Year 12 into 13 Maths Bridging Tasks

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1 Year 1 into 13 Maths Bridging Tasks Topics covered: Surds Indices Curve sketching Linear equations Quadratics o Factorising o Completing the square Differentiation Factor theorem Circle equations Trigonometry Page 1 of 18 14/06/018

2 Contents: As Core Maths Quick Fire Review As Core Maths Quick Fire Review... 5 As Core Maths Quick Fire Review As Core Maths Quick Fire Review As Core Maths Quick Fire Review As Core Maths Quick Fire Review As Core Maths Quick Fire Review As Core Maths Quick Fire Review Page of 18 14/06/018

3 AS CORE MATHS QUICK FIRE REVIEW 1 1. Simplify the following: 3 5 a) 43 b) Factorise the following: a) 4x 5 b) 1x 7x 1 3. Simplify these surds: a) b) 3 4. For y x 5x 6 i) In completed square form ii) As a product of linear factors (factorise) iii) Using your answers to a) sketch the graph clearly labelling the key features 5. Express 4 1 in the form a b Page 3 of 18 14/06/018

4 Answers Review 1 1a 7 b 5/4 a (x - 5)(x + 5) b (4x - 1)(3x - 1) 3a 17 3 b 3 4i iii 5 49 x 4 ii (x + 6)(x 1) Page 4 of 18 14/06/018

5 AS CORE MATHS QUICK FIRE REVIEW 1. Without using a calculator and showing all of the working, find a value for the following a) b) Sketch the following graphs on the same axes a) y 3x y x b) Solve the equation: x 3x c) Use your answers to a) and b) to solve the inequality x 3x 3. Rationalise the denominators: a) 3 3 b) c) Expand and simplify ( x 3)( x )( x 1) Page 5 of 18 14/06/018

6 Answers Review 1a 3 b a) b x = 1 or x = -4 c x < 4 or x > 1 3a 6 9 b 5 1 c x x 7x 6 Page 6 of 18 14/06/018

7 AS CORE MATHS QUICK FIRE REVIEW 3 1. Express 5 3 in the form a b c. Sketch the following graphs y 4 x and y x 1 the same axes labelling all important features. Hence solve the inequality 4 x x 1 3. The equation y x 5x c has two distinct real roots. a) Write down the discriminant b) Hence or otherwise find all of the values of c for which this is true 4. Find the equation of the line that is parallel to 1 y x 3 and passes through the point (,-1) 5. Find the value of the gradient of the curve 4 3 y 3x 7x x 3 at the point x 1 6. a) Find the equation of the circle with centre (4, 3) and radius 5. b) Find the co-ordinates of the points where the circle cuts the x axis. Page 7 of 18 14/06/018

8 Answers Review x 1 3a D = 5 8c b 5 c 8 4 y = x 4 5 dy 1x dx dy 31 dx 3 1x so when x -1 6a 4 y 3 5 x b (0,0) and (8,0) Page 8 of 18 14/06/018

9 AS CORE MATHS QUICK FIRE REVIEW 4 1. Differentiate the following functions with respect to x a) 1 y x 3 x 1 b) y 4x 3 5x c) y 4 4x. What are the gradients and intercepts of the following straight lines: a) x y 5 x 1 b) 5 y Page 9 of 18 14/06/018

10 Answers Review 4 dy 1a x 3 dx dy b 1x 5 dx c dy dx 8x a m = 1 c = 5 b m = c = Page 10 of 18 14/06/018

11 AS CORE MATHS QUICK FIRE REVIEW 5 1. Sketch y ( x ) labelling the important features 3. For the function f ( x) x 3x 4x 1 a) Find f ( 1), f ( ) and f ( 3), hence find a factor of f (x) b) Use your answer to a) to fully factorise the function f (x) c) Solve the equation f ( x) 0 Page 11 of 18 14/06/018

12 Answers "Beauty is the first test: there is no permanent place in the world for ugly mathematics." Godfrey Harold Hardy Review a f(-1) = 1 f(-) = 0 f(-3) = -30 factor is (x + ) b (x + )(x + 1)(x 6) c x = -1, 6, - Page 1 of 18 14/06/018

13 AS CORE MATHS QUICK FIRE REVIEW 6 1. A circle has the equation x y 4x y 4 0 (a) Write the equation in the form x a y b r [] (b) Hence write down the radius, and the coordinates of the centre.. Two numbers differ by 1 and have a product of 10. If n is the smallest number. a) Explain why n n 10 0 b) Find the exact values of the two numbers 3. ( x 1) is a factor of the equation 3 x x 5x ax 6 f a) Use the factor theorem to find a. b) Fully factorise and solve the equation f x 0 4. A quadratic function has vertex at,1 express the function in the form f x x bx c 5. Simplify and hence solve the equation x 1 x 3 x 3 x 5 0 Page 13 of 18 14/06/018

14 Answers Review 6 1a ( x ) ( y 3) 3 b r = 3, centre = (, -1) a a n = 1 and an = 10 so 10 n 1 n b 1 41 n = therefore n n a a = -1 b f(x) = (x + 1)(x + 3)(x+), so roots x = -, -1, 4 y ( x ) 1 x 4x 5 5 x = -3, 3 Page 14 of 18 14/06/018

15 1. The diagram shows a triangle ABC. AS CORE MATHS QUICK FIRE REVIEW 7 The lengths of AC and BC are 4.8 cm and 1 cm respectively. The size of angle BAC is 100. a) Show that angle ABC = 3. correct to 3 significant figures. b) Calculate the area of triangle ABC, giving your answer correct to 3 significant figures. Page 15 of 18 14/06/018

16 Answers Review 7 1a as given b area = 4.1 Page 16 of 18 14/06/018

17 AS CORE MATHS QUICK FIRE REVIEW 8 1. Solve a) cos x = 0.4 for 0 < x < 70. b) sin x = -0.3 for 0 < x < 360. c) tan x = 1.6 for -360 < x < 360. d) sin 3x = 0.76 for 0 < x < In a quadrilateral ABCD, BC = 6. m, AD = 1.5 m, CD = 8.7 m, angle ABC = 6 and angle ACB = 49. a) Calculate the length of the diagonal AC, correct to 1 d.p. b) Show that angle ADC = 5, to the nearest degree c) Calculate the area of the triangle ADC correct to 3 s.f. Page 17 of 18 14/06/018

18 Answers Review 8 "The more you know, the less sure you are. Voltaire 1a x = 66.4, 93.6, 46.4, b x = 197.5, 34,5 c x = -30, -1, 58, 38 d x = 16.5, 43.5, 136.5, a find angle BAC = 69 deg, then sine rule gives AC = 5.9 b use cosine rule, answer as give c Area = 3.0 Page 18 of 18 14/06/018

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