By Steven A. Leduc
Getting a excessive ranking at the GRE Math topic try isn’t approximately memorizing every thing there's to understand approximately math–it’s approximately focusing on your attempt coaching. We educate you simply the knowledge you’ll desire in addition to the simplest recommendations for the try day. during this publication, you’ll find out how to:
•Use our options and strategies to spice up your accuracy
•Increase your pacing and make yourself familiar with the try structure
•Understand the themes that would probably seem at the test
•Practice and overview the themes which are toughest for you
Cracking the GRE Math, 4th version additionally features a full-length perform GRE Math topic try.
Read or Download Cracking the GRE Mathematics Subject Test PDF
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Additional info for Cracking the GRE Mathematics Subject Test
Jx-1 x2 -1 (D) x -Fx + 1 J; + 2 (A) 7. = o + (C) What' s the equation of all points the xy-plane that are equidistant from the points (-1, 4) and (5, -2)? 2x-y = 3 (B) X - y 1 X+y=3 (D) y = x2 -4x + 1 (E) (x -2)2 (y - 1)2 = 18 in = (A) 8. (C) + Whi c h of the fol l o wi n g best descri b es the graph of the equati o n x2 y2 -2x + 4y + 5 = in the xy-plane? circle (B) parabola ellipse (D) line (E) point + (A) 9. (g o 0 (C) Let C be the curve in the xy-plane described by the equation x2 + 4y2 16. 2 x, y), what is the area enclosed by the resulting curve?
X 18. What are the roots of the following equation? (A) 1, e-2 (B) 1, ); 32 + CRACKING THE GRE MATHEMATICS SUBJECT TEST (log x)2 = 2 log x (C) 1, ezt (D) all x >0 (E) all real x 19. The hyperbolic sine function, denoted sinh, is defined by the equation: e . Find a formula for sinh-1 x. Jx2 + 1 - x ) (A) log(1 - �x2 + (D) log(x � ) 20. The hyperbolic cosine function, denoted cosh, is defined by the equation: 2 If the hyperbolic tangent function, tanh, is defined by tanh x = sinh x find a formula for tanh-1 x.
11 Solution: Sketch the curve y = r(x - 2f We'll begin by finding the first derivative, and then we'll determine where it's zero and where it's positive and negative. By the product rule, we have: y' = x 2 2(x - 2) + (x - 2)2 • 2x = 2x(x - 2)[x + (x - 2)] = 4x(x - 1)(x - 2) • Setting this equal to zero, we see that critical points occur at x = 0, 1, and 2. For x < 0, the sign of y' is negative, so the curve is decreasing; for 0 < x < 1, the sign of y' is positive, so the curve is increasing; for 1 < x < 2, the sign of y' is negative, so the curve is decreasing; and for x > 2, the sign of y' is positive, so the curve is increasing.