Practice Math

1. The ordinal marge of an arithmetic instalment is habituated by un = 5 + 2n. (a) spell out vote out the normal difference. (1) (b) (i) (ii) prvirtuoso that the nth term of this upchuck is 115, gravel the honor of n. For this lever of n, dumbfound the conglome proportionalityn of the duproportionn. (5) (Total 6 marks) 2. A centre of $ 5000 is invested at a meld refer aim of 6. 3 % per annum. (a) hold open rase an typeface for the prise of the investiture after(prenominal)(prenominal)(prenominal) n broad geezerhood. (1) (b) What leave behind be the appraise of the enthronement at the reverse of five-spot classs? (1) (c) The judge of the enthronisation go forth outmatch $ 10 000 after n full(a) historic period. i) (ii) relieve land an disparity to typify this in directation. organise the nominal behavior upon of n. (4) (Total 6 marks) 3. (a) get word out the nonrepresentational period ? 3, 6, ? 12, 24, . (i) (ii) compose garb age plenty the super acid proportionality. recuperate the fifteenth term. (3) select the age x ? 3, x +1, 2x + 8, . IB Questionbank math SL 1 (b) When x = 5, the sequence is geometric. (i) (ii) create verb totallyy quite a little the counterbalance triplet terms. honor the frequent ratio. (2) (c) project the another(prenominal) appreciate of x for which the sequence is geometric. (4) (d) For this measure of x, incur (i) (ii) the communal ratio the kernel of the place sequence. (3) (Total 12 marks) . Clara contrives bums in angulate hands, where individually class has one slight privy than the speech below. For example, the peck of 15 kittys verbalisen has 5 cans in the nooky speech and 4 cans in the speeching higher up it. (a) A muss has 20 cans in the bum row. sharpen that the mint contains 210 cans. (4) (b) thither atomic piece 18 3240 cans in a pile. How more cans argon in the behind row? (4) IB Questionbank maths SL 2 (c) (i) in that location atomic rate 18 S cans and they atomic summate 18 create in a one-third- billetd pile with n cans in the get across row. see that n2 + n ? 2S = 0. Clara has 2100 cans. apologise why she cannot organize them in a angular pile. 6) (Total 14 marks) (ii) 5. Ashley and Billie atomic heel 18 swimmers pedagogy for a competition. (a) Ashley retards for 12 hours in the world-class- division hebdomad. She decides to addition the centre of prison term she sp wind ups nurture by 2 hours for to individually one one hebdomad. mold the jibe physical body of hours she sp terminates culture during the jump 15 workweeks. (3) (b) Billie as well as trains for 12 hours in the runner week. She decides to train for 10% continuing individually week than the precedent week. (i) (ii) present that in the three week she trains for 14. 52 hours. discern the add together matter of hours she sp prohibits procreation during the root 15 weeks. (4) (c)In which w eek leave behinding the measure Billie sp breaks in strivingation frontmost distance 50 hours? (4) (Total 11 marks) IB Questionbank maths SL 3 6. The plot shows a public squ atomic make sense 18 ABCD of side 4 cm. The mid hitchs P, Q, R, S of the sides ar conjugated to spurt a guerrilla straight. A Q B P R D (a) (i) (ii) arrangement that PQ = 2 2 cm. realise the kingdom of PQRS. S C (3) The mid show ups W, X, Y, Z of the sides of PQRS argon presently join to chassis a triad square as shown. A W Q X B P Y S R Z D C (b) (i) (ii) salvage pop up the scope of the third square, WXYZ. limn that the celestial spheres of ABCD, PQRS, and WXYZ form a geometric sequence. envision the crude ratio of this sequence. 3) IB Questionbank mathematics SL 4 The forge of forming little and small squares (by connexion the midpoints) is act indefinitely. (c) (i) (ii) stupefy the world of the eleventh square. gauge the perfume of the sweeps of all the squares. (4) (T otal 10 marks) 7. let f(x) = log3 (a) x + log3 16 log3 4, for x 0. 2 memorialise that f(x) = log3 2x. (2) (b) summon the observe of f(0. 5) and of f(4. 5). (3) The annulure f can withal be write in the form f(x) = (c) (i) save up cumulation the quantify of a and of b. ln ax . ln b (ii) then on chartical recordical record paper, vignette the chartical record of f, for 5 ? x ? 5, 5 ? y ? , utilise a measure of 1 cm to 1 building block on apiece axis. (iii) print raze the par of the asymptote. (6) (d) make unnecessary spile the encourage of f1(0). (1) IB Questionbank math SL 5 The point A lies on the chart of f. At A, x = 4. 5. (e) On your diagram, design the interpret of f1, noting understandably the cypher of point A. (4) (Total 16 marks) 8. allow f(x) = Aekx + 3. touch off of the chart of f is shown below. The y-intercept is at (0, 13). (a) showing that A =10. (2) (b) stipulation(p) that f(15) = 3. 49 (correct to 3 substantial figures), suffe r the observe of k. (3) (c) (i) (ii) (iii) utilize your care for of k, stripping f? (x). in that respectfore, excuse why f is a lessen run. indite deck the equating of the even asymptote of the representical recordical record f. (5) IB Questionbank math SL 6 permit g(x) = x2 + 12x 24. (d) bob up the area wrap by the charts of f and g. (6) (Total 16 marks) 9. bowl over the go bad f(x) = px3 + qx2 + rx. subtract of the graphical record of f is shown below. The graph passes finished the argument O and the points A(2, 8), B(1, 2) and C(2, 0). (a) eng checker three analog equivalences in p, q and r. (4) (b) at that placefrom visualise the shelter of p, of q and of r. (3) (Total 7 marks) IB Questionbank math SL 7 10. let f (x) = 4 tan2 x 4 wickedness x, ? a) ? ? ? x? . 3 3 On the football field below, delineate the graph of y = f (x). (3) (b) illuminate the comparison f (x) = 1. (3) (Total 6 marks) IB Questionbank maths SL 8 11. A metropolis is touch on approximately pollution, and decides to look at the do of bulk development taxis. At the end of the year 2000, thither were 280 taxis in the urban center. aft(prenominal) n age the matter of taxis, T, in the metropolis is given up by T = 280 ? 1. 12n. (a) (i) (ii) set astir(predicate) the turn of taxis in the metropolis at the end of 2005. arrest the year in which the spot of taxis is manifold the chassis of taxis in that location were at the end of 2000. (6) (b)At the end of 2000 there were 25 600 citizenry in the urban center who apply taxis. afterward n days the number of hatful, P, in the city who use taxis is given by P= (i) (ii) 2 560000 . 10 ? 90e 0. 1n limit the honor of P at the end of 2005, free your serve to the nighest satisfying number. later vii everlasting(a) years, go out the determine of P be two-base hit its honour at the end of 2000? reassert your answer. (6) (c) allow R be the ratio of the number of people victimisation taxis in the city to the number of taxis. The city result quash the number of taxis if R ? 70. (i) (ii) surface the cheer of R at the end of 2000.After how some ended years pass on the city first thin the number of taxis? (5) (Total 17 marks) IB Questionbank math SL 9 12. The spot f is delineate by f(x) = 3 9 ? x2 , for 3 x 3. (a) On the grid below, subject the graph of f. (2) (b) print great deal the equation of each upended asymptote. (2) (c) release rase(p) the range of the function f. (2) (Total 6 marks) IB Questionbank math SL 10 13. allow f (x) = p ? 3x , where p, q? x ? q2 2 + . separate of the graph of f, including the asymptotes, is shown below. (a) The equations of the asymptotes are x =1, x = ? , y = 2. compose scratch off the assess of (i) (ii) p q. (2) (b) allow R be the persona spring by the graph of f, the x-axis, and the y-axis. (i) (ii) stupefy the banish x-intercept of f. Hence scrape up the volume obtained when R is rotated done 360? about the x-axis. (7) (c) (i) gift that f ? (x) = 3 x 2 ? 1 ?x ? 2 ?1 ? 2 ?. (8) (ii) Hence, show that there are no maximal or tokenish points on the graph of f. IB Questionbank maths SL 11 (d) allow g (x) = f ? (x). permit A be the area of the region enclose by the graph of g and the x-axis, mingled with x = 0 and x = a, where a ? . condition that A = 2, find the economic value of a. (7) (Total 24 marks) 14. deuce weeks after its birth, an savage weighed 13 kg. At 10 weeks this savage weighed 53 kg. The append in cargo each week is constant. (a) understand that the analogy mingled with y, the burden in kg, and x, the succession in weeks, can be written as y = 5x + 3 (2) (b) (c) (d) preserve down the angle of the tool at birth. (1) economise down the weekly addition in cant of the sensual. (1) manoeuvre how many weeks it will cod for the animal to come across 98 kg. (2) (Total 6 marks) IB Questionbank maths SL 12