prove whether the following statement (*) is true or false: > (*) For all real numbers a and b, |a+b| Statement (*)…
- Question 9A student wishes to evaluate the function f(x)=xsin x, where x is in radians, but has a calculator that only works in degrees. What could…
- Question 10The real numbers a, b, c and d satisfy both 0 0
- Question 11A spiral line is drawn as shown. This spiral pattern continues indefinitely. Which one of the following points is not on the spiral line?
- Question 12Which one of A–F correctly completes the following statement? > Given that a 0 for all x with a<x<b, the trapezium rule produces an…
- Question 13f(x) is a function for which ∫_0^3(f(x))^2 d x+∫_0^3 f(x) d x=∫_0^1 f(x) d x Which of the following claims about f(x) is/are necessarily…
- Question 14An arithmetic sequence T has first term a and common difference d, where a and d are non-zero integers. Property P is: > For some positive…
- Question 15Which one of the following is a necessary and sufficient condition for Σ_(k=1)^nsin(frackπ3)=frac√32 to be true?
- Question 16The Fundamental Theorem of Calculus (FTC) tells us that for any polynomial f: fracdd x∫_0^x f(t) d t=f(x) A student calculates fracdd…
- Question 17A set of six distinct integers is split into two sets of three. The first set of three integers has a mean of 10 and a median of 8. The…
- Question 18In this question, f(x)=ax^3+bx^2+cx+d and g(x)=px^3+qx^2+rx+s are cubic polynomials. If f(x)-g(x)>0 for every real x, which of the…
- Question 19Nine people are sitting in the squares of a 3 by 3 grid, one in each square, as shown. Two people are called *neighbours* if they are…
- Question 20x is a real number and f is a function. Given that exactly one of the following statements is true, which one is it?