7. Binomial Expansion - revision and challenging questions O-level Additional Maths

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6. Binomial Expansion - revision and challenging questions O-level Additional Maths

Answer:

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.

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4. Surds, Indices and Logarithms Revision and Challenging questions O-level Additional Maths

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3

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.

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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.

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.