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Edit AQA MPC4 Notes 3 May 2013 at 11:07 Only me ----------------------------------------------------------------------------------------------------------- 1. BINOMIAL SERIES EXPANSION

Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

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Page 1: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

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AQA MPC4 Notes 3 May 2013 at 11:07

Only me

----------------------------------------------------------------------------------------------------------- 1. BINOMIAL SERIES EXPANSION

Page 2: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 3: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 4: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 5: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 6: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 7: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 8: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 9: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 10: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 11: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 12: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 2. RATIONAL FUNCTIONS AND DIVISION OF POLYNOMIALS

Page 13: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 14: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 15: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 16: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 17: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 18: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 19: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 20: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 21: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 3. PARTIAL FRACTIONS AND APPLICATIONS

Page 22: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 23: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 24: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 25: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 26: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 27: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 28: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 29: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 30: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 31: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 32: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 33: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 34: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 4. IMPLICIT DIFFERENTIATION AND APPLICATIONS

Page 35: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 36: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 37: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 38: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 39: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 5. PARAMETRIC EQUATIONS FOR CURVES AND DIFFERENTIATION

Page 40: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 41: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 42: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 43: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 44: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 45: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 46: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 47: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 48: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 49: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 50: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 51: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 52: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 6. FURTHER TRIGONOMETRY WITH INTEGRATION

Page 53: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 54: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 55: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 56: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 57: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 58: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 59: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 60: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 61: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 62: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 63: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 64: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 65: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 66: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 7. EXPONENTIAL GROWTH AND DECAY

Page 67: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 68: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 8. DIFFERENTIAL EQUATIONS

Page 69: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 70: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

----------------------------------------------------------------------------------------------------------- 9. VECTOR EQUATIONS OF LINES

Page 71: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 72: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 73: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 74: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 75: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 76: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 77: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 78: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 79: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 80: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 81: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence
Page 82: Edit AQA MPC4 Notes - · PDF fileEdit AQA MPC4 Notes ... Given that x is small, find the binomial expansion Of (4 — in ascending powers of x up to and including the term in x3. Hence

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