Qiuyun TMUA Simulation Test Paper 1
20 questions · 75 min · Difficulty 50 · by Qiuyun
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Questions in this paper
- Question 1The coefficient of x^5 in the expansion of (ax^2+3x+2)^3 is 81. Find all possible values of the constant a.
- Question 2Evaluate ∫_1^8(frac√[3]x-1√[3]x)^2d x.
- Question 3Given a geometric sequence \a_n\, we have the first term a_1=dfrac43 and the common ratio q=dfrac43. Which of the following statements is…
- Question 4Consider the polynomial P(x)=x^4-6x^3+11x^2-7x+1. Which of the following statements is correct?
- Question 5S is the complete set of values of x which satisfy both the inequalities: -x^2+4x-3≥0 x≥2. The set S can also be represented as a single…
- Question 6Given that tanθ=dfrac√52 and θ∈(π,dfrac3π2), and M=(1+sinθ×cosθ)/(3cos^2θ-sin^2θ) What is the value of M?
- Question 7Consider the following two functions: f(x)=|log_(10)x|. For g(x), it is an odd function and it has a period of 4, and: g(x)=-x^2+2x, 0≤…
- Question 8Which one of the following shows the graph of y=frace^x+e^(-x)e^x-e^(-x)?
- Question 9An arithmetic sequence has a first term 14. Given that S_5>S_4 and S_5>S_6, what is one of the possible values of its common difference?
- Question 10Find the remainder when 2x^(2024)-9x^(2022)-81x^(2020)+2x+84 is divided by x^3-3x^2-x+3. Which of the following is the product of the…
- Question 11Given that f(x)=√(x^4-3x^2-6x+13)-√(x^4-x^2+1) Which of the following is the maximum of f(x)?
- Question 12By using the trapezium rule with 2 strips to evaluate the integral of a parabola from 0 to 2, we need to calculate the area of an…
- Question 13Find the total number of x, with x having the form of dfracπ k, k∈ℤ and x∈[-dfracπ2,dfracπ2], for which [(1-sin x)cos x]'≥0.
- Question 14Given the function f(x)=x^3-3x^2-9x+10 What is the value of f(-2022)+f(-2020)+f(-2018)+…+f(2020)+f(2022)+f(2024)?
- Question 15Given that for f(x): f(x+2)[1-f(x)]=1+f(x) Now, we know that f(0)=2, f(1)=3. What is the value of f(2028)?
- Question 16Given two functions: f(x)=x^3-2x^2-3x+p g(x)=ln x These two functions have 2 intersections that both have non-negative y-coordinates. Which…
- Question 17The two roots of the quadratic 12x^2-5x-3 are distinct real numbers. For every non-negative integer n, let s_n be the sum of the nth powers…
- Question 18A line which passes (0,0) is drawn tangent to the quadratic function x^2-3x+b at the point on the curve where x=1. Another line which…
- Question 19S_n is the sum of the first n terms of A_n. The first term a_1=1 and the sequence \(S_n)/(a_n)\ is an arithmetic sequence whose common…
- Question 20If x is a real number, let lfloor xrfloor be the greatest integer that is less than or equal to x. If n is a positive integer, let S(n) be…