Juan Set 1 Paper 1
25 questions · 94 min · Difficulty 47 · by Juan
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
Questions in this paper
- Question 1The numbers 2, 3, 4, 5, 6, 7, 8 and 9 are to be placed into the boxes below, one different number per box, so that all the equalities hold…
- Question 2Let a, b, and c be distinct digits such that a· b<45<b· c<50<a· c. What is a+b+c?
- Question 3Let a, b, c, d be positive integers, and let M=6^a·5^b, N=10^c·9^d be positive integers such that gcd(M,N)=2^3·3^2·5, lcm(M,N)=2^5·3^3·5^5…
- Question 4Five distinct prime numbers have a sum equal to 100, and their product is equal to the six-digit natural number ABCABC (where the digits…
- Question 5Let x be a real number different from -1, 0, and 1. Consider the set \x^3,x^2,x,-x,-(1)/(x)\. When the elements of this set are ordered…
- Question 6Let a and b be positive real numbers, and consider the equations x^2+ax+b=0, ax^2+(b+3)x+a=0. Given that the solution set of each of these…
- Question 7Let P(x) and Q(x) be polynomials with real coefficients such that P(x)+Q(x) is a second-degree polynomial, and P(x)· Q(x…
- Question 8For an arithmetic sequence (a_n), it is given that a_1· a_2· a_3=2, a_2· a_3· a_4=14. What is the product a_3· a_4· a_5?
- Question 9Let n be a positive integer. In the expansion of (x^2+x)^n the coefficient of the term with x^(19-n) and the coefficient of the term with…
- Question 10Sena has chosen a series A consisting of three films and a series B consisting of another three films, so that she can watch a different…
- Question 11A shopping mall has two entrance gates. In front of the first gate there are 2 parking lots named Blue and Red; in front of the second gate…
- Question 12Let a and b be non-consecutive positive integers such that ln(a!)=ln(b!)+3ln2+2ln3+ln7. What is a+b? (Note that n!=n·(n-1)·(n-2)…3·2·1)
- Question 13Let a be a nonzero real number and b, c be real numbers. For the function f defined on the set of real numbers by f(x)=ax+b, and its…
- Question 14Let a and b be real numbers. The function f, defined on the set of real numbers by f(x)= x^2-ax+6,&x≤ a, 2x+a,&a b is known to be…
- Question 15Let n be a positive integer and a a nonzero real number. For a polynomial function f of degree n with leading coefficient a, it is given…
- Question 16In the coordinate plane, for the function y=f(x), it is given that: - the tangent line to the graph at the point (2,f(2)) is y=3x-1, - the…
- Question 17Let a be a positive real number such that ∫_1^4(a√(x)+x√(a))d x=(59)/(3)a. What is a?
- Question 18Let f be a function defined and continuous on the set of real numbers, and let g be defined by g(x)=2x+2. It is given that ∫_(-1)^1f(g(x))d…
- Question 19Which of the following is the simplified form of the expression below? (1-cos(4x))/(sin(4x)+2sin(2x))
- Question 20Let x, y, z be distinct elements, one each, of the set \(π)/(4),(3π)/(4),(5π)/(4)\, such that sin x<tan y<sec z. Which of the following is…
- Question 21Bonus question. Let a triangle ABC have side lengths |BC|=a units, |AC|=b units, and |AB|=c units, satisfying 2a^2=2b^2+2c^2+3bc. Given…
- Question 22Bonus question. Let 0<x<(π)/(2) satisfy 2cos^2x+9sin^2x+2sin(2x)=9. What is the value of cot x?
- Question 23Bonus question. Let a and b be positive real numbers. In the coordinate plane, the lines y=-√(3)x and y=ax+b, together with the x-axis…
- Question 24Bonus question. A circle drawn in the coordinate plane is known to satisfy: - it has exactly one common point with the line…
- Question 25Bonus question. In the coordinate plane, translating a point A by 15 units in the negative direction along the x-axis produces a point that…