tmua.fyi Paper 1 Challenge 2
20 questions · 75 min · Difficulty 41 · by tmua.fyi
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Questions in this paper
- Question 1The diagram shows the graph of y=f(x), where f(x)=(x-1)^2(x+2). Find the complete set of values of k for which the equation |f(x)|=k has…
- Question 2The diagram shows the two tangents drawn from the origin O to the circle of radius 2 with centre C=(3,4), touching it at P and Q. What is…
- Question 3Let n be an integer greater than 6 for which n-1 and n+1 are both prime. What is the largest integer that must be a factor of n^2(n^2+16)?
- Question 4How many solutions does sin3x=cos2x have for 0≤ x≤2π?
- Question 5Evaluate ∫_0^1 x(1-x)^7 d x.
- Question 6How many distinct tangents to the curve y=x^3-3x pass through the point (0,2)?
- Question 7How many ordered pairs (a,b) of non-negative integers satisfy √ a+√ b=√(2009)?
- Question 8The real numbers x,y and z satisfy x^3+y^3+z^3-3xyz=1. What is the smallest possible value of x^2+y^2+z^2?
- Question 9The line y=mx+1 is a tangent to the circle x^2+y^2-6x+8=0. What is the sum of the possible values of m?
- Question 10Which sketch shows the graph of y=frac1x^2-1?
- Question 11Find the set of real values of x for which |x-2|<|2x+1|.
- Question 12The trapezium rule with two strips of equal width is used to estimate ∫_1^3frac1x d x, as shown. Which statement is correct?
- Question 13Two circles, of radii 1 and 2, touch each other and both touch the line ℓ. A third circle lies in the region between them, touching both…
- Question 14Find the sum of the real solutions of 4^x-3·2^(x+1)+8=0.
- Question 15Find the total area of the regions enclosed between the curve y=x^3-x and the line y=3x.
- Question 16A chord of length 6 is drawn in a circle of radius 6. The minor segment cut off is shaded. What is the area of the shaded segment?
- Question 17How many ordered pairs (m,n) of positive integers satisfy m^2-n^2=2025?
- Question 18An angle θ satisfies sinθ+sin^2θ=1. Find cos^2θ+cos^4θ.
- Question 19Find the complete set of values of k for which the equation x|x|-2x+k=0 has three distinct real roots.
- Question 20The diagram shows the graph of y=ax^2+bx+c. Which of the following is true?