Clavis TMUA Set A Paper 1
20 questions · 75 min · Difficulty 21 · by Clavis
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
Questions in this paper
- Question 1Find the value of ∫_1^9frac(√(x)-1)^2√(x) dx.
- Question 2An arithmetic progression has first term 3 and common difference d, where d≠0. The 1st, 4th and 13th terms of this arithmetic progression…
- Question 3The circles C_1 and C_2 have equations C_1:x^2+y^2=25 C_2:(x-a)^2+(y-a)^2=9 where a is a real constant. Find the complete set of values of…
- Question 4How many solutions does the equation sin2x=tan x have in the interval 0≤ x≤2π?
- Question 5The equation 9^x-k3^x+27=0 has two distinct real solutions for x, where k is a real constant. Find the complete set of values of k.
- Question 6In the triangle ABC, AB=5, AC=8, and the area of the triangle is 10√3. Find the sum of the two possible values of BC^2.
- Question 7In the expansion of (2+ax)^6, where a is a non-zero constant, the coefficient of x^2 is equal to the coefficient of x^3. Find the value of…
- Question 8The curve with equation y=x^3+ax^2+bx has a stationary point at (2,-4). Find the value of a+b.
- Question 9The curve y=x^2+kx+10 lies entirely above the line y=2x+1. Find the complete set of possible values of k.
- Question 10Find the area of the finite region enclosed by the curve y=x(4-x) and the line y=x.
- Question 11Evaluate Σ_(n=1)^(80)log_4(2^n).
- Question 12The graph of y=f(x) has a maximum point at (3,5). The graph of y=2f(x-1)+4 has a maximum point at (p,q). Find the value of p+q.
- Question 13The points A(1,2) and B(7,10) are the endpoints of a diameter of a circle. The point P lies on the circle and PA=8. Find the length of PB.
- Question 14The trapezium rule with 4 strips of equal width is used to estimate ∫_0^4(x^2+1) dx. Find the positive difference between this estimate and…
- Question 15A convergent geometric series has first term a and common ratio r. The sum to infinity of the series is 9, and the sum of the first two…
- Question 16How many integers x satisfy |x-2|+|x+3|≤9
- Question 17A set of 12 numbers has mean 7. The two numbers 4 and 10 are removed from the set and replaced by two numbers, each equal to k. The mean of…
- Question 18A bag contains 3 red counters and 2 blue counters. Two counters are removed at random, one after the other, without replacement. Given that…
- Question 19The equation x^3-12x+q=0, where q is a real constant, has a repeated root. Find the complete set of values of q.
- Question 20A sector of a circle has radius r and angle θ radians, where θ<2. The perimeter of the sector is 20 and its area is 21. Find the value of r.