NJC H2 Maths Exponential Logarithm and Modulus Functions and their Graphs Practice Questions

National Junior College Mathematics Department 2016 Exponential, Logarithmic and Modulus Functions and their Graphs Page 1 of 2 National Junior College 2016 – 2017 H2 Mathematics Revision: Exponential, Logarithmic and Modulus Functions and their Graphs Practice Questions 1. Sketch the graph of  3log 4yx , labelling all axial intercepts and asymptotes in exact form. 2. Solve the following equations. (a) 23xx (b) 42xx   (c) 2 65xx (d) 6 6 5x x x   3. Find the values of a and b for which 22 43x x can be expressed in the form   2 2 x ba  . Hence, sketch the curve 22 4 3xxy  for the interval 23 x  , Indicating the exact coordinates of the x-intercepts.4. 4. If   62 2 2349 r rr x x   can be simplified to 3 k x , find the values of the constants r and k. 5. (a) Use the substitution 3xy to find the values of x which satisfy the equation   13 9 3 1 3x x x    . [AO Maths N03/P1] (b) Solve the equation   22 3 2 10 0xx   . [AO Maths N05/P1] 6. A curve is defined by 3xyk , where k is a constant. If the curve passes through the point  0,2A , find the value of k, and sketch the curve for positive values of x. 7. Prove that lne x x . 8. If a, b, and c are positive numbers other than 1, show that •log lo og 1l •gb c aa b c  . 9. Solve the following equations. (a)  lg 2 5 1 lgxx   (b) 42log log 12yy [AO Maths N01/P2] (c)  lg 3 lg lg7xx   (d) 2 21 1 8 24 y y y    [AO Maths N02/P2] 10. Solve the following simultaneous equations. (a) 23yx and 21y x  (b) 2 3 19xy and 3xy 11. Solve the simultaneous equations given below:

National Junior College Mathematics Department 2016 Exponential, Logarithmic and Modulus Functions and their Graphs Page 2 of 2 (a)  ln 3 2ln6 ln9xy   and   2 e ee x y  (b)  3 9 27 qp  and  22log 1 2 og 17 1l qp 12. Solve 1e 2 exx  . 13. 2012/H1/AJC/Promo/7 On first January 1990, Mr. Andrew invests $1000 in an account with Bank A which pays 5% interest compounded annually on 31 st December of each year. The amount of money in the account, $M, at the end of t years is given by 1000(1.05)tM  . (i) How much will there be in his account on 31st December 1997? (ii) State the year when the amount of investment first exceeds $4000. Starting from 1990, Mr. Andrew also decides to save $100 on 1 st January every year in another account with Bank B which pays the same compound interest annually. The amount of money $N at the end of t years is given by 2100(1.05 1)tN  . State the year in which the money in the account with Bank B first exceeds the amount in the account with Bank A. 14. 2012/H1/NJC/Promo/4 (a) Solve   2 ln 2ln 3xx  , giving your answer in exact form. (b) Show that    24log log 3 13ab can be simplified to a2 = 3b + 13. Hence, find the exact values of a and b which satisfy the following simultaneous equations 93 27 b a  ,    24log log 3 13ab *Majority of questions are taken from Panpac Additional Mathematics Numerical Answers 3. (a) 1,3x (b) 1x (c) 2,3x (d) 1, 6x  4. 2 ;33kr 5. (a) 1,0x (b) ln 5 ln 2x 6. 2k  9. (a) 5 8x (b) 256y (c) 0.5x (d) 1.5y 10. (a) 1 ; 1xy (b) 28 13, ; 2, 555x y x y    11. (a) 3, 5xy (b) 6.5, 1.5pq 12. ln 2x 13. (i) $ 1477.46 (ii) 2018 (iii) 2003 14. (a) 3ee ,x  (b) 5, 4ab