2019-20 N. American Planner_DP Sample

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USEFUL INFORMATION MATHEMATICAL LAWS, FORMULAE, SYMBOLS MENSURATION Cone Surface area of cone = x r 2 + rs Volume of s cone = r 2 h h 3 r Box Volume = l x w x h Parallelogram D a h A A b l b b B B C a Area of ABCD = bh Triangle C Area of ∆ABC = bh 2 h h w h Cylinder Surface area of cylinder = 2 rh+2 r 2 Volume of cylinder = r 2 h Circle Sphere Circumference Surface area of circle = of sphere = 2 r 4 r 2 r r h Area of circle Volume of r = r 2 sphere = 4 r 3 3 Rectangle Perimeter = 2(l+w) Area = lxw Trapezium B a c h A b D Area of Trapezium ABCD = ½ h (a+b) A c l b w C B a Area of ∆ABC = ab 2 Pyramid Volume of pyramid = Bh h 3 (B = B area of base) Arc r r L Arc length L = r Sector Area A = ½ r 2 QUADRATICS Solution of equation ax 2 + bx + c = 0 is given by the formula x = -b± b 2 -4ac 2a If b 2 - 4ac > 0, 2 solutions If b 2 - 4ac = 0, 1 solution If b 2 - 4ac < 0, no solutions b 2 - 4ac is called the discriminant CALCULUS d (x n ) = nx n-1 ∫x n dx = ( l ) x n+1 + c, n ≠ -1 dx n+1 d (e ax ) = ae ax ∫e ax dx = ( l ) e ax + c dx a d (log e x) = l ∫( l )dx = log e x + c, for x >0 dx x x d (sin ax) = a cos ax ∫sin ax dx = - l cos ax + c dx a d (cos ax) = -a sin ax ∫cos ax dx = l sin ax + c dx a d (tan ax) = +asec 2 ax ∫sec 2 ax dx = l tan ax + c dx a product rule: d (uv) = u dv + v dx dx du dx v dv - u dv quotient rule: d ( u ) = dx dx dx v v 2 chain rule: dy = dy du dx du dx PYTHAGORAS THEOREM c 2 = a 2 + b 2 Cosine Rule: c 2 = a 2 + b 2 - 2ab cos Sine Rule: a = b = c sinA sinB sinC Area of Triangle = ½ b.c.sin COMPLEX NUMBERS z = x + yi = r (cos + isin ) = rcis lzl = x 2 + y 2 = r - < Arg z z 1 z 2 = r 1 r 2 cis( 1 + 2 ) z1 = r1 cis ( - ) 1 2 z 2 r 1 z n = r n cis n (de Moivre’s theorem) FACTORISING a 2 + 2ab + b 2 = (a + b) 2 a 2 - 2ab + b 2 = (a - b) 2 a 2 - b 2 = (a + b) (a - b) a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) a 3 - b 3 = (a - b) (a 2 + ab + b 2 ) ALGEBRA – EXPANDING a (b + c) = ab + ac (a - b) 2 = a 2 - 2ab + b 2 (a + b) 2 = a 2 + 2ab + b 2 (a + b)(a - b) = a 2 - b 2 (difference of two squares) (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (a - b) 3 = a 3 - 3a 2 b + 3ab 2 - b 3 (x + a) n = x n + (n)x n-1 a + (n)x n-2 a 2 + ... ( n )x 2 a n-2 = ( n )xa n-1 + a n 1 2 n-2 n-1 TRIGONOMETRY Sohcahtoa sin = opposite cos = adjacent hypotenuse hypotenuse tan = opposite = sin adjacent cos cos = 1 sec = 1 cot = 1 sin cos tan cos 2 + sin 2 = 1, 1 + tan 2 = sec 2 cos 2 + 1 = cosec 2 sin (a + b) = sin a cos b + sin b cos a sin (a - b) = sin a cos b - sin b cos a cos (a + b) = cos a cos b - sin a sin b cos (a - b) = cos a cos b + sin a sin b tan (a + b) = tan a + tan b 1 - tan a tan b tan (a - b) = tan a - tan b 1 + tan a tan b sin 2 = 2 sin cos tan 2 = 2 tan 1 - tan 2 cos 2 = cos 2 = sin 2 = 2 cos 2 - 1 = 1 - 2 sin 2 sin a + sin b = 2 sin ½ (a + b) cos ½ (a - b) sin a - sin b = 2 cos ½ (a + b) sin ½ (a - b) cos a + cos b = 2 cos ½ (a + b) cos ½ (a - b) cos a - cos b = -2 sin ½ (a + b) sin ½ (a - b) © Print & Marketing Services (Vic) Pty Ltd 156 2018/19 Intl Planner_DP_REAR.indd 156 25/5/18 3:15 pm
USEFUL INFORMATION MATHEMATICAL LAWS, FORMULAE, SYMBOLS FORMULA VARIABLES UNITS FORMULA VARIABLES UNITS d = ut + 1 at 2 2 d – distance u – initial velocity a – acceleration t – time m. metres m/s m/s 2 s, seconds P = VI P – Power V – Voltage I – Current w, watts v, volts A, amps d = vt d – distance v – average velocity t – time m, metres m/s s, seconds W = Vlt W – electrical energy V – Voltage I – current t – time J V A s v = u + at v – final velocity u – initial velocity a – acceleration t – time m/s m/s m/s 2 s, seconds l = Q t I – current Q – electric charge t – time A C, Coulombs s v 2 = u 2 + 2ad v – final velocity u – initial velocity a – acceleration d – distance displacement m/s m/s m/s 2 m V = IR (ohm’s law) V – Voltage I – current R – resistance V A O, ohms a = v - u t a – acceleration v – final velocity u – initial velocity t – time m/s 2 m/s m/s m V = W Q V – potential difference W – work Q – electric charge V J C F = ma F – resultant force m – mass a – acceleration N, Newtons kg, kilograms m/s 2 P = W t P – Power w – work t – time W J s Fg = Gm1m2 r 2 Fg – gravitational force G – universal gravitational constant 6.67 x 10 -11 m1m2 – masses of 2 objects r – distance objects apart m/s m/s kg m E k = 1 mv 2 2 E k – kinetic energy m – mass v – velocity J kg m/s d = m v D – density m – mass V – volume kg/m 3 kg m 3 E p = mgh E p – potential energy m – mass g – gravitational field strength h – height J kg N/kg m P = mv P – momentum m – mass v – velocity kg m/s kg m/s F e = kQ 1 Q 2 r 2 F e – electrical force k – Coulomb’s constant 9x10 9 Q 1 Q 2 – electrical charges r – distance charges apart N N/m 2 /c 2 c m W = Fd W – work F – force d – distance J, joules N m H = CmDT H – heat energy c – specific heat m – mass DT – change in temperature J J/kg ºC kg ºC, celsius F = -kd (Hooke’s Law) F – restoring Force k – spring constant d – spring’s displacement from natural length N - m 157 2018/19 Intl Planner_DP_REAR.indd 157 25/5/18 3:15 pm
Page 2 and 3: USING THE PLANNER Weekly ATL Focuse
Page 4 and 5: SELF-MANAGEMENT SKILLS GOALS AND IN
Page 6 and 7: SELF-MANAGEMENT SKILLS GOAL ACTION
Page 8 and 9: SELF-MANAGEMENT SKILLS GOALS, INDIC
Page 10 and 11: SELF-MANAGEMENT SKILLS REFLECTION O
Page 12 and 13: SELF-MANAGEMENT SKILLS BUILDING UP
Page 14 and 15: THINKING SKILLS HABITS OF MIND When
Page 16 and 17: THINKING SKILLS HABITS OF MIND RESP
Page 18 and 19: SOCIAL SKILLS PEOPLE IN MY LIFE To
Page 20 and 21: THINGS TO DO : WEEK 13 MONDAY AUGUS
Page 26 and 27: THINGS TO DO : WEEK 3 MONDAY SEPTEM
Page 28 and 29: THINGS TO DO : WEEK 10 MONDAY SEPTE
Page 30 and 31: THINGS TO DO : WEEK 17 MONDAY SEPTE
Page 32 and 33: TERM TWO MY PERSONAL LEARNING GOALS
Page 34 and 35: TERM THREE MY PERSONAL LEARNING GOA
Page 36 and 37: TERM FOUR MY PERSONAL LEARNING GOAL
Page 38 and 39: COMMUNICATION SKILLS PARTS OF SPEEC
Page 42 and 43: COMMUNICATION SKILLS COMMUNICATING
Page 44 and 45: SELF-MANAGEMENT SKILLS RELAXATION T
Page 46 and 47: MEANING AND PURPOSE daily wellbeing
Page 48 and 49: FEELINGS CHART Aim to use it a coup
Page 56: FEELINGS CHART Aim to use it a coup

2019-20 N. American Planner_DP Sample

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