Sec 3 A Maths Questions - Please Help

• kkhing

  28 Apr 12, 17:38

  Hi,

  Please help with these A Maths questions. Thansk a lot.

  Q4 and Q5

  

   Q8B and Q9B

  

   

• wee_ws

  28 Apr 12, 19:06

  Hi,

    It would help if you could highlight specific difficulties you faced in tackling these questions.

    Let me address Q4.

    1. In the first part, consider rewriting it in the form

    quadratic expression > 0,

    then consider the appropriate condition for the discriminant.

    2. The second part is related to the first. First, observe the denominator and determine the value of m that is satisfied by it. Then consider the fact that

    A / B > 0 and B > 0 leads to A > 0.

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  28 Apr 12, 19:24

  Hi,

    For Q5, it will be useful to follow these steps:

    1. Rewrite it in the form

    quadratic expression = 0.

    2. Determine the expressions

    α + β and αβ

    in terms of p and q.

    3. Consider the fact that

    (α - β)^2 + 2αβ = α^2 + β^2

    to solve for the value of q.

    4. With the value of q, consider the fact that

    (α + β)^2 - 2αβ = α^2 + β^2

    to solve for the value of p, which should be positive.

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  29 Apr 12, 07:28

  Hi,

    For Q8(b), consider this approach:

    1. First term on RHS could be rewritten using the fact that

    a log b = log b^a.

    2. First term and second term on RHS could then be combined using the fact that

    log a + log b = log ab.

    3. Apply change of base for RHS using the fact that

    log_{m} a = [ log_{n} a ] / [ log_{n} m ].

    You should then be able to proceed. Thanks.

  Cheers,
  Wen Shih

• wee_ws

  29 Apr 12, 07:32

  Hi,

    Consider these steps for Q9(b):

    1. Take log with base e to both sides.

    2. LHS could be simplified by the use of these useful results:

    (i) ln ab = ln a + ln b,

    (ii) ln a^b = b ln a.

    3. Make x the subject.

    Thanks.

  Cheers,
  Wen Shih