PAPER. n ( 8, k ) Diagram Diagram shows part of a straight line graph drawn to represent and n.. Find the values of k [4 marks] 2. log ( 3,9 ) ( 7,) log Diagram 2 Diagram 2 shows part of a straight line graph drawn to represent = k n, where k and n are constants. Find the values of k and n. [4 marks] 78
3. 2,7 (2, - 3 ) Diagram 3 Diagram 3 shows that the variables and are related in such awa that when is plotted against, a straight line that passes through the points (2, 7 ) and (2, - 3 ) is obtained. Epress in terms of. [3 marks] 4. log 3 Diagram 4 ( 5, -7 ) Diagram 4 shows part of the graph of log against. The variables and are related b the a equation where a and b are constants. Find the values of a and b. b [4 marks ] 79
5. log 2 4 Diagram 5 Diagram 5 shows part of the graph of log against. The variables and are related b the equation = a ( b ) where a and b are constants. Find the values of a and b. [3 marks] 6. log 2-4 log Diagram 6 Diagram 6 shows part of a straight line graph when log against log is plotted. Epress in terms of. [4 marks] 8
3 7. The variable and are related b equation pk, where k and p are constant. Diagram 7 shows the straight line obtained b plotting log against. log (, 8 ) ( 2, 2 ) O Diagram 7 a) Reduce the equation 3 pk to linear form Y = mx + c. b) Find the value of, i) log p, ii) k. [4 marks] 8
. Use graph paper to answer this question. PAPER 2 Table shows the values of two variables, and obtained from an eperiment. Variables 2 n and are related b the equation 2 r, where r and n are constants. r 2 3 4 5 6 7 8 3.2 2 27.5 36.6 45.5 Table (a). Plot against, using a scale of 2 cm to unit on both aes. Hence, draw the line of best fit. Use our graph in (a), to find the value of (i). n, (ii). r, (iii). when =.5. 2. Use graph paper to answer this question. Table 2 shows the values of two variables, and obtained from an eperiment. Variables h and are related b the equation k, where h and k are constants. 2 3 4 5 6 5. 6.9 9.7 2.5 5.4 8.3 Table 2 (a). 2 Plot against, using a scale of 2 cm to 5 units on the 2 cm to units on the -ais. Hence, draw the line of best fit. Use our graph in (a), to find the value of (i). h, (ii). k, (iii). when = 2.5. 2 -ais and 82
3. Use graph paper to answer this question. Table 3 shows the values of two variables, and obtained from an eperiment. Variables n and are related b the equation, where n and w are constants. w 3 4 5 6 7 8 3 87 76 68 62 57.4 Table 3 (a). Plot log against log, using a scale of 2 cm to. unit on the log -ais and 2 cm to.2 units on the log -ais. Hence, draw the line of best fit. Use our graph in (a), to find the value of (i). n, (ii). w, (iii). when = 2. 4. Use graph paper to answer this question. Table 4 shows the values of two variables, and obtained from an eperiment. Variables b and are related b the equation a, where a and b are constants..2.4.6.8.2.4 2.4 8.5 6.74 5.66 4.9 3.87 Table 4 (a). Plot against, using a scale of 2 cm to.2 unit on the -ais and 2 cm to.2 units on the -ais. Hence, draw the line of best fit. Use our graph in (a), to find the value of (i). a, (ii). b, (iii). when =.9. 83
5. Use graph paper to answer this question. Table 5 shows the values of two variables, and obtained from an eperiment. Variables and are related b the equation pm, where m and p are constants..5 3. 4.5 6. 7.5 9. 2.5 3.24 4.37 5.75 7.76. Table 5 (a). Plot log against, using a scale of 2 cm to unit on the -ais and 2 cm to. units on the log -ais. Hence, draw the line of best fit. Use our graph in (a), to find the value of (i). m, (ii). p, (iii). when = 4.8. 6. Use graph paper to answer this question. Table 6 shows the values of two variables, and obtained from an eperiment. Variables and are related b the equation hk, where h and k are constants. 3 4 5 6 7 8.2 6.4 26.2 42 67. 7.4 Table 6 (a). Plot log against, using a scale of 2 cm to unit on the -ais and 4 cm to.5 units on the log -ais. Hence, draw the line of best fit. Use our graph in (a), to find the value of (i). h, (ii). k, (iii). when = 35.6. 84
ANSWER PAPER No. Solution Marks. Calculate gradient from graph n k 2 2. log 2log 5 Calculate gradient from graph n 2 k 5 3. c = -5 5 5 4. log = - log b + log a Gradient = -2 b = a = 5. log = b + log a or log = blog + log a a = b = - ½ 6. Gradient = ½ log = ½ log + 2 log /2 or log 2 or log /2. 2 7(a) 3log k 3 (b)(i) log ( 3log ) log k p log p 8 (ii) k 85
PAPER 2 No. Solution Marks (a) 2 3 4 5 6 7 4 4.4 5 5.5 6. 6.5 Uniform scale for -ais and -ais 6 points plotted correctl Draw the line of best fit n 2r r (b) Calculate gradient from graph (i) n =.77 (ii) r =.275 (iii) From graph, 3.6 = 5.4 2.(a) 2 4 9 6 25 36 5. 3.8 29. 5 77 9.8 Uniform scale for -ais and -ais 6 points plotted correctl Draw the line of best fit 2 k h (b) Calculate gradient from graph (i) h 2 (ii) k 3 (iii) From graph, = 2 = 8 86
3.(a) log.48.6.7.78.85.9 Uniform scale for -ais and -ais 6 points plotted correctl Draw the line of best fit log wlog log n (b) Calculate gradient from graph (i) 2.3 n 99.526 (ii) w.6 log 2.2 (iii) From graph, log 2..94.88.83.79.76 2.2 3.825 4.(a).2.4.6.8.2.4 5.55 5.38 5.22 5.6 4.9 4.74 Uniform scale for -ais and -ais 6 points plotted correctl Draw the line of best fit a b (b) Calculate gradient from graph (i) a -.8 (ii) b 5.7 (iii) From graph 4.9 = 5.65 87
5.(a).5 3. 4.5 6 7.5 9 log.4.5.64.76.89 Uniform scale for -ais and -ais 6 points plotted correctl Draw the line of best fit log log m log p Calculate gradient from graph (i).84 m or m.234 (ii).26 p or.897 (iii) log 4.8.68 = 5 6.(a) All values of log are correct 3 4 5 6 7 8 log..2.42.62.82 2.3 Uniform scale for -ais and -ais 6 points plotted correctl Draw the line of best fit log log k log h Calculate gradient from graph (i).2 k or k.588 (ii).425 h or h 2.66 (iii) log 35.6.55 = 5.7 88