tmua.fyi Mock Paper 1
20 questions · 75 min · Difficulty 18 · by tmua.fyi
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Questions in this paper
- Question 1The first three terms of a geometric sequence are √2,2,2√2. What is the seventh term?
- Question 2Evaluate ∫_1^4(3x-2)/(√ x) d x.
- Question 3The line y=2x+c does not intersect the curve y=x^2-4x+7. Find the set of values of c.
- Question 4Find the sum of all real solutions of x-5√ x+6=0.
- Question 5Find Σ_(n=0)^∞(cos(nπ))/(3^n).
- Question 6The circle C has equation x^2+y^2-6x+8y+21=0. Find the length of the tangent to C drawn from the origin.
- Question 7Evaluate Π_(n=2)^(99)(1-frac1n^2).
- Question 8Find the area of the region enclosed between the graphs of y=|x-1| and y=3-|x-1|.
- Question 9Find the maximum value of f(x,y)=-2x^2-y^2+8x+6y-5.
- Question 10Find the coefficient of x^5 in the expansion of (1+x)^3(1+2x)^4.
- Question 11For how many integer values of k does the equation x^3-3x^2=k have three distinct real solutions?
- Question 12A quadratic curve has a minimum point at (2,-3) and passes through (0,5). What is the coefficient of x^2?
- Question 13Given that log_a b=3 and log_b c=4, find log_a c.
- Question 14How many solutions does 2sin^2 x=sin x+1 have in the interval 0≤ x<2π?
- Question 15Let F(n)=∫_0^n(2x-1) d x for positive integers n. What is the largest n for which F(n)<90?
- Question 16How many real solutions does 9^x-10·3^x+9=0 have?
- Question 17The parabola y=x^2 is rotated 180°about the origin and then translated by the vector binom20. What is the equation of the resulting curve?
- Question 18Evaluate cos^2 1°+cos^2 2°+cos^2 3°+…+cos^2 89°.
- Question 19The region between the curves y=x and y=x^3 for 0≤ x≤1 is divided by the vertical line x=a into two parts of equal area. Which equation…
- Question 20The line L is a tangent to the curve y=x^4-4x^3+8x at two distinct points. Find the y-intercept of L.