SS3 QUESTIONS FOR 2018 MATHSCHAMP. 3. How many vertices has a hexagonal prism? A. 6 B. 8 C. 10 D. 12

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1 SS3 QUESTIONS FOR 8 MATHSCHAMP. P ad Q are two matrices such that their dimesios are 3 by 4 ad 4 by 3 respectively. What is the dimesio of the product PQ? 3 by 3 4 by 4 3 by 4 4 by 3. What is the smallest positive iteger for which 4 4 3(mod5)? 3 No such iteger 3. How may vertices has a heagoal prism? Which of the followig is NOT true? A cube is a cuboid A coe is a pyramid A pyramid is a prism A cylider is a prism 5. If log.438 ad log y.84, fid log y 6. Fid the legth, correct to the earest cm, of the logest stick which ca be put iside a ope rectagular bo whose sides are cm, 8cm ad 4cm. 4cm 3cm 3cm cm 7. A cylidrical ca 8cm i diameter ad cm high cotais 4cm depth of water. If a heavy metal rod 4cm i diameter ad 6cm log is placed i the ca, how much does the water level rise if the rod is placed vertically? cm cm cm 3 6cm I the diagram below, ABP, AODR are straight lies ad O is the cetre of the circle ABCDEF P B A C O F D R E

2 Use the iformatio to aswer questios 8-8. How may right agles ca be idetified from the diagram? How may cyclic quadrilaterals ca be idetified from the diagram? 8 9. Which arc subteds the refle arc FABCD AOC? arc ABC arc FED arc AFEDC. Which of the followig agles is equal to ADC CDR? ABC BAD BCD. If M ad N are the poits (-3,8) ad (5,-7) respectively, fid MN. 8 uits uits 5 uits 7 uits 3. Give that Y is m o a bearig of 3 from X, how far south of Y is X? m 5m 5m 3m 4. The equatio of the lie through the poits (4,) ad (-8,-) is 3y p q where p ad q are costats. Fid the value of p q Give that p ad q are two simple logical statemets, which of the followig is the cotrapositive of the logical statemet p q? p q q p q p p q

3 6. Which of the followig logical statemets is equivalet to the implicatio, A studet is allowed to wear a white shirt if he is i the fial year? If a studet is allowed to wear a white shirt, the he is i the fial year If a studet is ot allowed to wear a white shirt, the he is ot i the fial year If a studet is ot i the fial year, the he is ot allowed to wear a white shirt A studet is allowed to wear a white shirt oly if he is i the fial year 7. A curve is such that whe y, or 3. Fid the equatio of the curve. y 6 y 5 6 y 6 y If 3 : y : ad y: z :, fid 3 9 : z. :3 3: 4 3:8 : 9. The graphs of y ad y itersect at which of these poits? (,),(,) (,),(,) (,),(,) (,),(,). The legth of a chord ad the radius of a circle are equal. Calculate the agle subteded by the chord at the cetre of the circle th. Fid the term of the sequece 3, 4 6, 8 9, 6, 3( ) Let p ad q be two logical statemets give by p : Heis healthy ad q : Heis eat. Write i symbolic form the statemet he is uhealthy oly if he is dirty. p q p q p q p q

4 3. Cosider the two statemets: I. All isurace salesme are philosophers II. All philosophers are mathematicias. Which of the followig statemets is NOT a valid coclusio from the two give statemets? Every isurace salesma is a mathematicia Some mathematicias are either isurace salesme or philosophers Every mathematicia is a philosopher Some mathematicias are both isurace salesme ad philosophers 4. How may solutios eist for the equatio rage betwee ad 36? 3 4 si 8.54 for values of i the 5. Evaluate log4.3 log4.48 log Fid the iter-quartile rage of the followig set of marks: 3, 9, 4, 8, 6, 9,, 6, 5, 9, The probability that a ma smokes cigarette is.5 ad that he driks alcohol is.7. If the probability that he smokes cigarette or driks alcohol or both is.8, calculate the probability that he smokes cigarette ad driks alcohol Give that X 3 ad Y 4, fid the matri XY X

5 3 9. Fid 3 d. 3 k 3 k k 3 k 3 3. If the mid-poit of the lie PQ is (,3) ad the poit P is (-,), fid the coordiates of the poit Q. (8,6) (5,6) (,4) (6,5) 3. Fid the equatio of the perpedicular bisector of the lie joiig P(,-3) to Q(-5,). 8y+4+3= 8y-4+3= 8y-4-3= 8y+4-3= 3. P m r Q I the diagram, PQ is a straight lie, (m+) =, (+r) = 3, ad (m+r) =. Fid the ratio : : m r. :3: 4 3:4:5 4:5:6 5:6:7 33. Q y P S I the diagram, PQ is parallel to RS. Fid i terms of z y ad R z. 4 y z 8 y z 36 y z 36 y z

6 34. M ad N are two subsets of the uiversal set. If ( ) 48, M ( ), ( M N) 4, fid ( M N) N ( ) 3 ad 35. How may lies of symmetry does a isosceles triagle have? A bag cotais 3 blue marbles, 4 white marbles ad 3 red marbles. Two marbles are draw from the bag. Fid the probability that oe is red ad oe is white Give that A 5,7,8,,5, what is the possible umber of subsets that ca be formed from the set A? Number of babies Number of villages X X 3 The table shows the umber of babies bor i some villages o a certai day i a district. The mea of the distributio is 6. Use this iformatio to aswer questios 38 to Fid the media of the distributio Fid the mode of the distributio Fid the rage of the distributio Which of the followig is a eample of a symmetric matri?

7 Which of the followig matrices is sigular? m: 43. The ratio of the price per litre of petrol to that of kerosee is. If the price of petrol is icreased by 5% ad that of kerosee icreased by %, fid the ew ratio of their costs. m 5 :3 3 : m 3 : m : 5 Trasformatio N, which is give by is composed of two sigle y y trasformatios. Use this iformatio to aswer questios 44 to The ames of the two trasformatios are Traslatio ad Reflectio Elargemet ad Traslatio Reflectio ad Rotatio Rotatio ad Elargemet 45. Fid the image of the poit (3, ) uder N. (, 4) (,3) (,) (5, ) 46. Fid the poit which is mapped by N oto the poit (7,4). (, 4) (,3) (,) (,3) 47. Every year, the populatio of a village is foud to decrease by a factor of. If the 6 populatio of the village o Jauary,98 was 3,58, what was the approimate populatio o Jauary,? A compay s maager estimated that the cost C, i aira, of producig items is C = The compay sells each item for N. The compay makes a profit whe the total icome from sellig a quatity of items is greater tha the total cost of producig that quatity of

8 items. Which of the followig iequalities gives all possible values of for which the maager estimates that the compay will make a profit? C D A The semicircle above has a radius of If the legth of CD is 3 diameter i term of r? r B cetimetre, ad chord CDis parallel to the diameter AB. the legth of AB, what is the distace betwee the chord ad the 3 r 3 r r 5 3 r 5. A ad B are two poits 5km apart, the bearig of A from B beig 5. It is required to fi a third poit X, which is kow to be eactly km from B ad o a bearig of 5 from What is the bearig of B from X, correct to the earest degree?

NOTES AND FORMULAE SPM MATHEMATICS Cone

FORM 3 NOTES. SOLID GEOMETRY (a) Area ad perimeter Triagle NOTES AND FORMULAE SPM MATHEMATICS Coe V = 3 r h A = base height = bh Trapezium A = (sum of two parallel sides) height = (a + b) h Circle Area