# Mathematics Higher Level

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1 Mthemtics Higher Level Higher Mthemtics Exmintion

2 Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below: Pper Pper There re 70 mrks vilble in totl for this pper nd the time lloction is hour nd 30 minutes. Clcultors cnnot be used in this pper nd the pper is divided into two sections: Section A contins 0 objective test type questions worth mrks ech. Ech question hs 4 possible nswers only one of which is correct. The mjority of these questions should be firly stright-forwrd nd will ssess your knowledge of the bsic theory of the course. Section B will contin questions worth 30 mrks in totl nd re clled written response questions. The exminers re looking for written solutions to these questions. There will usully be 3 to 5 questions in this section. There re 60 mrks vilble for this pper nd the time lloction is hour 0 minutes. Clcultors cn be used in this pper, however you will find tht for mny of the questions you will not need to use clcultor. In ll of the questions in this pper the exminers re looking for written solutions. There will usully be 6 to 9 questions in this pper. Exmintion Guide Pge

3 . Formul List Mthemtics Higher Level A formul list is given in the Higher exmintion nd is printed inside both exmintion ppers. The formule given re... Circle: The eqution The eqution x y gx fy c = 0 represents circle centre ( g, f) nd rdius ( x ) ( y b) r + = represents circle centre (, ) b nd rdius r. g + f c. Sclr Product : b. = b cos θ, where θ is the ngle between nd b. or b b. = b + b + b 3 3, where = nd b = b. b 3 3 Trigonometric formule: sin(a ± B) = sin A cos B ± cos Asin B cos(a ± B) = cos A cos B sin A sin B sin A = sin A cos A = cos A cos A sin A = cos A = sin A Tble of stndrd derivtives : f( x ) f ( x) sin x cos x cos x sin x Tble of stndrd integrls : f( x ) f ( x) dx sin x cos x + C cos x sin x + C Exmintion Guide Pge 3

4 Section : Essentil Formule Mthemtics Higher Level. Formule nd fcts from previous levels There re number of formule, from both Stndrd Grde/Intermedite, tht you will find very useful for the Higher Mthemtics exmintion. These re listed below nd you should know them. Qudrtic Formul is b ± b 4c x=, 0. Trigonometric identities : sin A + cos A = sin A tn A = cos A Trigonometric exct vlues... ngle in degrees sin 0 3 cos 3 0 tn Trigonometric Grphs y y = sin x y y = cos x x x Exmintion Guide Pge 4

5 . Higher Level Formule Mthemtics Higher Level You will find the following very helpful. You must know the following: Given ny two points ( x, y) nd ( x, y ) then the : midpoint is given by x + y, x + y distnce between them is ( x x ) + ( y y ) y y grdient of line through the points is m=, where x x x x Grdient cn lso be found using m = tn θ Sequences Any sequence given by recurrence reltion of the form u = + n+ un b hs limit L if nd only if < <. This limit L cn be found by solving b L = L + b OR L = The discriminnt : = b 4 c. ( ) n n f x = kx f ( x) = knx n k n+ kx dx = x + c, n n + n n+ ( x + b) dx = ( x + b) + c, n n ( + ) Logrithmic nd Exponentil form x y = log y = x Lws of Logrithms. log pq = log p + log q 4. log. p log = log p log q 5. log = 0 q n 3. log p = nlog p Exmintion Guide Pge 5

6 Section 3 : Attempting Exmintion Questions Mthemtics Higher Level 3. Objective Test Questions This is the first set of questions tht you will meet in the exmintion. Although it is up to you how long you spend ttempting these questions try not to spend more thn 45 minutes nswering them. The mjority of objective test questions cn be nswered directly from the question without looking t the options. You should ttempt s mny questions s you cn in this mnner. Below is n exmple of n objective test question nd how it will look in the exmintion. Exmple A sequence is defined by the recurrence reltion Wht is the vlue of u? 7 u 5u 8 u 4 = + = n+ n with 5 A B 4 C 8 5 D 9 Options Question Your working for this question should look like this : u = 5 n u + + n 8 u = 5 u + 8= = 4 u 6 5 = 5 u + 8 = = So the nswer is 9 nd nswer D You would then shde in D on the nswer grid for this question. There is no penlty for guessing here nd so if you re relly stuck nd do not know the nswer to ny question mke guess. Do not leve ny objective question without n nswer when you submit your exmintion pper. Exmintion Guide Pge 6

7 3. Written Response Questions Mthemtics Higher Level Section B of Pper nd Pper consist of number of questions where the exminer wnts to see written solution to the question. There re two importnt instructions on the front of the exmintion pper tht you must remember.. Full credit will only be given where the solution contins pproprite working. It is importnt tht you show ll working, where it is needed. Questions worth or more mrks need some sort of working. If question is worth 4 mrks nd you simply write down the nswer it is highly unlikely tht you will receive ny mrks for tht question. The exminer must be ble to see where your nswer hs come from.. Answers obtined by redings from scle drwings will not receive ny credit. Therefore you must not use ny form of scle drwing to nswer ny question. Even if your nswer were correct you would receive no mrks. If you remember these two rules nd try to show the exminer where ech of your nswers hs come from, you should be ble to pick up s mny mrks in the exmintion s possible. Along with these two rules, there re some bsic fcts which if you remember when nswering questions in Higher Mthemtics, you should not drop mrks needlessly. These re: In generl : If question sttes Show tht..., you must show ll the steps in your solution nd end up with the result requested. Do not stop your solution until you get to tht finl result required. If exct vlues re sked for you will receive no mrks for pproximte vlues. More specificlly : Alwys simplify frctions s fr s possible. e.g. Write 8 s 9 Don t write frction with s the denomintor. e.g. 43 must be written s 43 Never leve deciml point on the numertor or denomintor of frction e.g. should be written s 50 (here nd would lso be uncceptble.) should be written s 90 You must evlute squre roots of perfect squres up to nd including 00. e.g. You must write 49 s 7 but could leve 96 (which is 4) unsimplified. Clculus questions involving sine nd cosine should lwys be ttempted using rdins do not use degrees nd then convert to rdins. You my lose more thn one mrk here if you do not del with the Mthemtics correctly!! Exmintion Guide Pge 7

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