Sarah swims in a rectangular-shaped swimming pool 18 feet wide and 24 feet long. About how many feet long is a diagonal of the surface of the water in the pool? 24 F. 21 G. 30 H. 42 J. 441 K. 900 18 ACT Practice Plane Geometry xx a2 + b2 = c2 {Pythagorean Theorem} 182 + 242 = x2 {substituted given values into Pythagorean Theorem} 324 + 576 = x2 {evaluated exponents} 900 = x2 {added 324 and 576} x = 30 {took square root of each side} © Mr. Sims Let a, b, c, and d be positive real numbers such that a10 < b10 < c10 < d10. Which of the numbers a, b, c, or d is the greatest? A. B. C. D. E. ACT Practice Intermediate Algebra All the numbers are shown as being less than d10 a therefore d is the greatest number b c d Cannot be determined from the given information © Mr. Sims What value of x makes the equation 7x – 3(2x – 4) = 10 true? F. -12 G. -2 H. J. 2 − 13 7x – 3(2x – 4) = 10 7x – 6x + 12 = 10 x + 12 = 10 -12 ACT Practice Elementary Algebra {used distributive property} {combined like terms} -12 x = -2 {subtracted 12 from each side} 22 13 K. 22 © Mr. Sims Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 5 and -2x + y = 10 ? A. B. C. D. E. (-3,4) (-1,3) (1,2) (5,0) 35 3 , − x + 2y = 5 -2x + y = 10 10 3 ACT Practice Elementary Algebra 2x + 4y = 10 {multiplied top equation by 2} -2x + y = 10 {bottom equation stays the same} 5y = 20 {added the two equations together} y = 4 {divided each side by 5} x + 2y = 5 x + 2(4) = 5 x+8=5 {top equation} {substituted 4, in for y, into top equation} {multiplied 2 by 4} -8 -8 x = -3 {subtracted 8 from each side} © Mr. Sims ACT Practice Elementary Algebra For nonzero numbers x and y, which of the following −x expressions is NOT equivalent to ? y F. G. −x −y The entire fraction is negative - the negative sign could be on the top, middle, or bottom - therefore it is the same as G and H x −y 𝑥 𝑦 H. − J. −πx πy K. − simplify by cancelling the π’s on top and bottom, then it equals − 1 y x divide by multiplying by reciprocal, −1 ⋅ x y , then it equals − x y x y © Mr. Sims ACT Practice Elementary Algebra 5 1 5 Percent that is shaded 17 = {shaded area divided by total area} 25 = 0.68 = 68% {divided} 1 Area of entire object = 5 x 5 {length x width} = 25 in2 {multiplied} Area of unshaded squares = 8 x 1 {eight 1 in2 squares} = 8 in2 {multiplied} Area of shaded squares = 25 – 8 {total minus unshaded} = 17 in2 {subtracted} {changed to percent moving decimal right two places} © Mr. Sims ACT Practice Intermediate Algebra substitute 3 in and determine which one yields nearly 898 100 ⋅ 33−1 = 100 ⋅ 32 = 100 ⋅ 9 = 900 © Mr. Sims ACT Practice Coordinate Geometry Happy makes as much or more at 2 hours and after Smiley charges $10 for scheduling a party Happy does not charge for scheduling © Mr. Sims
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