O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · May/June 2013 · Q98 Marks
The graph of y = k(3ˣ) + c passes through the points (0, 14) and (–2, 6). Find the value of k and of c.
- (a)The graph of y = k(3ˣ) + c passes through the points (0, 14) and (–2, 6). Find the value of k and of c.[3]
- (b)(i)The variables x and y are connected by the equation y = e^(2x) + 25 - 24e^(-x). Find the value of y when x = 4.[1]
- (b)(ii)Find the value of eˣ when y = 20 and hence find the corresponding value of x.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [M1] (a) 14 = k + c and 6 = k/9 + c o.e.
- [A1] (a) c = 5
- [A1] (a) k = 9
- [B1] (b)(i) 79.2 or 79.158574 rot to 4 or more sf
- [M1] (b)(ii) e^(2x) + 5e^x – 24(= 0) or (e^x)² + 5e^x – 24(= 0) o.e.
- [M1] (b)(ii) factorise their 3 term quadratic
- [A1] (b)(ii) e^x = 3
- [A1] (b)(ii) x = ln 3 or 1.1(0) or 1.0986122 rot to 3 or more sf as only answer from fully correct working
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