Unit 3 Booklet

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(d) (e) (f) y y y (0,4) (0,1) (0,-1) x x x 3. Each of the following parabolas can be represented by an equation of the form y = (x + a) 2 + b, (where a and b are integers). Write down the equation of each one. (a) (b) (c) y y y (1,1) x (2,3) x (3,0) x (d) (e) (f) y y y (-3,2) x (-4,0) x (-5,-3) x (g) (h) (i) y y y x x x Mathematics Support Materials: Mathematics 3 (Int 2) Ð Student Materials 17
B . The nature and coordinates of turning points Exercise 2 y 1. (a) Write down the coordinates of the minimum turning point of this parabola. (b) Write down the equation of the axis of symmetry. (the dotted line). (c) The equation of the parabola is of the form y = (x + a) 2 + b. x Find the values of a and b and hence write down the equation of the parabola. 2. For each of the following parabolas: (i) write down the coordinates of its minimum turning point. (ii) write down the equation of its axis of symmetry. (iii) write down the equation of the function represented by the parabola. (a) (b) (c) y y y x x x (d) (e) (f) y y y x x x 3. Without making a sketch, write down the coordinates of the minimum turning points and the equation of the axes of symmetry of these parabolas. (a) y = (x Ð 4) 2 + 1 (b) y = (x Ð 2) 2 + 7 (c) y = (x Ð 8) 2 + 3 (d) y = (x + 1) 2 + 2 (e) y = (x Ð 1) 2 Ð 3 (f) y = (x + 3) 2 Ð 7 (g) y = (x Ð 5) 2 (h) y = (x + 2) 2 (i) y = x 2 + 3 Mathematics Support Materials: Mathematics 3 (Int 2) Ð Student Materials 18
Page 1 and 2: Students should investigate graphs
Page 3 and 4: E. Trigonometric identities The two
Page 5 and 6: Mathematics Support Materials: Math
Page 7 and 8: ALGEBRAIC OPERATIONS A. Reducing al
Page 9 and 10: 4. By finding a common denominator
Page 11 and 12: 2. Multiply out the brackets: (a)
Page 13 and 14: 7. Find m. For example: if 2 m = 8,
Page 15 and 16: 3. Multiply out the brackets: (a) x
Page 19: A . Recognising quadratics from the
Page 23 and 24: C . Solve quadratic equations graph
Page 25 and 26: 4. The following are harder and tak
Page 27 and 28: 3. Write down the coordinates of th
Page 29 and 30: A . Sine, cosine and tangent graphs
Page 31 and 32: (e) y 20 (f) y 80 180° 360° x 180
Page 33 and 34: C . Solving trigonometric equations
Page 35 and 36: E . Trigonometric identities Exerci
Page 37 and 38: 5. What are the periods of the foll
Page 39 and 40: (c) y (d) y (Ð2,5) (3,Ð1) x x 9.
Page 43 and 44: (f) h Ð g gh (g) 7n + k kn (h) y
Page 45 and 46: Exercise 8 1. (a) 1 (b) 1 (c) 1 (d)
Page 47 and 48: 4. (a) (2,6) (b) x = 2 (c) y = Ð(x
Page 49 and 50: Further trigonometry Exercise 1 1.
Page 51 and 52: Exercise 3 1. (a) 30, 150 (b) 45, 3
Page 53 and 54: Specimen assessment questions 1. (a
Page 55: Mathematics Support Materials: Math

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