MioMath 2024 Paper 1
20 questions · 75 min · Difficulty 56 · by MioMath
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Questions in this paper
- Question 1Solve the equation log_4(3x-1)^2=(log_4(12x-4))/(log_4(3x-1)).
- Question 2Find the number of real solutions to the equation 8·3^(2x)+27·2^(2x)=32·6^x.
- Question 3Which of the following is equal to (√(3)+√(2))^6-(√(3)-√(2))^6
- Question 4Given that θ^2≤2π and sin(θ^2)=(1)/(2) find the product of all possible solutions for θ.
- Question 5Given (1)/(1-sinθ)=5 find Σ_(r=1)^∞cos^r(θ+(π)/(2)).
- Question 6A square has side length 1. Find the largest possible area of an equilateral triangle inscribed in the square.
- Question 7Find the number of points (x,y) where x and y are integers, such that y≥|x| and y+|x|≤20
- Question 8Find the number of intersection points between y^2-x^2=0 and y=x^3-x^2-8x+14
- Question 9Let R be the set of all points (x,y) in the xy-plane such that: (x+y)^2-6(x+y)+8≤0, (x-y)^2+4(x-y)+3≤0. (Note: The boundaries of the region…
- Question 10Given real numbers p,q,r such that p+q+r=0 and 0<r<p, find the number of solutions of the equation psin^2θ+qsinθ+r=0 within the interval…
- Question 11Given a geometric sequence S_n=\a_n\ such that: a_1+a_2+…=1 and a_1-a_2+a_3-a_4+a_5-…=2 find the value of the summation…
- Question 12Given the equations of two curves: y=x^3-x^2-7x+19 and y=x+7 How many regions do these two curves divide the plane into?
- Question 13Given b>1 and the following equations: y=ax^2+b and x^2+y^2=1 Let P and Q be the only two distinct intersection points of the circle and…
- Question 14Circle C_1 has the equation (x-3√(2))^2+(y-3√(2))^2=18. A new circle, C_2, is drawn so that it passes through the point (0,3√(2)) and is…
- Question 15Point S lies on the line y=(1)/(2)x with OS=2√(15). Point T lies on the x-axis, with ST=4, and ∠ OTS>∠ OST. Find the area of △ OST.
- Question 16The curve C is defined as y=x^3-x+17. The tangent and the normal to C at the point where x=-1 form a triangle with the y-axis. Find the…
- Question 17ABCD is a cyclic quadrilateral. The lengths of its sides are AB=x, BC=2x+1, CD=3x+8, and DA=4x-1. Angle DAB is a right angle. Find the…
- Question 18Let O be the center of a circle, and M be a point outside the circle. Two tangents are drawn from M to the circle O, touching the circle at…
- Question 19Find the area enclosed by the curves y=p|x|-p y=-(1)/(p)|x|+p when p is a positive constant.
- Question 20Let f(x) be the greatest integer less than or equal to x e.g. f(4)=f(4.9)=4 Evaluate ∫_0^(50)lfloor√(x)rfloord x.