tmua.fyi Paper 1 Challenge 1
20 questions · 75 min · Difficulty 25 · by tmua.fyi
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
Questions in this paper
- Question 1The positive real numbers x and y satisfy log_2 x+log_4 y=4 and log_2 y+log_4 x=5. Find the value of log_2(xy).
- Question 2A circle passes through the three points (0,0), (6,0) and (0,8). Find the length of the tangent drawn from the point (10,10) to this circle.
- Question 3Find the coefficient of x^5 in the expansion of (1+x)(1-2x)^7.
- Question 4A geometric series has all terms positive. The sum of its first two terms is 10 and its sum to infinity is 18. Find the least value of n…
- Question 5How many solutions does the equation tan x=2sin x have in the interval 0°<x<360°?
- Question 6Find the minimum value of (x^2+x+4)/(x) for x>0.
- Question 7Find the area of the finite region enclosed between the curves y=4-x^2 and y=x^2-4.
- Question 8The cubic x^3+ax^2+bx+6 has x=1 and x=2 among its roots. Find its third root.
- Question 9Find the complete set of values of x satisfying (x-1)/(x-2)≥2.
- Question 10How many four-digit whole numbers have digits that are strictly increasing from left to right (for example, 1358)?
- Question 11How many integers n with 1≤ n≤100 are such that n^2+n+1 is divisible by 3?
- Question 12As θ varies over all real values, the expression (10)/(2+cosθ) takes a maximum value and a minimum value. Find the sum of these two values.
- Question 13Find the largest integer x for which 2^x>3^(x-1).
- Question 14The points A(1,1) and B(5,3) lie above the x-axis. A path runs from A to a point P on the x-axis and then to B. Find the least possible…
- Question 15Evaluate Σ_(r=1)^(20)(2r-1)^2.
- Question 16The function f is defined for all real x≠3 by f(x)=(2x+1)/(x-3). Which value can f(x) never take?
- Question 17Find the term independent of x in the expansion of (2x^2-frac1x)^6.
- Question 18The curve y=x^3+ax^2+bx has a point of inflection at (1,0). Find the gradient of the curve at that point.
- Question 19How many real solutions does the equation |x^2-4|=x+2 have?
- Question 20The function f is defined for x≥3 by f(x)=x^2-6x+11. Find f^(-1)(6).