O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · May/June 2011 · Q66 Marks
The figure shows the graph of a straight line with lg y plotted against x. The straight line passes through the points A (5,3) and B (15,5). [Figure 6.1]
- (i)Express lg y in terms of x.[3]
- (ii)Show that y = a(10ᵇˣ) where a and b are to be found.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- (i) lg y – 3 = ⅕(x – 5); B1 for gradient, M1 for use of straight line equation; A1
- (ii) Either b = ⅕; B1 for b = ⅕
- y = 10(¹/₅x+2) = 10⁵.10²; M1 for use of powers of 10 correctly to obtain a
- a = 100; A1
- Or lg y = lg a + lg 10ᵇˣ; M1 for use of logarithms correctly to obtain a
- lg y = lg a + bx , lg a = 2; A1 for a
- a = 100; B1 for b = ⅕
- b = ⅕
- Or 10³ = a (10)⁵ᵇ; M1 for simultaneous equations involving powers of 10
- 10⁵ = a(10)¹⁵ᵇ; B1 for b = ⅕, A1 for a = 100
- b = ⅕ , a = 100
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