tmua.me Medium Set E Paper 1
20 questions · 75 min · Difficulty 43 · by tmua.me
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Questions in this paper
- Question 1The points P, Q, R and S are the midpoints of the sides AB, BC, CD and DA of rectangle ABCD, respectively. The perimeter of rhombus PQRS is…
- Question 2A differentiable function f satisfies f'(x)=3x^2-18x+15 for all real x. The curve y=f(x) has two stationary points, A and B. What is the…
- Question 3A water bill consists of a fixed monthly charge of 6 pounds plus a fixed price for each unit of water used. A household's January bill is…
- Question 4A straight line with y-intercept -3 meets the curve y=x^2 at two distinct points P and Q. The sum of the x-coordinates of P and Q is 4…
- Question 5A sequence has nth term u_n=an^2+bn+c (n=1,2,3,…), where a, b and c are real constants. It is given that u_4-u_1=15 u_7-u_4=33. What is…
- Question 6Triangle ABC has BC=7, angle BAC=60°, and area 6√3. What is its perimeter?
- Question 7For which real values of k does the equation √(x)+2√(5-x)=k have exactly one real solution for x?
- Question 8Players A and B play games until one of them has won two games. There are no draws. In each game, A has probability 2/3 of winning…
- Question 9A function f, defined for all real x, satisfies f"(x)=6x f'(1)=2. What is the positive difference between the x-coordinates of the two…
- Question 10The integer n satisfies n≥6. In the expansion of (1+x)^n, the coefficients of x^4, x^5 and x^6, in that order, form an arithmetic…
- Question 11A polynomial P(x) has degree 4 and leading coefficient 1. It is divisible by x^2+1. When P(x) is divided by x^2-1, the remainder is 4x+6…
- Question 12There are two distinct circles which pass through both (1,0) and (5,0) and are tangent to the line y=x. What is the sum of their areas?
- Question 13A histogram represents waiting times t, in minutes. Its classes and frequency densities are shown below. c|ccc Waiting time & 0≤ t<4 & 4≤…
- Question 14The function f is given by f(x)=acos(bx)+c, where x is measured in radians and a and b are positive constants. The maximum value of f is 7…
- Question 15The curve C has equation y=x^4-6x^2. For a real number a, let L_a be the tangent to C at the point with x-coordinate a. For which values of…
- Question 16The expression (2x^2-frac1x)^6 is expanded as a sum of powers of x, where x≠0. What is the sum of the coefficients of all the terms in…
- Question 17For certain real values of k, the equation x^4-6x^3+(k^2+13)x^2-(2k+12)x+5=0 has at least one real solution for x. What is the sum of all…
- Question 18A three-digit positive integer N has digits whose sum is 12. Its tens digit is the arithmetic mean of its hundreds digit and its units…
- Question 19In trapezium ABCD, the vertices are named in order around its boundary and AB is parallel to DC. The lengths are AB=6, DC=2, AD=4. The…
- Question 20The function f is defined by f(x)=(2x+3)/(x+2), x≠-2. For which real values of x is f(f(x))>1?