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Question 1. 1. Evaluate (Start a new page) Marks 4.51 174 . correct to 2 significant figures. 15.6 219 . 2. Simplify fully 50 + 98 – 9 2 3. Rationalise the denominator of 1 2 8 62 2 4. Solve 3x² + 4x – 1 = 0 , giving answers in simplest surd form. 3 5. Factorise x3 – 27 1 Question 2. (Start a new page) 1. Solve | 3x – 4 | = 1 – 5x 2. Solve 2x 1 3x 4 – = 5 3 2 3. Solve and graph the solution on a number line: 3 3 3 | 2x + 7 | < 5 4. Simplify fully x 2 49 2 x 2 13x 7 3 2 Question 3. (Start a new page) Marks 1. Determine whether the function f(x) = 7x5 + 5x is odd, even or neither. (Reasons must be shown) 2. If f(x) = x2 + 1 for x 0 1 for 0 < x < 2 3 – x for x > 2 2 (a) Evaluate f( –1 ) – f( 5 ) 1 (b) Draw a neat sketch of this function over the domain –3 x 3 3 2. On separate diagrams, draw a neat sketch of the following ( showing all essential features) (a) y = 3x 2 (b) y = 6x – x2 2 4. State the natural domain of y = Question 4. 1 x2 (Start a new page) 1. Find the value of x correct to 2 decimal places xm 2 2 15·6m 57º 2. Find the exact area of ABC where AC = 6m, BC = 8m and ACB = 45º. 2 3 3. Marks P 16m 17m 39º Find the size of PQR to the nearest minute 2 R Q 3. A man walks 7km on a bearing of 200º T from town A to town B. He then walks 3km due north from town B to town C. (a) Draw a diagram showing his journey. 1 (b) Calculate the distance and bearing of town C from town A. 4 Question 5. (Start a new page) 1. A (–2,–1), B (7,2) and C (–3,4) are the vertices of a triangle. (a) Calculate the length of AB in simplest form. 2 (b) Show that the equation of AB is x – 3y – 1 = 0. 2 (c) Find the perpendicular distance from point C to the line AB. 2 (d) Hence find the exact area of ABC ( in simplest form). 1 2. Shade the region that simultaneously satisfies x + y 5 and y 2 3 3. The lines 3x + 4y = 9 and 2x – 3y = –11 meet at point P. (a) Find the coordinates of P. 3 (b) Find the equation of the circle with centre P and radius 4 units. 1 4. Find the value of k for which the lines 5x – 2y = 0 and 3x + ky = 7 are parallel. 3 4 Question 6. (Start a new page) Marks 1. Find the exact value of sec 135º. 2. Given sin A = 1 3 and tan A < 0, find the exact value of cos A. 7 2 3. Solve the following for 0º x 360º (a) cos x ( 2sin x + 1) = 0 3 (b) sin x = cos x 2 4. Fully simplify the following: sin A 1 sin A + sin A 1 sin A 5. Draw a neat sketch of y = cos x showing all essential features. Question 7. 3 for 0º x 360º 2 (Start a new page) 1. For the arithmetic series 56 + 53 + 50 + ....... (a) Find an expression in simplest form for the nth term. 2 (b) What is the value of the first negative term of the series? 3 2. The second and sixth terms of a geometric series are 2 and 2 125 3 respectively. Calculate the common ratio and the first term. 3. The cost of constructing a multi-storey building is $60 000 for the first floor, $65 000 for the second floor and an extra $5 000 for each successive floor. Calculate the cost of the building if it has 30 floors. 3 5