O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2020 · Q77 Marks
Solve the simultaneous equations 10^(x+2y) = 5, 10^(3x+4y) = 50, giving x and y in exact simplified form.
- (a)Solve the simultaneous equations 10^(x+2y) = 5, 10^(3x+4y) = 50, giving x and y in exact simplified form.[4]
- (b)Solve 2x^(1/3) - x^(1/3) - 10 = 0.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] x + 2y = lg5 or 3x + 4y = lg50
- [M1] Solves their linear simultaneous equations
- [A1] x = lg2 or equivalent simplified form
- [A1] y = (1/2)lg(5/2) or equivalent simplified form
- If A0 A0 then SC1 for a correct pair of unsimplified values or a correct pair of decimal values correct to at least 3sf
- [M1] (x^(1/3))² + 2(x^(1/3)) - 5 oe
- [M1] x^(1/3) = -2, 5/2
- [A1] x = -8, 125/8
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