A-LevelMathematicsAlgebra9709/22 · May/June 2021 · Q25 Marks
The solutions of the equation 5|x| = 5 – 2x are x = a and x = b, where a < b. Find the value of |3a – 1| + |7b – 1|.
- The solutions of the equation 5|x| = 5 – 2x are x = a and x = b, where a < b. Find the value of |3a – 1| + |7b – 1|.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [B1] Solve 5x = 5-2x to obtain x = 5/7
- [M1] Attempt solution of linear equation where signs of 5x and 2x are the same
- [A1] Obtain x = -5/3
- [M1] Substitute their values correctly
- [A1] Obtain |-6|+|4| and hence 10
- Alternative method for Question 2
- [B1] State or imply non-modulus equation 25x² = (5−2x)²
- [M1] Attempt solution of 3-term quadratic equation
- [A1] Obtain 5/7 and -5/3
- [M1] Substitute their values correctly
- [A1] Obtain |-6|+|4| and hence 10
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