Need to differentiate between identity and equation. To prove an identity, always show that LHS is equal to RHS or RHS is equal to LHS.
Answer:
Thursday, February 28, 2013
11. Trigonometry - revision and challenging questions for O level Additional Maths examination O-level Additional Maths
Need to differentiate between identity and equation. To prove an identity, always show that LHS is equal to RHS or RHS is equal to LHS.
Answer:
10. Trigonometry - revision and challenging questions for O level Additional Maths examination O-level Additional Maths
Comments:
Always express trigonometric ratios as sines and cosines.
Answer:
9. Partial fractions - revision and challenging questions for O level Additional Maths examination O-level Additional Maths
Comments:
The first step in solving Partial fraction questions is to make sure that if the fraction is improper, express it in mixed fraction first.
Answer:
Monday, February 25, 2013
5. Binomial Expansion - revision and challenging questions O-level Additional Maths
The key to solving questions on Binomial Expansion is to master the use of general term.
Answer:
Answer:
3. Surds, Indices and Logarithms Revision and Challenging questions O-level Additional Maths
Comments:
This question requires manipulation of logarithmic expressions using its definition. Students need to practise to acquire the technique of manipulation.
Answer:
Sunday, February 24, 2013
2. Remainder and factor theorem revision and challenging questions O-level Additional Maths
It is given that P(x) is a polynomial such that
Write down the quotient and remainder when
Comments:
This question tests the student's knowledge on Division Algorithm of polynomials. Question can be solved by inspection.
Answer:
a. Quotient: 4x + 8 Remainder: x + 6
b.
Write down the quotient and remainder when
Comments:
This question tests the student's knowledge on Division Algorithm of polynomials. Question can be solved by inspection.
Answer:
a. Quotient: 4x + 8 Remainder: x + 6
b.
1. Remainder and factor theorem revision and challenging questions O-level Additional Maths
a. State the Remainder Theorem.
b. The polynomial f(x) leaves a remainder 5 when divided by (x-1) and remainder -1 when divided by (x+2). Find the remainder when f(x) is divided by (x-1)(x+2).
Comments:
Students are expected to be familiar with Remainder theorem and Division algorithm for polynomials. Most students are familiar with Remainder theorem, but not Division algorithm. To solve part b students need to have knowledge of Divison Algorithm.
Answers:
a. When a polynomial f(x) is divided by the linear polynomial ax + b, its remainder can be expressed as
f(-b/a).
b. f(1) = 5, f(-2) = -1.
When f(x) is divided by (x-1)(x+2), the remainder should be linear, ie. of the form ax + b.
Using the division algorithm for polynomials,
Dividend = Divisor x Quotient + Remainder,
f(x) = (x - 1)(x + 2) x Q(x) + ax + b
f(1) = a + b, and f(-2) = -2a + b
5 = a + b, -1 = -2a + b,
giving a = 2 and b = 3.
Hence the remainder is 2x + 3.
b. The polynomial f(x) leaves a remainder 5 when divided by (x-1) and remainder -1 when divided by (x+2). Find the remainder when f(x) is divided by (x-1)(x+2).
Comments:
Students are expected to be familiar with Remainder theorem and Division algorithm for polynomials. Most students are familiar with Remainder theorem, but not Division algorithm. To solve part b students need to have knowledge of Divison Algorithm.
Answers:
a. When a polynomial f(x) is divided by the linear polynomial ax + b, its remainder can be expressed as
f(-b/a).
b. f(1) = 5, f(-2) = -1.
When f(x) is divided by (x-1)(x+2), the remainder should be linear, ie. of the form ax + b.
Using the division algorithm for polynomials,
Dividend = Divisor x Quotient + Remainder,
f(x) = (x - 1)(x + 2) x Q(x) + ax + b
f(1) = a + b, and f(-2) = -2a + b
5 = a + b, -1 = -2a + b,
giving a = 2 and b = 3.
Hence the remainder is 2x + 3.
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