Category: 1. H2 maths tips (9758)

Using Functions to explain Graph Transformations

Transformations of graph can be written in terms of functions, so we can see the sequence of transformations.

Example 1

transformed

Example 2

transformed 1

Challenging Probability problem 2

Problem

Vegetarian club consists of 2 married couples and 8 singles. The club is to select a delegation of 4 members to participate in an overseas conference. Find the probability that the delegation contains exactly one married couple.

Answer: 8/45

Solution

Case 1: 1 couple + 1 of the other couple + 1 single

(2 couples choose 1 couple) X (2 choose 1 from the other couple) X (8 singles choose 1) = 32

Case 2: 1 couple and 2 singles

(2 couples choose 1 couple) X (8 singles choose 2) = 56

No restrictions  = 12 C 4 = 495

Probability = (32+56) / 495 = 8/45

Challenging Sequences and Series problem 2

seq

seq2

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