Victory for the ACT Student Text 15e

464 • C AMBRIDGE P RACTICE T EST R EINFORCEMENT

52. (G) (p. 390) Mathematics/Algebra and Functions/Solving Algebraic Equations or Inequalities with One Variable/ Equations Involving Integer and Rational Exponents . If 2 2 x x 2 1 2 = + − , then x x 2 1 2 + = − . Thus: x x 2 1 2 + + = ( ) ( ) x x 1 1 0 + + = . This equation holds true only if x 1 = − . 53. (E) (p. 390) Mathematics/Algebra and Functions/Evaluating, Interpreting, and Creating Algebraic Functions/Functions as Models . If Joshua is x years old now and Jessica is 3 years younger, then Jessica is now x 3 years old. Four years ago she was ( ) x x 3 4 7 − − = − years old. 54. (F) (p. 391) Mathematics/Algebra and Functions/Evaluating, Interpreting, and Creating Algebraic Functions/Functions as Models . The amount collected is equal to the number of students multiplied by the amount that each student contributed. Therefore: $ x y xy 18 18 students student dollars : And adding three more students, but with all paying one dollar less, changes the equation to ( ) ( ) x y 3 1 18 + − = . 55. (A) (p. 391) Mathe atics/Number and Quantity/Basic Arithmetic Manipulations . First, simplify each radical in the expression: ( ) 2 1 112 2 1 16 7 2 1 4 7 2 7 ^ ^ ^ h h h

28 4 7 2 7

( ) 2 63 2 9 7 2 3 7 6 7 ^ ^ ^ h h h Now, combine the parts as indicated in the stem: 2 1 112 28 2 63 2 7 2 7 6 7 6 7 − + = − + =

The stem asks for the value of x

, so

add the two equations to eliminate the y

variable:

56. (G) (p. 391) Mathematics/Algebra and Functions/Solving Simultaneous Equations .

1 1

1

+ =

x y

4

+ − = 1 1

3

x y

4

2

& x 1

=

=

2

x

57. (D) (p. 391) Mathematics/Geometry/Triangles/Properties of Triangles . The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Check each of the answer choices: A. 1 3 6 >+ 8 B. 2 4 7 >+ 8 C. 2 10 12 > + 8 D. 4 6 8 >+ 9 4 8 6 >+ 9 6 8 4 >+ 9 E. 4 4 10 >+ 8