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191031
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A circle with a radius of 12 inches is cut out of a sector with a central angle of 120 degrees. Use the remaining sectors to make a cone. What is the altitude of the cone?
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In the xy-plane, if line k passes through the points (3,-4) and (a,b), where b=4a-16 and a≠3, what is the slope of k?
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OG18-数学分册
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The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac4 3\pi$$, what is the length of line segment RU?
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PREP07 Test 1
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If the average (arithmetic mean) of the 4 numbers n+2, 2n - 3, 4n + 1, and 7n + 4 is 15, what is the value of n?
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If $$x \ge 0$$ and $${x}=\sqrt{8xy-16y^2}$$ , then, in terms of y, x =
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If 3x + 19 = - 3 - x, then x =
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OG18
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If $$(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}) = r(\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})$$, then r =
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OG19 OG20 OG2022
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If($$\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})=r(\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18}$$) ,then r=
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Magoosh
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$$(2\sqrt{3}+\sqrt{5})(2\sqrt{3}-\sqrt{5})$$
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OG17 OG18 OG19 OG20 OG2022
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City X has a population 4 times as great as the population of City Y, which has population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
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Manhattan
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If the price of a certain stock increased by $$\frac{1}{5}$$ during the first month and then decreased by $$\frac{1}{4}$$ during the second month, what was the ratio of the stock price at the end of the two months to the original price?
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190603
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As shown in the figure, ABE and CDE are isosceles triangles, BC and AD are parallel, and the sum of the perimeter of ABE and CDE is 32. What is the range of AB length?
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200301 还原机经选题: 数论&代数
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If s = 1/(1+2+3+4)+1/(1+2+3+4+5)+...+1/(1+2+3+...+98+99), what's the range of s?
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PREP07 Test 1
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The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2 : 3, what is the ratio of the area of region R to the area of region S ?
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181215
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The four sides of the square is tangent to the circle, as shown in the picture. The radius is 0.5. What is the area of the shaded part?
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191020
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A fair coin is tossed twice，what's the probability of getting at least one head?
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191020
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As shown in the figure, a semicircle is spliced with a rectangle. The rectangle is x in width and y in length. If the area of semicircle is 1/3 of the area of rectangle. What is the ratio of the arc of the semicircle to x?
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191020
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Each letter of the word “College” is written on a piece of paper (7 pieces of paper in total). Now just take one piece of papers randomly. What is the probability of getting a letter that happens to appear twice (l or e)?
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Magoosh
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$$If x^{4} = y^{16}$$, then y =
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Magoosh
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k is a positive number. If k is twice its reciprocal, and j is twice k, then jk =
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