DPiD Maths Mock Set 1 Paper 1
20 questions · 75 min · Difficulty 67 · by DPiD Maths
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Questions in this paper
- Question 1Let k be a real number. The equation |x^2+3kx|=2k|x-3| has n solutions for a given k. Find the sum of all values of n in \0,1,2,3,4,5\ that…
- Question 2Find the complete set of x for which frac1√(6-log_3(x^4)) is defined.
- Question 3A circle of radius 7 is drawn centred at the origin. How many squares of side length 1 and integer coordinate vertices intersect the…
- Question 4Let x be a real number. Find the maximum value of 3^(6x-2x^2-5).
- Question 5Define P(x)=(x-1^2)(x-2^2)…(x-100^2). How many integers n are there such that P(n)≤0?
- Question 6Find the constant term of (|x|+frac1|x|-3)^3.
- Question 7Real numbers a, b, c satisfy a+b+c=0 with 0<a<c. Find the number of solutions to csin^2θ+bsinθ+a=0 in 0<θ<π.
- Question 8The ellipse is (x^2)/(9)+y^2=1. Given point M(2,0) and point P on the ellipse, find the minimum value of |PM|.
- Question 9Given f(x)=|x^2-10x+13| and g(x)=6x+frac6x. With constant m∈mathbb R, let ε=f(x)-g(m), where ε^2+12ε=0. Find the maximum number of…
- Question 10Let a_n=fracn·2^(n+1)(n+1)(n+2), where n is a positive integer. Find a_1+a_2+a_3+…+a_(254).
- Question 11A curve y=x^2-4x is rotated 180°about the origin, then translated by binom23. Find the equation of the new curve.
- Question 12Suppose x and y are positive reals such that x-y^2=1 and x^2+y^4=41. Find x.
- Question 13A rectangular sheet of paper is folded along its diagonal, making a pentagon that has an area of (11)/(16) of the area of the original…
- Question 14Tom needs to pay £100 for his dinner. He has an unlimited supply of £2 coins and £5 and £10 notes. In how many ways can he pay?
- Question 15What are the last 6 digits of 11×101×1001×10001×11?
- Question 16Let O be the point (0,0). Let A, B, C be three points in the plane such that OA=30, OB=30, and OC=14, chosen so that the area of triangle…
- Question 17Alice and Bob repeatedly flip a fair coin. Alice wins if 1 head followed by 3 tails appears. Bob wins if 5 heads in a row appears. They…
- Question 18Let p(x) and q(x) be two cubic polynomials such that p(0)=-6, q(0)=10, and p(q(x))=q(p(x)) for all real numbers x. Find the ordered pair…
- Question 19An ant starts at the origin, facing in the positive x-direction. Each second, it moves 1 unit forward, then turns counterclockwise by…
- Question 20Ava and Ben play a game on a 12×12 board. For some positive integer k, Ava chooses k squares and writes an A in each of them. Ben then…