(i)

(ii)

Area of R

As

Cultivating Champions, Moulding Success

(a)(i)

Let

(a)(ii)

*Students are expected to prove that gives the maximum area.

(b)(i)

latex x$-axis

Sub into

(b)(iii)

When the line is a tangent to C,

When

When

(i)

When

Equation of tangent:

Equation of normal:

(ii)

Hence, tangent cuts curve again at

(iii)

At Q,

At R,

(i)

For tangents to be parallel to the -axis,

Sub into

Thus, equations of tangents which are parallel to -axis are

(ii)

units per second.

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

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! ðŸ™‚ For ease of navigation, some bigger topics sorted according to topics.

- Trigonometry
- Integrations
- Permutations & Combinations (Combinatorics)
- Vectors
- Complex Numbers
- APGP, Sequences & Series
- Statistics
- Importance of Prelims
- A-levels vs IB Mathematics
- How I encourage Students to study Mathematics in JC.
- Helping Students with Math Course
- Common Pitfalls in A’levels Math #1
- Common Pitfalls in A’levels Math #2
- Common Pitfalls in A’levels Math #3
- Why is anything to the power of 0 always 1?
- Classical Mathematical Fallacies #1
- Classical Mathematical Fallacies #2
- Classical Mathematical Fallacies #3
- Confusion on when to put Â± sign
- Difference between H1 and H2 Math
- Partial Fractions made easy
- The Modulus Sign #1
- The Modulus Sign #2
- The Modulus Sign #3
- The Modulus Sign #4
- An easier approach to remembering discriminant
- Finding the Coefficient of Terms
- Help to start Maclaurin’s Questions
- Understanding A-level differentiation questions
- A different perspective to transformation
- Solving roots of higher order
- Proving a function is symmetrical about y-axis
- All tangents are straight lines
- Prime Numbers and their uses.
- My Favourite Pure Mathematics Topic
- Python
- Tricks to squaring numbers
- Why we need to be close to zero for an approximation to be good?
- Learning Math or Learning to do Math
- H3 Mathematics
- Why study Mathematics?
- Importance of Mathematics in Finance
- Some things that JC students should know
- Review of Basic Probability (Undergraduate)

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

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

Total Volume

Total Surface Area,

Thus, gives a minimum total surface area.

(ii)

(iii)

(iv)

If the box has square ends, then

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

(i)

Differentiating the given equation by ,

(ii)

Tangent parallel to x-axis

Then,

Therefore, coordinates are and .

Quite straight forward with the implicit differentiations at (i). Students should understand what it means when tangents are parallel to x-axis. Lastly, since the question wants coordinates, students are expected to give in coordinates instead of merely the x and y values!

(i)

(ii)

Since the first two terms are equal,

Third term

Students should know how to find coefficient of terms efficiently. Refer here if they don’t. This is rather simple since they only expect students to do up to 3 terms.