sat數(shù)學(xué)考試試題-資料下載頁
2025-04-04 02:49本頁面
【正文】 (d)15 (e) 9Question 10: The inequality |2x 1| 5 must be true in which one of the following cases? I. x 5 II. x 7 III. x 01. Three unit circles are arranged so that each touches the other two. Find the radii of the two circles which touch all three.2. Find all real numbers x such that x + 1 = |x + 3| |x 1|.3. (1) Given x = (1 + 1/n)n, y = (1 + 1/n)n+1, show that xy = yx. (2) Show that 12 22 + 32 42 + ... + (1)n+1n2 = (1)n+1(1 + 2 + ... + n). 4. All coefficients of the polynomial p(x) are nonnegative and none exceed p(0). If p(x) has degree n, show that the coefficient of xn+1 in p(x)2 is at most p(1)2/2. 5. What is the maximum possible value for the sum of the absolute values of the differences between each pair of n nonnegative real numbers which do not exceed 1?6. AB is a diameter of a circle. X is a point on the circle other than the midpoint of the arc AB. BX meets the tangent at A at P, and AX meets the tangent at B at Q. Show that the line PQ, the tangent at X and the line AB are concurrent.7. Four points on a circle divide it into four arcs. The four midpoints form a quadrilateral. Show that its diagonals are perpendicular.8. Find the smallest positive integer b for which 7 + 7b + 7b2 is a fourth power.9. Show that there are no positive integers m, n such that 4m(m+1) = n(n+1). 10. ABCD is a convex quadrilateral with area 1. The lines AD, BC meet at X. The midpoints of the diagonals AC and BD are Y and Z. Find the area of the triangle XYZ. 11. A square has tens digit 7. What is the units digit?12. Find all ordered triples (x, y, z) of real numbers which satisfy the following system of equations:xy = z x yxz = y x zyz = x y z 第 11 頁 共 11 頁
數(shù)學(xué)相關(guān)推薦
鄂ICP備17016276號(hào)-1