OxbridgeMind TMUA Paper 1
14 questions · 53 min · Difficulty 28 · by OxbridgeMind
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1 question has been withdrawn and is left out of practice sessions.
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Questions in this paper
- Question 1Given that dfraca^xb^(3x)c^(2x)=5 where a, b and c are positive real number then x=
- Question 2It is known that x+3 is a factor of f(x)=x^3+2kx^2+(k+1)^2x+21. The sum of the possible values of k is
- Question 3The complete set of values of x for which (x^4-1)(x+3)>0 are:
- Question 4The perpendicular bisector of the line segment joining the point (-2,15) and (4,1) cuts the y-axis at the y-coordinate
- Question 5Find the number of real solutions in the interval 0<θ<dfrac5π2 of the equation cos^2θ+7sinθ=7.
- Question 6Consider the simultaneous equations: 3x^2+15y=6 2x+5y=3 the sum x+y therefore equals
- Question 7Five students took a math's test and got scores A, B, C, D, E with E>D, C>B, B>D and A>D. How many ways could the candidates be ranked?
- Question 8Let F_k=F_(k-1)+F_(k-2) where F_0=0, F_1=1. Define the series s(x)=Σ_(k=1)^∞(F_k)/(x^k) for x>2. What is the value of s(x)?
- Question 9Withdrawn
- Question 10A runner leaves their home and reaches their destination after an hour. The velocity of the runner varies according to the function…
- Question 11Which sketch represents |x|^3+|y|^3=1?
- Question 12What is the largest integer n such that n+3 perfectly divides n^2+27?
- Question 13For k>0, the function f(x)=(k+frac52)x^2+3k^2x+6k has its minimum at x=-1. Find k.
- Question 14a, b, c and d are positive integers such that a+cfrac1b+cfrac1c+cfrac1d=(15)/(11). Which one of the four integer is largest
- Question 15The real roots of the equation 4^(2x)+3=2^(2x+2) are p and q where p>q. The value of p-q can be expressed as: