MioMath 2024 Paper 2
20 questions · 75 min · Difficulty 59 · by MioMath
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Questions in this paper
- Question 1If a+b, b+c, a-c are all even What can be inferred about the parity of a,b,c?
- Question 2An arithmetic sequence (S_n) is defined by its first term a_1, number of terms n, and common difference d. Consider the following…
- Question 3If the statement P: “For any n such that nnot≡1pmod6, n is not prime” is false, then which of the following is true?
- Question 4Find the number of positive integer solutions for the equation n which satisfy ((n-1)!)!=(n-1)!
- Question 5Laud Polygon: For any interior angle A, there exists an angle B such that B=2A or B=(A)/(2). A polygon is quiet if it is not a laud…
- Question 6For positive integers a, b and c, define three least common multiples: L=lcm(a,b), M=lcm(b,c), and N=lcm(a,c). Which of these is not…
- Question 7Given that 0≤ f(x)≤1 for 0<x<4, and that: ∫_0^2f(x)d x=1 ∫_1^3f(x)d x=1.5 Which of the following are possible values for ∫_0^4f(x)d x? - I…
- Question 8Let P be the statement “f(x) is divisible by (x+2)(x-3)” and Q be the statement “f(x) is divisible by 4x^2-4x-24”. Which option gives the…
- Question 9Which of the following is a necessary but insufficient condition for sin x>(1)/(2)?
- Question 10For a cubic function ax^3+bx^2+cx+d, there are two local extrema, one at x>0 and the other at x<0. What is the necessary and sufficient…
- Question 11Given the function f(x)=x^3+px^2+q, it has a local maximum at x=0 and 3 distinct roots. Find the conditions for p and q.
- Question 12Given a geometric sequence (S_n) with the parity of first term a_1, the parity of the number of terms n, and the parity (odd or even…
- Question 13Given that f'(x) ∫_(1/2)^1f(x)d x - II. ∫_0^(1/2)f(x)d x<∫_0^(1/2)f(x^2)d x - III. f(0)<f(1)
- Question 14Given that f(x)=ax^2+bx+c, which of the following is a sufficient condition for there to be a real number k such that f(|x|)=k has 4…
- Question 15A car starts from depot and moves repeatedly between 4 stations in the following pattern: 1, 2, 3, 4, 3, 2, 1, 2, 3, … It follows the below…
- Question 16Given the sequence u_(n+1)=3u_n-6 with u_n∈mathbb Z, which of the following statements is true? - 1. If 6| u_6, then 3| u_3. - 2. If 10|…
- Question 17Given the function f(x)=(a)/(x)+bx^2, determine which of the following conditions are true if f(x) has a local minimum and a positive root.
- Question 18The expansion of the expression (x^p+(1)/(x^q))^n has a constant term. Which of the following is/are necessary and sufficient conditions…
- Question 19Define the left branch of a quadratic function as the portion to the left of its vertex, and similarly, define the right branch. Let f(x)…
- Question 20Consider the following attempt to solve an equation. The steps have been numbered for reference. Equation: 3cos x=√(x), where x is in…