Author: gjooheng

H2 maths tutor

Challenging Inequality problem 3

lg

Challenging Maclaurin’s series problem 2

mac

Solving Inequalities involving Modulus function

Consider the following 3 cases:

inequality

Challenging Probability problem 1

Problem

A bag contains 10 orange-flavoured, 14 strawberry-flavoured and 16 cherry-flavoured sweets which are of identical shapes and sizes. Benny selects a sweet at random from the bag. If it is not cherry-flavoured, he replaces it and selects another sweet at random. He repeats the process until he obtain a cherry-flavoured sweet. Calculate the probability that

i) the first sweet selected is strawberry-flavoured and the fourth sweet is orange-flavoured;

ii) he selects an even number of sweets

Solution

prob

Challenging Normal Distribution problem 1

1

Square root of x squared

Is Tex2Img_1405304270 ?

The answer is no. Correct answer is Tex2Img_1405304384

See the following example how this concept is applied in H2 math

Example 1

Differentiate Tex2Img_1405304606 with respect to x

Tex2Img_1405304802

Therefore

Ans: -1 if sin x > 0, 1 if sin x < 0

Example 2

normal

Challenging differentiation problem

Use implicit differentiation to differentiate the following with respect to x:

y=x(x+1)(x+2)(x+3)(x+4)(x+5)

Solution

ln y= lnx+ln(x+1)+ln(x+2)+ln(x+3)+ln(x+4)+ln(x+5)

Tex2Img_1404708880

Tex2Img_1404708998

Challenging Permutation question 4

In how many ways can 9 balls of which 4 are red, 4 are white and 1 black be arranged in a line so that no red ball is next to the black?

Answer: 175

Solution

Case 1: 1st ball is black in the whole row of 9 balls

Then the 2nd ball must be white. The rest of the 4 red and 3 white balls can be arranged in Tex2Img_1404380765= 35 ways

Case 2: last ball is black

Then the 2nd last ball must be white. The rest of the 4 red and 3 white balls can be arranged in Tex2Img_1404380765 = 35 ways

Case 3: Black ball is not the 1st or last ball

Then the black ball must be between 2 white balls. Consider WBW as one unit. Together with 4 red balls and 2 white balls, these can arranged in Tex2Img_1404380967 = 105 ways

Using the addition principle, total number of ways = 35+35+105= 175