A Assignment beta Cover Sheet Name: Question Done Backpack Topic Comment Drill Consolidation i C3 Differentiation trig 4sec xtan x ii C3 Differentiation trig 6cot 3xcosec 3x iii C3 Differentiation trig cosec xcot x i ( 4x 3) 4 + c 6 ii sin( 5x + 4) + c 5 iii cos( 3 4x ) + c 4 3i C Log evaluation - 3ii C Log evaluation 3 3iii C Log evaluation /3 4i sec3x + c 3 4ii ( b ) cos ecx + c 4iii tan x + c a C3 Differentiation all & factorising to sec 7x( 7 cos x tan 7x sin x) b C3 Differentiation all & factorising to 0 c C3 Differentiation all & factorising to x + x + C3 Find normal π x = 3a C4 Finding dy/dx from dx/dy cos y 3b C4 Finding dy/dx from dx/dy y (3sin y + y cos y ) 3c C4 Finding dy/dx from dx/dy cos y 3( + y tan y) 4a C Solving trig equations π, 7π, 3π, 9π 4b C Solving trig equations 0.3 c, 3.46 c,.8 c, 5.96 c 5a C3 Proving trig identities PROOF 5b C3 Proving trig identities PROOF 6 C3 Find normal PROOF 7 C3 Differentiation & factorising to PROOF 8 C3 Algebraic division A =, B = 4, C = 6, D = X:\Maths\TEAM - A\A Assignments 6-7\A Mechanics\MPM()beta 6-7.docx Updated: 5/09/06
M Practice Challenge 9 M Impulse 0.4Ns, 6.33 ms - 0 C TOOLS 5.04 X:\Maths\TEAM - A\A Assignments 6-7\A Mechanics\MPM()beta 6-7.docx Updated: 5/09/06
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω It is a mathematical fact that the casting of this pebble from my hand alters the centre of gravity of the universe. T Carlyle A Maths with Mechanics Assignment β (beta) due w/b 6/9 Come along to the Maths Association Talk 9 th September at 4:30pm in room 3 Geometry Ancient And Modern (It s free! Come along!) Maths Trip: Maths In Action University Lectures in London. 0 a ticket (0 tickets available) 5 th November Maths Trip: Maths In Action University Lectures in London. 0 a ticket (0 tickets available) 4 th December Drill Part A Differentiate the following functions with respect to x: (a) f (x) = sec x (b) f (x) = cot 3x (c) f (x) = cosec x Part B Find the following integrals by considering what has been differentiated (a) ( 4x 3) 3 dx (b) cos( 5x + 4) dx (c) sin( 3 4x) dx Part C Find the exact values of the following (a) log3 (b) log (c) log8 9 8 Part D Find the following integrals by considering what has been differentiated ( a) sec3x tan3xdx (b) cos ecxcot xdx (c) sec xdx Current work. Differentiate the following using the correct notation: (a) f(x) = cos xsec 7x (b) f(x) = tan xcot x (c) y = x x +. Find the equation of the normal to y = cosecx at the point where ( π,) 3. Find dy, in terms of y, given that dx (a) x = tan y (b) x = y 3 sin y (c) x = 3ysec y X:\Maths\TEAM - A\A Assignments 6-7\A Mechanics\MPM()beta 6-7.docx Updated: 5/09/06
Consolidation 4. Solve the following equations in the interval 0 θ π. Give exact answers where you can, but otherwise give your answers to 3sf: (a) 3 sin θ + sin θ = (b) 4 tan θ tanθ = 5. Prove the following identities: (a) sec x + tan x sec x tan x (b) cos(90º x) sinx 6. The maximum point on the curve with equation y = x sin x where 0 < x < π is A. Show that the x coordinate of A satisfies the equation tan x + x = 0. 7. Show that d dx + cot x cosecx = cot x cot x 8. Show that 4x3 6x + 8x 5 can be written in the form Ax + Bx + C + D x + x + where A, B, C and D are constants to be found. M Practice (Preparation for M) 9. Two uniform smooth spheres, A of mass 0.03kg and B of mass 0.kg, have equal radii and are moving directly towards each other with speeds of 7 ms - and 4ms - respectively. The spheres collide directly and B is reduced to rest by the impact. State the magnitude of the impulse experienced by B, and find the speed of A after impact. 0.Challenge Question The area of each large semicircle is. What is the difference between the black and grey shaded areas? x 0. a) Differentiate show all working b) Integrate sec x with respect to x Preparation: Read* about the inverse of functions, the one to one condition for a function to have an inverse. Also transforming graphs including the modulus functions f (x) and f ( x ) and the difference between them C3 new textbook pages 3-30 and 63-8 C3 old textbook pages -8 and 54-7 * you are not expected to work through questions in this preparation section but read the textbook to understand the topic. X:\Maths\TEAM - A\A Assignments 6-7\A Mechanics\MPM()beta 6-7.docx Updated: 5/09/06
X:\Maths\TEAM - A\A Assignments 6-7\A Mechanics\MPM()beta 6-7.docx Updated: 5/09/06