Zetta Paper 1
19 questions · 71 min · Difficulty 48 · by Zetta
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
1 question has been withdrawn and is left out of practice sessions.
Question paper ↗Answer key ↗Original question paper (before corrections) ↗Original mark scheme (before corrections) ↗R2Drew2 Video ↗
Questions in this paper
- Question 1Given that ∫_1^a(ax+2) dx=(5√2)/(2)-2, find the value of a.
- Question 2Given that the points (-2,0), (-frac12,(√3)/(2)) and (-frac12,-(√3)/(2)) all lie on the circle C with radius r and centre (a,0). Find r-a.
- Question 3What are the solution(s) to ln(x^2+4x-90)=ln(-2x+1) for all real x?
- Question 4You are given that p(x)=-6+x+x^2+x^3+x^4+x^5+…. Find the value of x such that p(x)=0.
- Question 5After Euclid High School's last basketball game, it was determined that frac14 of the team's points were scored by Alexa and frac27 were…
- Question 6Evaluate Σ_(n=1)^(6000)frac1n(n+1).
- Question 7Let A(n) be the area of a regular polygon with n sides, each of length 1, where n≥3. Find, in terms of n, an expression for…
- Question 8Which of the following expressions is closest to the value of √(100001)-√(100000)?
- Question 9A circle of radius r is dropped into the curve y=x^2 such that it only touches the curve. The circle's centre is (0,c). Express c in terms…
- Question 10Simplify √(3-2√2).
- Question 11Withdrawn
- Question 12Xander rolls 3 fair six-sided dice. Given that at least 2 of them show a 3, what is the probability that the third also shows a 3?
- Question 13In the cube ABCDEFGH with opposite vertices C and E, J and I are the midpoints of segments FB and HD, respectively. Let R be the ratio of…
- Question 14The graph of tan(x^2+y^2)=1 is shown below (angles in radians). The graph consists of a central circle surrounded by infinitely many…
- Question 15Given that x is in radians, write sin(2arctan(x)) without using trigonometric functions.
- Question 16a, b and c are positive integers so that (frac ac+frac ab+1)/(frac ba+frac bc+1)=17. How many solutions are there to the inequality…
- Question 17Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent…
- Question 18Let S be the set of all points with coordinates (x,y,z), where x, y, and z are each chosen from the set \0,1,2\. How many equilateral…
- Question 19Find the number of integer values of k in the range -500≤ k≤500 for which the equation log(kx)=2log(x+2) has exactly one real solution.
- Question 20Given that f(x)=x^(2008)-2x^(2007)+3x^(2006)-4x^(2005)+…+2007x^2-2008x+2009 and that g(x)=(2012x+2009)/((1+x)^2), which of the following is…