By Alfred S. Posamentier

Designed for high-school scholars and academics with an curiosity in mathematical problem-solving, this stimulating assortment comprises greater than three hundred difficulties which are "off the overwhelmed direction" — i.e., difficulties that provide a brand new twist to widely used themes that introduce unusual subject matters. With few exceptions, their answer calls for little greater than a few wisdom of common algebra, although a touch of ingenuity could help.

Readers will locate right here thought-provoking posers concerning equations and inequalities, diophantine equations, quantity conception, quadratic equations, logarithms, mixtures and chance, and lots more and plenty extra. the issues diversity from relatively effortless to tough, and plenty of have extensions or diversifications the writer calls "challenges."

By learning those nonroutine difficulties, scholars won't in basic terms stimulate and advance problem-solving abilities, they're going to collect beneficial underpinnings for extra complicated paintings in mathematics.

**Read Online or Download Challenging Problems In Algebra PDF**

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**Additional info for Challenging Problems In Algebra**

**Example text**

Find an equation of the plane (in R3) that contairu the points (1, 0, 0), (0, 1, 0), and {0, 0, 1). 15. The equation of a plane in R3 is 3x I 2z = 1. Give a point-normal form for this y equation. 16. A plane (in R3) has equation {2, -1, 3) equation in standard form. o ((x, )I z) - ( -1, 3, 0)) - 0. Give this 17. Find an equation of the line in R 3 that completely contains the vector v - (1, 0, 2). + t(O, 1, 0) and 18. Determine the point (in R3) of intersection of the line x(t) - (1, 0, 1) the plane x I y I z; - 0.

29. - + j 0 x1 x4"5 =3 30. Find the midpoint of the line segment that joins (2, 1, 3, 5) with (6, 3. 2, 1). 31. Prove the properties ofTheorem 2. 32. The angle bt:twt:t:n two nonuro v«tors u and v in R"' is defined to he the unique number 9, 0 :s; 8 :s; 'If radians such that cos 8 Find the cosine of the angle between the vectors (3, 1, 1, 2, 1) and (0, 2, 1, 2, 0). CIIull llvll). 33. Prove the properties ofTheorem 3. 34. Describe the plane determined by the points (3, 1, 0, 2, 1), (2, 1, 4, 2, 0), and (-1, 2, 1, 3, 1).

33. Jx2 I y 2 I c1x I CzY I c3 = 0. Suppose the points (1, 1), (0, 2), and (k, 1) lie on the same circle. Solve for the equation of the circle when k = -1, 0, 1, 2, and 3. ) For what values of k is there no solution? 34. Use a CAS or a graphing calculator to plot the points and corresponding solution for the given values of kin Exercise 33. 35. Since a CAS can perform symbolic manipulation, solve directly for the: equation of the circle: with points ( 2, 0), (1, 3), (5, k). For what value of k is there no solution?