1.11.2 Integrating standard functions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119

Question 53

The concentration $C\,$ of a catalyst in a chemical reaction vessel, measured in mg/L, is modelled by the equation

\frac{100}{5(3t - k)}, \quad t \neq \frac{k}{3}

where $t\,$ is the time in seconds since the start of the reaction, $k\,$ is a positive constant, and $\neq 3$ .

Find $dCdt\displaystyle \frac{dC}{dt}$ , giving your answer in simplest form in terms of $k$ .

[3]

The rate of change of the concentration at time $t = 1$ is -15 mg/L/s.

Find the two possible values of $k$ .

[3]

Given also that $k < 3$ ,

find the equation of the normal to the curve of $C\,$ against $t\,$ at the point where $t = 1$ , writing your answer in the form $a t + b C + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

[3]

Show, using algebraic integration, that

\int_{1}^{3} \frac{100}{5(3t - k)} \, dt = \lambda \ln 2

where $\lambda\,$ is a constant to be found.

[4]

1.11.2 Integrating standard functions

Question 53

The concentration $C\,$ of a catalyst in a chemical reaction vessel, measured in mg/L, is modelled by the equation

\frac{100}{5(3t - k)}, \quad t \neq \frac{k}{3}

where $t\,$ is the time in seconds since the start of the reaction, $k\,$ is a positive constant, and $\neq 3$ .

Find $dCdt\displaystyle \frac{dC}{dt}$ , giving your answer in simplest form in terms of $k$ .

[3]

The rate of change of the concentration at time $t = 1$ is -15 mg/L/s.

Find the two possible values of $k$ .

[3]

Given also that $k < 3$ ,

find the equation of the normal to the curve of $C\,$ against $t\,$ at the point where $t = 1$ , writing your answer in the form $a t + b C + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

[3]

Show, using algebraic integration, that

\int_{1}^{3} \frac{100}{5(3t - k)} \, dt = \lambda \ln 2

where $\lambda\,$ is a constant to be found.

[4]

1.11.2 Integrating standard functions

Question 53

Markscheme

1.11.2 Integrating standard functions

Question 53

Markscheme

1.11.2 Integrating standard functions

Question 53

1.11.2 Integrating standard functions Questions

1.11.2 Integrating standard functions

Question 53

1.11.2 Integrating standard functions Questions