Calculus Exam Hints 1

CALCULUS EXAM HINTS NB: These sheets were written by experienced teachers and are intended as a GUIDE only.

IN GENERAL • • •

Read the cover sheet the night before the exam. Know your tables book and A4 sheets. Use them during all your revision. Use pencil for DIAGRAMS ONLY. Markers hate pencil answers!

DURING THE EXAM • • •

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Make a conscious effort to waste no time. Don’t look around the room etc. Use your reading time. Make sure you start on questions that will boost your confidence and momentum. Keep an eye on the time: o One minute/mark o Don’t get bogged down! Come back to problems. o Never finish early, IE: check your work. o Never give up!!! Aim for part marks. If you have a mental blank, experts say to take a couple of DEEP BREATHS. Don’t cross our questions until you have re-done them. The original may contain part marks. Don’t use liquid paper!!! Don’t use pencil. Show all working confidently. (Don’t scribble on the edge or back of the page, etc.) If you get an answer which is clearly incorrect (Eg: sinA = 1.5) DO NOT cross out the whole question as you may have earned part marks. Simply write: “Answer incorrect as -1 ≤ sinA ≤ 1” Then REDO if there is time! Always use the examiners’ hints. If you are asked to show a result in part (a) but can’t, you can still use this result to do other parts of the question. Read the question and underline key information like hence, decimal places, when, where particle stops and starting value. It helps if you know what the question asks for! “Justify your answer” means a calculator answer will NOT earn full marks.

SPECIFIC HINTS • • •

x2 = a2 → x = +a NOT JUST a. In related rate questions, you must differentiate in terms of the variables (IE: h, r). Numerical values are substituted in at the end to find the rate at a particular instant. To show a function is increasing, show f`(x) > 0 on that interval.

Calculus Exam Hints

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t – t If integrating write as t – t -1/2, then integrate t 3 1 sin 2x IS RUBBISH !!!! 3 must use cos(2x) formula. If integrating functions with absolute value IE:

∫

∫ •

2

sin x dx =

3 –1

( lxl + 1) dx , you must draw a sketch and break up into x + 1 and

-x + 1 according to the sketch. dy = ky PROBLEMS. If not given a numerical starting value for y, use In dt

•

Y0 etc… Then at the end you can express result as a % of the original. In x – v – a problems , remember constants of integration.

•

Remember volume formula is π

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You

∫

b a

2

y dx about the x - AXIS. Don’t

forget π !!!!! When integrating - don’t forget to change the limits when you make a substitution. Don’t round too early!!! (Use memories a,b,c,…) With (x – 2)2 = 121 DON’T EXPAND! x – 2 = ± 11 . To solve k2 + 4k – 12 < 0 Use a sketch.  5  5 If you have ( n – 1)ln(0·95) < ln   THEN (n – 1) > ln   ÷ ln 0·95  9  9 since ln 0.95 is NEGATIVE. 2

x = 9 ⇒ x = ±3 5 = x ⇒ x = 25 1-1 functions have inverses. When integrating a quotient, check if the derivative of the top line is the bottom line – then use ln.

REMEMBER • • • • • •

Read cover sheet the night before the exam. Set your calculator to radians. Make sure your tables book is clean. Be VERY familiar with your tables book and A4 notes. Do your diagrams with care and make them a reasonable size. Go flat out! Don’t waste a minute!!!!

GOOD LUCK!!

Calculus Exam Hints

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