Sed (CoderLovesEggs) Paper 2 with Solutions
20 questions · 75 min · Difficulty 75 · by Sed (CoderLovesEggs)
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Questions in this paper
- Question 1The equation x^2+1=c(x+1) has real solutions for x for precisely:
- Question 2The number of solutions to the equation log_2(x^3+2x^2+2x+1)=2log_2(x+1) is:
- Question 3Consider the statements P:∫_0^acos xd x=0; Q:∫_0^asin xd x=0. It follows that:
- Question 4A polynomial function has M maxima, m minima, and R distinct real roots. Which of the following equations is not possible?
- Question 5Let P,Q be two if-then statements. If P is sufficient for Q, then:
- Question 6Let -1≤ k≤1 and a>0. The precise range of a for which there exists a k such that sin(ax)=k has 2 solutions for 0≤ x≤2π is:
- Question 7The side lengths of a right triangle are in arithmetic sequence. Which of the following statements must be true? - I. The perimeter of the…
- Question 8A quadrilateral ABCD satisfies ∠ ABC=∠ BCD. Which of the following (additional) information, taken independently, is sufficient to…
- Question 9A degree 4 polynomial Q(x) satisfies Q(0)=0 and is tangent to y=x at two different points. It follows that the possible numbers of distinct…
- Question 10Consider the following statement: > A function f(x) is uniformly continuous if and only if for all ε>0, there exists δ>0 such that for all…
- Question 11A student attempts to prove the statement > For all primes p>3, p^3-3p^2 has at least 12 factors. Their proof is as follows. - (I)…
- Question 12Consider the n digit number B=b_1b_2… b_n, where each of b_i (1≤ i≤ n) equals either 0 or 1. A student wishes to deduce each digit b_i…
- Question 13Which of the following is a valid counterexample to the following statement? > The difference between the squares of 2 primes has at most 4…
- Question 14An irrational number is a number that cannot be expressed as dfrac pq, where p,q are integers. √2 and log_2 3 are irrational numbers. Let…
- Question 15Let a,b,c be positive integers. Then the equation a^b=2a^c=4b^c
- Question 16Consider the sequence - a_1=k; - a_n=-dfrac12a_(n-1)+3. for some number k. Which of the following must be true? - I. If there exists n>1…
- Question 17The function f(x)=Asin x+Bsin^3x+1 has unknown constants A,B. A student wishes to deduce the values of A and B, thereby deducing f(x). For…
- Question 18Let k be an integer. Approximating ∫_((k-1/4)π)^((k+1/4)π)frac1cos xd x using the trapezium rule with n strips results in an…
- Question 19x,y,z are numbers satisfying |x|+|y|+z P: z^2>y^2; > > Q: if |x|>|z|, then 2y<x+z. It follows that:
- Question 20Consider a set of distinct integers S. An element N in S is S-good if and only if there exist 2 other elements in S that have a mean of N…