Unattributed TMUA Mock Set A Paper 2
20 questions · 75 min · Difficulty 49 · by Unattributed
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Questions in this paper
- Question 1How many real solutions are there to the equation x|x|+1=3|x|?
- Question 2There is a statement p: “If x≥1 then 2^x+1≥3.” What is the contrapositive of the statement p?
- Question 3If log_2(log_3x)=log_3(log_4y)=log_4(log_2z)=0, then what is the value of (x+y+z)?
- Question 4Consider the following statement about the integer n: If n is even, then n is not a prime. Which of the following is a counterexample to…
- Question 5Write the expansion of (x^3+x^2+2)^4x and find the coefficient of x^4.
- Question 6Consider the following claim: The sum of two rational numbers is a rational number. Here is an attempted proof of this claim: - I…
- Question 7Consider the following statements: - P: x=1 - Q: x^2+x-6<0 Which of the following is true?
- Question 8The maximum coefficient of the expansion of (dfrac1x+x^2)^6 is a. How big is the area between the line y=dfrac320ax and the curve y=x^2?
- Question 9The function f(x)=x^3+ax^2+bx+c has two distinct stationary points at x_1 and x_2, and f(x_1)=x_1. How many distinct solutions does the…
- Question 10Consider the following statement: If x is a real number, such that x^2≤ x^4. Which is the sufficient but not necessary condition for the…
- Question 11The graph of the following function can be: y=sin x+e^xln|x|.
- Question 12For a positive number a, let I(a)=∫_0^a(4-2^(x^2)) dx. Then (dI)/(da)=0 when a equals
- Question 13Given that the radius of the sector AOB is 1 with the centre angle fracπ3, and C is a point on the arc as the graph shows, the maximum area…
- Question 14In a Cartesian coordinate system, define the “Manhattan distance” between two points as the sum of the absolute differences of their…
- Question 15P is a point moving along the line l:3x+4y-7=0. There are two lines PM and PN from the point P; PM and PN each meet the circle…
- Question 16The real numbers m and c are such that the equation x^2+(mx+c)^2=1 has a repeated root x, and also the equation (x-a)^2+(mx+c-1)^2=1 has a…
- Question 17A small circle of diameter 1 rolls anticlockwise along the inner wall of a large circle of diameter 2, where M and N are the two ends of a…
- Question 18There are two real numbers a and b with a>0, b>0. Consider the following statements about the function f(x). Which statement(s) is/are…
- Question 19x,a,b are all real numbers. If (a+2)^2+(b-3)^2=1, then what is the minimum value of (x-a)^2+(ln x-b)^2?
- Question 20Arrange the positive integers into a triangular array as shown in the left diagram. Then, following the given rules, take out the odd…