June Revision Exercise 3

JC Mathematics

Please do check through the solutions on your own, especially for questions that we did not have chance to properly discuss during class. You may whatsapp me too if you have a burning question.

Note: You should not spend more than 180mins on the entire exercise.

June Revision Exercise 3 Q1
June Revision Exercise 3 Q2
June Revision Exercise 3 Q3
June Revision Exercise 3 Q4
June Revision Exercise 3 Q5
June Revision Exercise 3 Q6
June Revision Exercise 3 Q7
June Revision Exercise 3 Q8
June Revision Exercise 3 Q9
June Revision Exercise 3 Q10
June Revision Exercise 3 Q11

List of Great and Helpful Math Articles

List of Great and Helpful Math Articles

JC Mathematics, Studying Tips

Here is a compilation of all the Math articles/ opinions KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂 For ease of navigation, some bigger topics sorted according to topics.

  1. Trigonometry
  2. Integrations
  3. Permutations & Combinations (Combinatorics)
  4. Vectors
  5. Complex Numbers
  6. APGP, Sequences & Series
  7. Statistics
  8. Importance of Prelims
  9. A-levels vs IB Mathematics
  10. How I encourage Students to study Mathematics in JC.
  11. Helping Students with Math Course
  12. Common Pitfalls in A’levels Math #1
  13. Common Pitfalls in A’levels Math #2
  14. Common Pitfalls in A’levels Math #3
  15. Why is anything to the power of 0 always 1?
  16. Classical Mathematical Fallacies #1
  17. Classical Mathematical Fallacies #2
  18. Classical Mathematical Fallacies #3
  19. Confusion on when to put ± sign
  20. Difference between H1 and H2 Math
  21. Partial Fractions made easy
  22. The Modulus Sign #1
  23. The Modulus Sign #2
  24. The Modulus Sign #3
  25. The Modulus Sign #4
  26. An easier approach to remembering discriminant
  27. Finding the Coefficient of Terms
  28. Help to start Maclaurin’s Questions
  29. Understanding A-level differentiation questions
  30. A different perspective to transformation
  31. Solving roots of higher order
  32. Proving a function is symmetrical about y-axis
  33. All tangents are straight lines
  34. Prime Numbers and their uses.
  35. My Favourite Pure Mathematics Topic
  36. Python
  37. Tricks to squaring numbers
  38. Why we need to be close to zero for an approximation to be good?
  39. Learning Math or Learning to do Math
  40. H3 Mathematics
  41. Why study Mathematics?
  42. Importance of Mathematics in Finance
  43. Some things that JC students should know
  44. Review of Basic Probability (Undergraduate)

Integration related articles

JC Mathematics

Here is a compilation of all the Integration articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂

1. Integrating Trigonometric Functions (1)
2. Integrating Trigonometric Functions (2)
3. Integrating Trigonometric Functions (3)
4. Integrating Trigonometric Functions (4)
5. Integrating Trigonometric Functions (5)
6. Leibniz’s Formula for \pi
7. Simpson’s Rule
8. Evaluating Integrals with Modulus

Trigonometric related articles

JC Mathematics

Here is a compilation of all the trigonometry articles KS has done. Students should read them when they are free to improve their mathematics skills. They will come in handy! 🙂

1. How to derive the sum to produce formula
2. Integrating Trigonometric Functions (1)
3. Integrating Trigonometric Functions (2)
4. Integrating Trigonometric Functions (3)
5. Integrating Trigonometric Functions (4)
6. Integrating Trigonometric Functions (5)
7. Easiest way to remember cosec, sec, and cot
8.

2010 A-level H2 Mathematics (9740) Paper 1 Question 6 Suggested Solutions

JC Mathematics

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Using GC, \beta = 0.347, \gamma = 1.532

(ii)
Using GC, Area = |\int_0.347^1.532 x^3 - 3x + 1 dx| = 0.781

(iii)
Area = \int_{-\sqrt{3}}^0 x^3 -3x + 1 dx - \sqrt{3} \times 1

= \frac{9}{4}

(iv)
\frac{dy}{dx}=2x^2 - 3 = 0

x = \pm 1

y = 3 \mathrm{~or~}-1

Thus, -1 \textless k \textless 3

KS Comments:

Take note to give (i) to 3 decimal places! For (iii), students can use GC to check their answers too! (iv), Students might want to consider using the GC to graph it out to help yourself find an efficient method