Math Grade 11 Exam

MCR 3U Exam Review – Answers
Part I - Algebraic Skills Review

  1. a)   (9x2+4)(3x+2)(3x-2) b)   (x-4)(x+3)     c)   (3x+2)(x-9) d)   (5x-4y)2

2. a)   (x+6) x≠±2
      (x-2)
b)   (x+2) x≠-3/2,   x≠1
      (x-1)
                            c)     4h (h+5)   h≠5,   x≠4,   x≠± 2/5
    (h-4)(5-2h)

d)   (x-4) x≠ ±3,   x≠ ±4 e)   [pic]   ,   [pic]
                      (x-3)

                      f)     2x2 + 5x - 9     x≠-3,   x≠±1
      (x+3)(x-1)(x+1)

3. a)   (x2+y2)(x+y)(x-y)       =       (x+y)(x-y)       =     (x+y)2
            (x+y)2                           (x+y)2(x-y)2             x2+y2


Part II – Functions & Transformations

1. a) Base Curve: y = x3
      Transformations:
Vertical stretch by a factor of 2
Translate horizontally by 3 units right
Translate vertically by 1 unit up

      1. b) Base Curve: y = √x
    Transformations:
Reflection in the x-axis
Horizontal compression by a factor of 2
Translate horizontally by 2 units right
          Translate vertically by 1 unit down

      1. c) Base Curve: y = |x|
    Transformations:
Reflection in the y-axis
Translate horizontally by 3 units left
Translate vertically by 1 unit up

      2. [pic]
      3.
      a) D: {x | x = -3, -1, 1}; R: {y | y = 4, 6, 2, 5}; NOT A FUNCTION
      b) D: {x | x ≥ -2, x [pic] [pic]}; R : {y | y ≥ [pic], y [pic][pic]}; FUNCTION
      c) D: {x | 3.5 ≥ x ≥ -3.5, x [pic][pic]}; R : {y | 3.5 ≥ y ≥ -3.5, y [pic][pic]}; NOT A FUNCTION


      4.
      a) Vertex: (4,3)
      b) Vertex: (-4,3)
      c) Vertex: ([pic])
      5.
      a) x = 6, x = -1
      b) x = [pic]
      c) x = [pic]


      6. If [pic] > 0, then there are 2 real number solutions. If [pic] = 0, then there is 1 real number solution. If [pic] < 0, then there are no real number solutions.

Part III – Radicals:
      1. a. [pic] b. [pic] c. [pic] d. [pic]
        2. a. [pic]     b.[pic] c.   [pic] d.[pic] e. [pic]
      3....