Qiuyun TMUA Simulation Test Paper 2
19 questions · 71 min · Difficulty 58 · by Qiuyun
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
1 question has been withdrawn and is left out of practice sessions.
Question paper ↗Mark scheme ↗Original question paper (before corrections) ↗Original mark scheme (before corrections) ↗
Questions in this paper
- Question 1Denote the constant term of [(p-2)x+(p-1)/(x^2)]^3 as f(p). Find the sum of the x-coordinates of all the stationary points of f(p).
- Question 2Withdrawn
- Question 3Which of the following functions provides a counterexample to the statement: f'(x)>0 is necessary for f(x) being strictly monotonic.
- Question 4In a castle, there are five knights named Elvin, Black, Carl, Daniel and Ethan. Each of them has a statement about their own skill level on…
- Question 5What is the area of the region enclosed by the graph of the equation x^2+y^2=|x|+y?
- Question 6If one of the expansions of (2x^3+y^2)^n is tx^6y^6, what is the area between the curve y=dfrac940tx and the curve y=dfrac320tx^2?
- Question 7What is the value of log_3 7×log_5 9×log_7 11×log_9 13×…×log_(21)25×log_(23)27?
- Question 8For the sequence \a_n\ (a_n∈ℕ^+), we define b_k as the maximum in a_1,a_2,…,a_k (k=1,2,… n) (n∈ℕ^+). We call the sequence \b_n\ the “M…
- Question 9The set of values of x that satisfies ax^2+bx+c>0 is x 6. Which of the following statements must be true? - I. a>0 - II. a+b+c>0 - III. The…
- Question 10As is shown in the graph, the unit circle intersects with the x-axis at the point A(1,0). The terminal sides of the acute angles α,β,α-β…
- Question 11Your classmate Max mentioned Mersenne primes and then said that numbers of the form 2^n-1 are always prime. Which of the following is a…
- Question 12Now we need to prove: log_a b=(ln b)/(ln a) How can we choose these steps and prove this statement? - (1) Assume ln b=m and ln a=n - (2)…
- Question 13Use the trapezium rule to approximate the value of the following definite integral, with the number of intervals n=4: S=∫_π^(5π)(sin x+x)d…
- Question 14Here is a true statement: A function f:M→ M is said to be a contraction mapping if there exists a number C<1 such that |f(x)-f(y)|≤ C×|x-y|…
- Question 15You and your friend are playing a game of distributing weights. Each of you has a bag containing a certain real, discrete amount of weight…
- Question 16Given two functions: f(x)=|x^2-6x+1| g(x)=4x+frac4x Now, m∈ℝ is a constant and denote ε=f(x)-g(m). The function about ε is: ε^2+8ε=0 Find…
- Question 17Consider the following attempt to solve the integral: R=∫_0^π e^(cos x)×(sin^3x)d x - I. u=cos x, (d u)/(d x)=-sin x, x=0⇒ u=1, x=π⇒ u=-1 -…
- Question 18The original function f(x)=dfrace^x+e^(-x)e^x-e^(-x) is rotated by dfracπ2 anticlockwise around the origin (0,0). Which of the following is…
- Question 19f(x) is continuous and now given the proposition Z:∫_0^2f(x)d x=0 and f(1)=0 which of the following options correctly describes the…
- Question 20Point A(1,1) is on the parabola C:x^2=2py (p>0). Given the statement S: A line with gradient k passing through B(0,-1) intersects the…