Nabla Tuition TMUA Paper 1
20 questions · 75 min · Difficulty 35 · by Nabla Tuition
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Questions in this paper
- Question 1A sequence is defined by x_1=1, x_(n+1)=frac11+x_n (n≥1). What is the value of x_6?
- Question 2The graphs y=x^2-4x+c y=2x-3 touch at exactly one point. Find c.
- Question 3The line y=mx+3 intersects the parabola y=x^2 at two points A and B. The horizontal distance between A and B is 4. Find m^2.
- Question 4The function f is defined by f(x)=(x-1)/(x+1), x≠-1. Find the solution of f(f(f(x)))=2.
- Question 5An acute angle θ satisfies sinθ=2cos^2θ. Find tan^2θ.
- Question 6Find the coefficient of x^5 in (1+x)^4(1+x^2)^3.
- Question 7A positive real number x satisfies x+frac1x=3. Find (x^2+1)/(x^2-x+1).
- Question 8The tangent to the curve y=x^2 at the point (a,a^2), where a>0, meets the coordinate axes at P and Q. If OP=OQ, where O is the origin, find…
- Question 9The tangent to the circle x^2+y^2=25 at the point (3,4) meets the coordinate axes at A and B. Let O be the origin. What is the area of…
- Question 10The circle (x-2)^2+(y+1)^2=9 is tangent to each of the two lines of the form y=x+c. What is the sum of the two possible values of c?
- Question 11How many solutions are there to 2sin^2(2x)-3sin(2x)+1=0 in the interval 0≤ x≤2π?
- Question 12A four-digit number is formed by choosing four distinct digits from 1,2,3,4,5,6 and arranging them at random. What is the probability that…
- Question 13The equation 4^x-a 2^x+1=0 has two real solutions whose difference is 2. Given that a>0, find a.
- Question 14An infinite geometric series has positive first term and common ratio r, where 0<r<1. The sum of the terms in odd-numbered positions is 14…
- Question 15The tangent to the curve y=frac1x, x>0, at the point whose x-coordinate is t meets the positive coordinate axes at A and B. What is the…
- Question 16Three distinct integers are chosen at random from 1,2,3,4,5,6,7,8. What is the probability that their sum is divisible by 3?
- Question 17The curve y=x-x^3 lies above the x-axis for 0<x<1. The line x=a, where 0<a<1, divides the area between the curve and the x-axis from x=0 to…
- Question 18A right circular cylinder is inscribed in a sphere of radius 3. The axis of the cylinder passes through the centre of the sphere. What is…
- Question 19The equation x^3-3x=k has three distinct real solutions p<q<r. For how many integer values of k do all three solutions lie in the interval…
- Question 20For a real constant k, the function f is defined by f(x)=x^3-3x+k. The equation f(f(x))=k has exactly seven distinct real solutions. Which…