Practice Math

1. The nth tidings of an arithmetic order is loving by un = 5 + 2n. (a) Write down the base unlikeness. (1) (b) (i) (ii) Loving that the nth tidings of this order is 115, perceive the estimate of n. For this estimate of n, perceive the sum of the order. (5) (Total 6 marks) 2. A sum of $ 5000 is invested at a junction curiosity-behalf scold of 6. 3 % per annum. (a) Write down an indication for the estimate of the siege behind n unmeasured years. (1) (b) What obtain be the estimate of the siege at the end of five years? (1) (c) The estimate of the siege obtain abound $ 10 000 behind n unmeasured years. i) (ii) Write down an disparity to delineate this instruction. Calculate the poverty estimate of n. (4) (Total 6 marks) 3. (a) Consider the geometric order ? 3, 6, ? 12, 24, …. (i) (ii) Write down the base fitness. Perceive the 15th tidings. (3) Consider the order x ? 3, x +1, 2x + 8, …. IB Questionbank Maths SL 1 (b) When x = 5, the order is geometric. (i) (ii) Write down the chief three tidingss. Perceive the base fitness. (2) (c) Perceive the other estimate of x for which the order is geometric. (4) (d) For this estimate of x, perceive (i) (ii) the base fitness; the sum of the infinite order. (3) (Total 12 marks) . Clara frames cans in triangular amasss, where each row has one hither can than the row beneath. For copy, the amass of 15 cans professionn has 5 cans in the foot row and 4 cans in the row over it. (a) A amass has 20 cans in the foot row. Profession that the amass contains 210 cans. (4) (b) There are 3240 cans in a amass. How numerous cans are in the foot row? (4) IB Questionbank Maths SL 2 (c) (i) There are S cans and they are unconfused in a triangular amass delay n cans in the foot row. Profession that n2 + n ? 2S = 0. Clara has 2100 cans. Interpret why she cannot frame them in a triangular amass. 6) (Total 14 marks) (ii) 5. Ashley and Billie are swimmers trailing for a two-of-a-trade. (a) Ashley courses for 12 hours in the chief week. She decides to growth the equality of season she spends trailing by 2 hours each week. Perceive the completion enumerate of hours she spends trailing during the chief 15 weeks. (3) (b) Billie to-boot courses for 12 hours in the chief week. She decides to course for 10% longer each week than the foregoing week. (i) (ii) Profession that in the third week she courses for 14. 52 hours. Perceive the completion enumerate of hours she spends trailing during the chief 15 weeks. (4) (c) In which week obtain the season Billie spends trailing chief abound 50 hours? (4) (Total 11 marks) IB Questionbank Maths SL 3 6. The diagram professions a balance ABCD of aspect 4 cm. The midpoints P, Q, R, S of the aspects are subsubappended to shape a assist balance. A Q B P R D (a) (i) (ii) Profession that PQ = 2 2 cm. Perceive the area of PQRS. S C (3) The midpoints W, X, Y, Z of the aspects of PQRS are now subsubappended to shape a third balance as professionn. A W Q X B P Y S R Z D C (b) (i) (ii) Write down the area of the third balance, WXYZ. Profession that the areas of ABCD, PQRS, and WXYZ shape a geometric order. Perceive the base fitness of this order. 3) IB Questionbank Maths SL 4 The manner of shapeing smaller and smaller balances (by attachment the midpoints) is continued indefinitely. (c) (i) (ii) Perceive the area of the 11th balance. Calculate the sum of the areas of all the balances. (4) (Total 10 marks) 7. Let f(x) = log3 (a) x + log3 16 – log3 4, for x > 0. 2 Profession that f(x) = log3 2x. (2) (b) Perceive the estimate of f(0. 5) and of f(4. 5). (3) The character f can to-boot be written in the shape f(x) = (c) (i) Write down the estimate of a and of b. ln ax . ln b (ii) Hence on graph Nursing essay, outline the graph of f, for –5 ? x ? 5, –5 ? y ? , using a layer of 1 cm to 1 ace on each axis. (iii) Write down the equation of the asymptote. (6) (d) Write down the estimate of f–1(0). (1) IB Questionbank Maths SL 5 The aim A lies on the graph of f. At A, x = 4. 5. (e) On your diagram, outline the graph of f–1, noting distinctly the fiction of aim A. (4) (Total 16 marks) 8. Let f(x) = Aekx + 3. Part of the graph of f is professionn beneath. The y-intercept is at (0, 13). (a) Profession that A =10. (2) (b) Loving that f(15) = 3. 49 (emend to 3 indicative figures), perceive the estimate of k. (3) (c) (i) (ii) (iii) Using your estimate of k, perceive f? (x). Hence, interpret why f is a decreasing character. Write down the equation of the lifeless asymptote of the graph f. (5) IB Questionbank Maths SL 6 Let g(x) = –x2 + 12x – 24. (d) Perceive the area enclosed by the graphs of f and g. (6) (Total 16 marks) 9. Consider the character f(x) = px3 + qx2 + rx. Part of the graph of f is professionn beneath. The graph passes through the derivation O and the aims A(–2, –8), B(1, –2) and C(2, 0). (a) Perceive three rectirectilinear equations in p, q and r. (4) (b) Hence perceive the estimate of p, of q and of r. (3) (Total 7 marks) IB Questionbank Maths SL 7 10. Let f (x) = 4 tan2 x – 4 sin x, ? a) ? ? ? x? . 3 3 On the grid beneath, outline the graph of y = f (x). (3) (b) Solve the equation f (x) = 1. (3) (Total 6 marks) IB Questionbank Maths SL 8 11. A city is careful environing dirt, and decides to seem at the enumerate of inhabitants using taxis. At the end of the year 2000, there were 280 taxis in the city. Behind n years the enumerate of taxis, T, in the city is loving by T = 280 ? 1. 12n. (a) (i) (ii) Perceive the enumerate of taxis in the city at the end of 2005. Perceive the year in which the enumerate of taxis is wrap the enumerate of taxis there were at the end of 2000. (6) (b) At the end of 2000 there were 25 600 inhabitants in the city who used taxis. Behind n years the enumerate of inhabitants, P, in the city who used taxis is loving by P= (i) (ii) 2 560000 . 10 ? 90e – 0. 1n Perceive the estimate of P at the end of 2005, giving your retort to the undeviating undiminished enumerate. Behind seven exhaustive years, obtain the estimate of P be wrap its estimate at the end of 2000? Justify your retort. (6) (c) Let R be the fitness of the enumerate of inhabitants using taxis in the city to the enumerate of taxis. The city obtain curtail the enumerate of taxis if R ? 70. (i) (ii) Perceive the estimate of R at the end of 2000. After how numerous exhaustive years obtain the city chief curtail the enumerate of taxis? (5) (Total 17 marks) IB Questionbank Maths SL 9 12. The character f is defined by f(x) = 3 9 ? x2 , for –3 < x < 3. (a) On the grid beneath, outline the graph of f. (2) (b) Write down the equation of each upright asymptote. (2) (c) Write down the stroll of the character f. (2) (Total 6 marks) IB Questionbank Maths SL 10 13. Let f (x) = p ? 3x , where p, q? x ? q2 2 + . Part of the graph of f, including the asymptotes, is professionn beneath. (a) The equations of the asymptotes are x =1, x = ? , y = 2. Write down the estimate of (i) (ii) p; q. (2) (b) Let R be the district limited by the graph of f, the x-axis, and the y-axis. (i) (ii) Perceive the indirect x-intercept of f. Hence perceive the bulk obtained when R is revolved through 360? environing the x-axis. (7) (c) (i) Profession that f ? (x) = 3 x 2 ? 1 ?x ? 2 ?1 ? 2 ?. (8) (ii) Hence, profession that there are no utmost or poverty aims on the graph of f. IB Questionbank Maths SL 11 (d) Let g (x) = f ? (x). Let A be the area of the district enclosed by the graph of g and the x-axis, among x = 0 and x = a, where a ? . Loving that A = 2, perceive the estimate of a. (7) (Total 24 marks) 14. Two weeks behind its nativity, an fleshly weighed 13 kg. At 10 weeks this fleshly weighed 53 kg. The growth in ponderosity each week is trustworthy. (a) Profession that the aspect among y, the ponderosity in kg, and x, the season in weeks, can be written as y = 5x + 3 (2) (b) (c) (d) Write down the ponderosity of the fleshly at nativity. (1) Write down the weekly growth in ponderosity of the fleshly. (1) Calculate how numerous weeks it obtain assume for the fleshly to obtain 98 kg. (2) (Total 6 marks) IB Questionbank Maths SL 12