StepMaths Mock Paper 2
20 questions · 75 min · Difficulty 59 · by StepMaths
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Questions in this paper
- Question 1A letter L is printed somewhere on the x-y plane. It then undergoes three transformations: it is rotated anti-clockwise about the origin by…
- Question 2Let a>0. What is the value of ∫_(-a)^a√(x^4+(a^4)/(x^4)+2a^2)d x
- Question 3How many solutions are there to the equation cos^3(x)-dfrac5cos^2(x)2+2cos(x)-dfrac12=0 for 0<x<2π?
- Question 4In Mauritius, the Prime Minister only tells the truth on Mondays, Tuesdays, Wednesdays and Thursdays. He tells lies on all other days. The…
- Question 5Claim: For any real function f and real number x, if f(f(x))=x, then f(x)=f^(-1)(x). Which of the following is a counter example to the…
- Question 6Two sequences are related by the following relationships: u_(n+1)=xu_n, u_1=1 q_n=(d(u_n))/(dx) Find the value of ∫_0^xΣ_(n=1)^∞q_nd x if…
- Question 7Use some or all of the lines below to prove the inequality (a+b)(frac1a+frac4b)≥9 holds if a>0 and b>0. - 1. (a+b)(dfrac1a+dfrac4b)≥9⇔dfrac…
- Question 83 consecutive positive integers are chosen randomly. Which of the following statements must be true? - 1. 1 of them is divisible by 3 - 2…
- Question 9A triangle is inscribed in a circle so that its vertices lie on the circumference. How many of the following statements are individually…
- Question 10Which of the following is sufficient to imply that an integer x is not a square number? - 1. |x| has an even number of factors - 2. The…
- Question 11A function f(x) of real numbers is called even if and only if f(x)=f(-x) for all x in the domain of f(x). It is called odd if and only if…
- Question 12Integers x and y satisfy 2x^6+y^2-2x^3y=80. Which of the following can be deduced? - 1. x=2 - 2. x^6 0 - 4. y is even
- Question 13Consider the false claim (d(x^2))/(dx)=x. Below is an attempt at the proof. - 1. We can write x^2 as x+x+x+… (x times) for any x - 2. Given…
- Question 14A quadrilateral has side lengths 1,5,7, and x. Which of the following values of x is not possible?
- Question 15Which of the following statements is true?
- Question 16In the diagram, line segments AC and DF are tangent to the circle at B and E, respectively. O is the centre of the circle, and radii are…
- Question 17For which of the following values of k do the lines y=1-x^2 and y=k-2|x| intersect more than twice? - 1. k=2.5 - 2. k=2 - 3. k=1.5 - 4. k=1…
- Question 18Which of the following does not provide a counter example to the claim that n^3+n^2+111 is always prime?
- Question 19A square of side length 2 units contains a circle of radius R_1 that is internally tangential to the square. A second smaller circle of…
- Question 20p,q,r are positive whole numbers and pq+pr=80, while pq+qr=425. Given p,q,r are prime, find the value of p+q+r.