Y1 Double Maths Assignment λ (lambda) Exam Paper to do Core 1 Solomon C on the VLE. Drill

Transcription

1 α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω Nature is an infinite sphere of which the centre is everywhere and the circumference nowhere Blaise Pascal Y Double Maths Assignment λ (lambda) Tracking Test next will be in lessons in the week beginning 8 th December. *any typos/wrong answers check with another student then s.cosby@bhasvic.ac.uk with the correct answers questions plus exam style paper and drill Exam Paper to do Core Solomon C on the VLE Drill Section A Solve the following equations on the interval 0 x 60 () sin ( x 90 ) = () cos( x + 80 ) = Section B Solve the following equations for x: () tan ( x ) = () log x = + log x 9 () log x = log x 6 () log x = + log x Section C Solve the following quadratic inequalities: () x x 0 0 () x + 7x + 0 () x 4x + 6 < 0 Section D Sketch the following quadratics, showing the turning points and intercepts: () y = x 6x 0 () y = 4x 4x () y = x 8x + Section E: () Find the shaded area 0.8 c.7 cm () Find the shaded area.4 cm 0.9 c X:\Maths\TEAM - Doubles & Furthers\FMA - Assignments\04-05 assignments\dmy()lambda 4-5

2 MECHANICS Section A C, Mechanics, C4 (a) Dynamics Draw labelled diagrams and form equations for the following situations (i) (ii) An object of mass m kg is being pushed up a smooth slope inclined at θ to the horizontal by a horizontal force of magnitude P N. An object of mass mkg is being pushed up a granite slope inclined at θ to the horizontal by a horizontal force of magnitude P N. The frictional force it suffers is / P N. (b) Kinematics Solve the following suvat problems (i) (ii) (iii) A, B and C are three points on a straight road such that AB = 80 m and BC = 60 m. A car travelling with uniform acceleration takes 4 seconds to travel between A & B, and seconds to travel between B & C. Modelling the car as a particle, find its acceleration and its velocity at A. A balloon which is stationary starts to rise with an acceleration of.5 m s. What is the velocity seconds later? If ballast is dropped at the end of seconds, what will be the velocity of the ballast after a further 4 seconds? A stone is projected vertically upwards from ground level at 0 m s. Find: (A) the height to which the stone rises, (B) the time to reach the greatest height, (C) the height of the stone after.5 seconds, (D) the times when the stone is at a height of 8 m, (E) the total time the stone is in the air, (F) the speed after seconds. (iv) A car accelerates at a constant rate, starting from rest at a point A and reaching a speed of 65 km s in 6 s. This speed is then maintained and the car passes a point B minutes after leaving A. (A) Sketch a speed-time graph to illustrate the motion of the car. (B) Find the distance from A to B. CORE 4 Find the values of the constants A, B, C and D in the identity x x 5 = Ax + Bx + C x + ( )( ) D Express the following as partial fractions x (a) f (x) = (x + )( x ) x + 5x+ 7 (b) f (x) = ( x + ) x 0 (c) f (x) = * ( x )( x + ) * this is an improper fraction X:\Maths\TEAM - Doubles & Furthers\FMA - Assignments\04-05 assignments\dmy()lambda 4-5

3 Section B C, C, Further Pure CORE d y 4 Given that y = cos x + sin x, find dx 5 On the curve with equation ( ) 6 and show that d y dx + 4y = 0 y = x +, the point P has x coordinate of 0. Find the equation of the tangent to the curve at P. 6 The tangent to the curve with equation y = tan x at the point x = π 8 meets the y axis at the point Y. Show that the exact distance OY (where O is the origin) is π. 7 Solve the following equations on the interval 0 θ π. Give exact answers where you can, but otherwise give your answers to sf: (a) sin θ + sin θ = (b) 4 tan x tan x = FURTHER PURE 8 Find the matrix which maps the points (, 0) and (, ) onto the points (6, ) and (5, ) respectively. [Use a proper method, not trial and error or guessing.] 9 Let R be the matrix representing a rotation of 45º anticlockwise about (0, 0). Write down the matrix R and evaluate R. What transformation is R? 0 (a) 4 Find the value of h for which = h 6 (b) 4 a a Find the value of a and b for which = 6 b Find the images of the points (, ), (0, ), and ( 4, ) under the linear transformations with the following matrices: (a) 0 0 (b) (c) 0 Challenge Question (A zeta) If x x + = 0, what is the value of Answers to Drill A: () 5,5 B() x =, () 9 C: () x 5 () x 4, x () x + x () 5,5 () 45, 05, 65, 5, 85, 45 x = 4, () 5.9, < x < X:\Maths\TEAM - Doubles & Furthers\FMA - Assignments\04-05 assignments\dmy()lambda 4-5

4 49 D: () intercepts (0, 0), (5, 0), (, 0), Turning point, () intercepts (0, ), ±, 0, Turning point, () () intercepts (0, ), Turning point (, ) E: () 8.56 cm () 0.4 cm Solomon mark scheme on the VLE Answers to Section A (bi) 0 40 = ms, u = ms a (bii) (biiic) 44.4m (biiid) 5.45s or 0.674s (biiie) 6.s (biiif) () A =, B =, C =, C = 4 v = 0ms (biiia) 45.9m (biiib).06s (a) (b) + + (x + ) ( x ) ( x + ) ( x + ) ( x + ) (c) + ( x ) ( x + ) Answers to Section B ms (bivb) 0855km (4) Proof (5) 8x y + = 0 (6) Proof (7a) π, 7π, π, 9π (7b) x = 0.,.46,.8, 5.96 rad (8) 0 (9) 0, 0, rotation 90º anticlockwise about (0, 0) (0a) h = 5 (0b) a = /8, b = 5/4 (a) (, ), (, 0) (, 4) (b) (, 4), (, 9) ( 7, 7) (c) (, ), (0, ), ( 4, 7) Challenge question ) 7 X:\Maths\TEAM - Doubles & Furthers\FMA - Assignments\04-05 assignments\dmy()lambda 4-5

5 M THS ASSIGNMENT COVER SHEET Name Current Maths Teacher Please tick honestly: Have you ticked/crossed your answers using the answers given? Have you corrected all the questions which were wrong? Yes No - explain why. How did you find this assignment? Use this space to outline any problems you ve had how you overcame them as well as the things which went well or which you enjoyed/learned from. X:\Maths\TEAM - Doubles & Furthers\FMA - Assignments\04-05 assignments\dmy()lambda 4-5