Proven Potential TMUA Sample Paper 1
19 questions · 71 min · Difficulty 41 · by Proven Potential
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Questions in this paper
- Question 1The graph y=3x^2-15x+18 is plotted on a set of axes. What is the turning point of the graph?
- Question 2The function f(x) is defined piecewise by f(x)= x^2,&0≤ x<√[3]k+1, √(x),&√[3]k+1≤ x≤1, 0,&otherwise. The probability that the variable lies…
- Question 3Three fair dice labelled 1 to 6 are rolled together, what is the probability that the numbers rolled could be the sides of an equilateral…
- Question 4How many solutions of x are there to the equation: sin(-x)cos(x)=sin(x)cos(-x)+0.5, 0≤ x≤2π?
- Question 5Which is the graph of y=e^(cos^2x)?
- Question 6ABC is a triangle. AB=5, ∠ CAB=30°, BC<5. What length of BC defines ABC uniquely?
- Question 7Withdrawn
- Question 8How many solutions are there to the equation below? |x|+|y|≤10, x, y are integers.
- Question 9You are given that S=1+log_3frac13+log_3frac19+log_3frac127+…+log_3frac13^(n-1)+log_3frac13^n. If S=-2, what is the value of n?
- Question 10You are given the equation (k+(1+x)^3)^5, |k|<100. The coefficient of x^9 is 2845, what is the coefficient of x^7?
- Question 11Three sides of a right angle triangle are of a geometric progression, what is the hypotenuse of the triangle in terms of the shortest…
- Question 12Estimate the number of solutions to the equation 10^(12)sin x=1-x^2.
- Question 13Two players, A and B, play a series of games. Each game is independent, and player A has a probability p=frac23 of winning any single game…
- Question 14What is the value of 2+binom n2+binom n3+binom n4+…+binom nn-2+binom nn-1?
- Question 15If the largest circle has radius 1, what is the area of the shaded region?
- Question 16A sequence is defined by a_(n+1)=frac11+a_n, a_1=1. What is the value of a_n as n→∞?
- Question 17How many solutions are there to the equation √(x+3)+√(7-x)=4?
- Question 18What is the minimum value of the function f(x)=|x-1|+|2x+3|?
- Question 19Two concentric circles have radii r and 2r. A chord of the larger circle is tangent to the smaller circle. Find the length of the chord in…
- Question 20How many solutions are there to the equation x^(x^2)=x^4?