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. a. x=13 restriction: x>5 b. x=-119 restriction: x4 Part IV – Trigonometry: 1) answers on solution sheet. 2) a) PA= 50°            b) PA= 340°     c) PA=140 d) PA= 212°      e) PA= 110°      f) PA= 250°       RAA= 50°             RAA= 20°         RAA= 40 RAA= 32°         RAA= 70°           RAA= 70° 3. a) 410, -310 b) 700, -20 c) 500, -220 d) 212, -508 e) 470, -250 f) 250, -110 4) a) sinθ= 2/5       cscθ= 5/ cosθ= √21/5   secθ= 5/√21     tanθ=2/√21   cotθ= √21/2 b) tanθ= 8/7         cotθ= 7/8     cosθ= 7/√113   secθ= √113/7     sinθ= 8/√113   cscθ= √113/8 c) secθ= 6/5         cosθ= 5/6     cscθ= 6/√11     sinθ= √11/6     cotθ= 5/√11     tanθ= √11/5 5. a) 51.3 b) 14 c) 31 6. a) 22.86, 157.14 b) 151.52, 208.48 c) 36.71, 143.29 d) 78.17, 258.17 7) a) cos 45°= 1/√2      b) tan 30°=[pic]     c) csc 45°= √2      d) sec 60°= 2 8) a=7.98 B= 18.54° C= 136.46° Part V – Periodic Functions: |Function |Amplitude |Period |Phase Shift |Axis of Function |Max |Min | | | | |(with direction) |(As an equation) | | | |y = 2sinӨ +5 |2 |360° |0 |y = 5 |7 |3 | |y = ¼cos(2Ө-60°) |¼ |180° |30° right |y = 0 |¼ |-¼ | |y = 5cos3(Ө- 45°) -7 |5 |120° |45° right |y = -7 |-2 |-12 | 2. a) Transformations: Vertical stretch by a factor of 2. Vertical translation up 1 unit. Phase shift 30° left. b) Transformations: Vertical compression by a factor of 2. Horizontal stretch by a factor of 3. Vertical translation 2 units down. Phase shift 60° right. 3.a) the function is y = 2sin [3(Ө - 15°)] – 1 b) the function is y = 3cos [2(Ө + 45°)] 4. a) y = -cos (Ө - 90°) + 1 , y = sin Ө + 1 b) y = 2cos (Ө - 150°), y = 2sin(Ө – 60) 6. a) Let “h” represent the height in metres Let “t” represent the time in seconds h(t) = -20cos (2t) +22 b) the height of the passenger at 90 seconds is 42 m. Part VI – Exponential Functions: 1. a) -63x-6y3 b) -4p10q8r12 c) 9 d) [pic] 2. [pic] 3. a) [pic] b) [pic] c) – 4 d) 81 4. a) y=1, y=0, xЄR, y>0, graph is increasing b) same as 4a) only graph is decreasing 5. a) vertical stretch X 2 b) vertical compression X [pic], horizontal shift 4 right, vertical shift up 2 #6) 28697814 #7) a) 2000 b) 5334 c) 98 Part VII – Sequences and Series: 1. a) t(n) = 6n + 1 b) Neither c) t(n) = 4(1/3) n – 1 d) t(n) = 2(-2) n – 1 2. 4.2, 2.7, 1.2, -0.3, -1.8, … 3. 3, 1.5, 3/4, 3/8, 3/16, … 4. -21, -19, -17,… 5. There are 15 terms in the sequence. 6. S11 = 253 7. Sn = 13,120 8. There are 1180 seats in the theatre. Part VIII – Financial Applications: 2.B) $983.40 3. $5,861.77 4.A) $19,319.05 B) $16,327.36