Gerard Sayson TMUA Mock Paper 1
20 questions · 75 min · Difficulty 56 · by Gerard Sayson
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Questions in this paper
- Question 1Find the area between the curve y=xln x and the x-axis from x=0 to x=2.
- Question 2It is given that (dy)/(dx)=(x^3+a^3)/(x^2-ax+a^2) where a is a constant, and y=2 when x=1. Find an expression for y.
- Question 3The real roots of the equation 4^x-3×2^(x+1)+5=0 are 2^α and 2^β. What quadratic expression has roots (α)/(α+β) and (β)/(α+β)?
- Question 4The function f is given as f(x)=x^2+6x+12. Let g be such that its graph is the clockwise rotation of the graph of y=f(x) by 135°about the…
- Question 5Use the trapezium rule involving four points equally spaced apart to approximate the integral ∫_0^(2π)√(1+sin^2x) dx and determine whether…
- Question 6Points A and B lie on a circle with centre O and radius r. The line segment AB is a diameter of the circle. Point C lies on the…
- Question 7A coin is known to be either fair or biased, in which case the probability of heads is 0.6. Before any tosses are made, the probability…
- Question 8240 people are divided into three groups A, B and C. The ratio of people in group A to that in group C is 1:3, and group B would occupy a…
- Question 9The region R is bounded by the curves y=dfrac√(2ln x)x and y=(ln x)/(x). The formula V=∫_a^bπ[f(x)]^2 dx can be used to find the volume…
- Question 10A right pyramid has a square base with a side length of √6 cm. Given that the volume of the pyramid is V=(16)/(3-√5) cm^3 find the exact…
- Question 11A continuous dataset is partitioned into three classes: 0≤ x<10, 10≤ x<k, k≤ x<40, where 10<k<40. The frequency densities of the three…
- Question 12Find the total length of the intervals in the range 0≤ x≤4π for which (sin x-cos x)(2cos x-1)≥0.
- Question 13Two geometric sequences (u_n) and (v_n) have the same first term a, where a≠0. One sequence has a common ratio of r and the other has a…
- Question 14Determine the exact value of tan1°tan2°…tan89°.
- Question 15The graph of a curve C is given below for certain values of x. What could be the equation of C?
- Question 16Which of the following is a necessary but not sufficient condition for p, such that the curves y=x^3-x and y=2x+p intersect exactly once?
- Question 17The following theorem is quoted during a lecture about mathematical analysis: Weierstrass M-test Let f_1,f_2,… be a sequence of functions…
- Question 18A student is to prove the following theorem: For any positive real numbers a,b,c∈mathbb R, if a^2+b^2+c^2=1 then a+b+c≤√3. The student uses…
- Question 19Consider the following theorem: Let f be a function on the real numbers whose first and second derivatives exist. If f'(c)=0 and f"(c) 0 is…
- Question 20Consider the following proof that everyone on Earth has the same name. - I. Let P(n) be the statement that every group of n people has the…