Clavis TMUA Set B Paper 1
20 questions · 75 min · Difficulty 20 · by Clavis
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Questions in this paper
- Question 1Find the value of ∫_0^4√(x)(x-6) dx.
- Question 2An arithmetic progression has 20 terms. The sum of the first 10 terms is 145, and the sum of the last 10 terms is 445. Find the common…
- Question 3The line y=2x+c is a tangent to the circle with equation x^2+y^2-6x+4y+8=0. Find the possible values of c.
- Question 4How many distinct solutions does the equation 2sin^2x=3cos x+3 have in the interval -2π≤ x≤2π?
- Question 5The angle θ satisfies 0<θ<fracπ2 and sin^2θ+sin^4θ+sin^6θ+sin^8θ+…=3. Find the value of cosθ.
- Question 6The diagram shows a circle with centre O and radius 6. The chord AB subtends an angle of (2π)/(3) at O. Find the exact area of the shaded…
- Question 7In the expansion of (1+2x)^n, where n is an integer with n≥3, the coefficient of x^3 is six times the coefficient of x^2. Find the value of…
- Question 8The tangent to the curve y=x^3-4x at the point where x=2 meets the y-axis at the point (0,c). Find the value of c.
- Question 9The equation x^2+(k-3)x+k=0 has two distinct real roots, and both roots are positive. Find the complete set of values of k.
- Question 10Find the value of ∫_(-2)^3|x-1| dx.
- Question 11The positive numbers x and y satisfy x^2y=32 (x)/(y^3)=frac12. Find the value of x.
- Question 12The graph of y=f(x) meets the x-axis at x=-2 and at x=6, and nowhere else. At which values of x does the graph of y=f(2x+4) meet the x-axis?
- Question 13The points A(-1,4), B(5,2) and C(k,k) are such that angle ABC is a right angle. Find the value of k.
- Question 14The trapezium rule with 3 strips of equal width is used to estimate ∫_1^4log_(10)x dx. Which one of the following is the estimate?
- Question 15The first three terms of a geometric progression are k+16, k+4, k where k is a positive constant. Find the sum to infinity of the…
- Question 16Find the complete set of values of x for which |2x-1|>|x+3|.
- Question 17The ten numbers x_1,x_2,…,x_(10) have mean 12, and the mean of their squares is 200. Find the value of Σ_(i=1)^(10)(x_i-12)^2.
- Question 18Box A contains 2 red counters and 3 blue counters. Box B contains 3 red counters and 1 blue counter. A fair coin is tossed. If it lands…
- Question 19The polynomial p(x)=x^3+ax^2+bx-6 is divisible by (x-1), and leaves a remainder of -12 when divided by (x+2). Find the value of ab.
- Question 20The curve with equation y=x^3-3x^2+k, where k is a real constant, meets the x-axis at exactly two distinct points. Find the possible values…