A-LevelMathematicsIntegration9709/12 · Feb/Mar 2024 · Q35 Marks
A curve is such that dy/dx = 3(4x+5)^(1/2). It is given that the points $(1,9)$ and (5, a) lie on the curve. Find the value of a.
- A curve is such that dy/dx = 3(4x+5)^(1/2). It is given that the points $(1,9)$ and (5, a) lie on the curve. Find the value of a.[5]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.
- [*M1] Integrate to obtain form k(4x+5)³/²
- [A1] Obtain correct ½(4x+5)³/² Or (unsimplified) equivalent. Condone missing +c so far.
- [DM1] Substitute x=1, y=9 to form an equation in c
- [A1] Obtain or imply [y=] ½(4x+5)³/² - 9/2 May be implied by [a =] ½(4(1)+5)³/² - 9/2.
- [A1] Substitute x=5 to obtain a=58
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