Permutation Without Repetition

WS#1G9

1. In how many ways can the letters of the word "APPLE" be arranged?

2. How many different ways can the numbers 1, 2, 3, 4, 5 be arranged?

3. In how many ways can a committee of 3 members be formed from a group of 6 people?

4. A box contains 6 red balls and 4 blue balls. How many different ways can you arrange the balls?

5. In how many ways can the letters of the word "BANANA" be arranged?

Metric Units Conversion Chart

Length:

1 millimeter (mm) = 0.1 centimeters (cm)

1 centimeter (cm) = 10 millimeters (mm)

1 meter (m) = 100 centimeters (cm) = 1,000 millimeters (mm)

1 kilometer (km) = 1,000 meters (m)

Imperial Units Conversion Chart

Length:

1 inch = 2.54 centimeters

1 foot = 12 inches

1 yard = 3 feet

1 mile = 1,760 yards

Combinations

WS#1G9

1. In a game, there are 10 players, and the coach needs to choose a captain and a vice-captain. How many different combinations of captain and vice-captain are possible?
   
   
2. A school has 5 different clubs, and each student can join only one club. If there are 25 students in the school, how many different ways are there for the students to join the clubs?

Equation of parabola from graph

Transformed equation of parabola is: \(y=af(x-h)^2+k\) \(……(1)\)

Where \(a=\)Vertical stretch or compression, \(h=\)horizontal shift (left or right) \(k=\)Vertical shift (up or down) From graph, \(h=3\) and \(k=-2\); plug \(h\) and \(k\) values in eqn \((1)\) \(y=a(x-3)^2-2\) /(……(2)\) To find \(‘a’\), use the given point \((1,0)\) as: \(0=a(5-3)^2-2\) \(0=4a-2\) \(a=1/2\);plug in eqn.(2) \(y=1/2 (x-3)^2-2\);which is the reqd.eqn.

Trigonometric Co-ratios

Learn to convert and use trigonometric co-ratio functions to solve trigonometric problems.

Operations with integers

A number without a decimal or fractional element is known as an integer, which includes both positive and negative numbers, including zero. Some examples are \(-3, -2, 0, 2, 3\) etc. Every integer has an opposite. For example, \(3\) has opposite as \(-3\) and \(-5\) has opposite as \(5\). 

Absolute value: A number's absolute value is its numerical value without taking the sign into consideration, and it is represented by the sign \(|a|\); where a is any number. \(e.g.\)\(|a|=a\) and \(|-a|=a\)