Afrikaans Albanian Amharic Arabic Armenian Azerbaijani Basque Belarusian Bengali Bosnian Bulgarian Catalan Cebuano Chichewa Chinese (Simplified) Chinese (Traditional) Corsican Croatian Czech Danish Dutch English Esperanto Estonian Filipino Finnish French Frisian Galician Georgian German Greek Gujarati Haitian Creole Hausa Hawaiian Hebrew Hindi Hmong Hungarian Icelandic Igbo Indonesian Irish Italian Japanese Javanese Kannada Kazakh Khmer Korean Kurdish (Kurmanji) Kyrgyz Lao Latin Latvian Lithuanian Luxembourgish Macedonian Malagasy Malay Malayalam Maltese Maori Marathi Mongolian Myanmar (Burmese) Nepali Norwegian Pashto Persian Polish Portuguese Punjabi Romanian Russian Samoan Scottish Gaelic Serbian Sesotho Shona Sindhi Sinhala Slovak Slovenian Somali Spanish Sudanese Swahili Swedish Tajik Tamil Telugu Thai Turkish Ukrainian Urdu Uzbek Vietnamese Welsh Xhosa Yiddish Yoruba Zulu

## RATES OF CHANGE

Changes in quantities over time are also known as rates of change and may be calculated from;

Rate of change

Under this topic we shall consider the rates of change of

1. Distance with time

2. Velocity with time.

The rates of change may also be obtained from gradients of graphs, so we shall specifically consider

1. Distance – time graphs

2. Velocity – time graphs

A VIDEO BELOW ABOUT RATE OF CHANGE1. DISTANCE – TIME GRAPHSExample;

1. Tony walks 3 km at a constant speed, taking 50 minutes. He then runs 5 km at a constant speed, taking 25 minutes. Draw a distance time graphs of Tony Journey. Using a scale of 2 cm = 1 km and 1 m a scale of 2 cm = 1 km and 1 cm = 10 minutes. Use the graph to find his average speed for the whole journey in m/s.

2. Mary travels by car. At constant speed, from her home to London which is 70 km a way. She leaves home at 2.00 pm and arrives at 2.45 pm. She stays in London for 2 hours, then return homes , taking 50 minutes. Draw a distance – time graph showing Mary’s journey to and from London. Use a scale of 1 cm= 20 minutes and 2 cm = 10 km. Use the graph to find her velocity.

2. VELOCITY- TIME GRAPHSFrom the velocity – time graphs we may obtain the distance covered by the body and the acceleration of the body.

Distance covered – Area under the curve.

Acceleration at a point – gradient of graph.

WAVES

THE VIDEO BELOW IS ABOUT DISTANCE TIME GRAPHSA UNIT CIRCLE

This is a circle whose radius is 1 unit.

Note ; The x- coordinate gives the cosine of the angle and the y- coordinate gives the sine of the angle , the coordinate can therefore be given in the form p(cosθ,Sin θ)

Where θ is the angle , the radius makes with the x-axis.

If the radius is multiplied by a scale 2, 3…..(Unit circle enlarged) then the coordinates are given in form of p(rcosθ,r sinθ)where r is 1,2,3…….

Example . Write down the coordinates of a point

STATISTICS 11

AVERAGES

Averages include;

1. Mean

2. Mode

3. Medium, etc.

The Mean.

The Median.

For grouped data the median is obtained from the formula.

A VIDEO BELOW SHOWING HOW TO SOLVE PROBLEMS WITH AVERAGE AND STATISTICS

QUADRATIC EXPRESSIONSREVISIONSolve the following equations by completing squares;

MINIMUM AND MAXIMUM VALUESA video about Factoring Quadratic ExpressionsFind the maximum or minimum value of each of each of the expression and when they occur;

To investigate whether -2 is the maximum or maximum value of the expression. we find that -2 ,8 the minimum vale.

For what value of x does this occur.

Find the maximum value of the following expressions.

## Attachments32

## ASSIGNMENT : RATES OF CHANGE AND QUADRATIC EXPRESSION ASSIGNMENT

MARKS : 30 DURATION : 24 hours

Add a note