Cracking The SAT Premium

12. D First, rewrite the equations so that they are in the slope-intercept form of a line, y = mx +

b,  where   m   =   slope.  The first   equation    becomes 3y  =   –x  +   42  or  y   =   – x +   14. The slope   of

this    first   line    is  therefore   – . The second  equation    becomes –y  =   –3x +   8   or  y   =   3x  −   8.  The

slope   of  this    line    is  therefore   3.  The slopes  of  the two lines   are negative    reciprocals of  each

other,  which   means   that    the two lines   are perpendicular   to  each    other.  The correct answer  is

(D).

13. 
    

    C The graph crosses the x-axis at three distinct points. When the function is set to 0, there
    should be three real solutions for x. Use Process of Elimination to solve this question. Set
    the equation in (A) to 0 to get 0 = (x − q)^2 . In this equation, the root is at x = q, thereby
    providing only one real value for x. Eliminate (A). Set the equation in (B) to 0 to get 0 = (x
    − q)(x + s). The solutions for this equation are x = q or x = –s. Therefore, there are only
    two real solutions for x. Eliminate (B). Set the equation in (C) to 0 to get 0 = (x − r)(x + s)
    (x + t). The solutions for this equation are x = r, x = –s, and x = –t. Therefore, there are
    three real solutions for x. The correct answer is (C).

    
    


14. 
    

    C When the quadratic is set to 0 the parabola crosses the x-axis at (–20, 0) and (20, 0).

    
    

Because parabolas   are symmetrical,    the vertex  of  the parabola    is  at  (0, 40).    Plug    this    point

into    the equation    to  get 40  =   a(0 –   20)(0   +   20).    Simplify    the right   side    of  the equation    to  get

40  =   a(–20)(20)  or  40  =   –400a.  Solve   for a   to  get a   =       =   – . Therefore,  the correct

answer  is  (C).

15. B The line shown has a negative slope. Because the graph transformation asks for the negative
    value of the transformed function, the resulting graph must have a positive slope. Therefore,
    eliminate (A). Graph transformation rules state that if the number is within the parentheses,
    then the graph moves left or right in the opposite direction of the sign, and if the number is
    outside the parentheses, the graph moves up or down in the same direction of the sign.
    Therefore, this line will move 2 to the right, and up 3. To follow the proper order of
    operations, draw out the graph transformation first, and then deal with the negative outside
    the brackets. Move the line two units to the right to get: