Tim Gan Math
Sign up free

2024 TJC H1 Q4

2024 TJC H1 Q4

13 marks
  1. Find
    1. \(\displaystyle\int \frac{1}{\sqrt{3-2x}} \, \mathrm{d}x.\)[2]
    2. \(\displaystyle\int \frac{x}{x-1} \, \mathrm{d}x, \text{ where}\hspace{0.5em} x > 1.\)[2]
  2. A curve \(C\) has equation \(y = \ln x - \frac{1}{2x}\).
    1. Sketch the graph of \(C\), stating the equation of the asymptote and the coordinates of the point where \(C\) crosses the \(x\)-axis.[2]
    2. Find the equation of the tangent to \(C\) at the point where \(x = 3\), giving your answer in the form \(y = mx + c\) where \(m\) and \(c\) are exact values to be determined.[3]
    3. Find the numerical value of the area of the region bounded by \(C\), the tangent in (b)(ii) and the \(x\)-axis.[4]

Solution:

Solution locked

680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.

Create free accountSign inGet the A Math course · from S$39.98/moA Math tuition

Create a free account to practise similar questions.

Create free accountSign inGet the A Math course · from S$39.98/moA Math tuition
Answer:(a)(i) \(-\sqrt{3-2x}+C\), \(x<\frac32\). (ii) \(x+\ln(x-1)+C\), \(x>1\). (b)(i) Asymptote \(x=0\), intercept \((1.42,0)\); sketch shown. (ii) \(y=\frac7{18}x+\ln3-\frac43\). (iii) \(0.273\) square units.

Need help? Join our A-Maths tuition classes.

Learn more