Basic Mathematics Form 3

Indice

1. 1. Relations

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   • Relations, ordered pairs and the Cartesian product
   • Domain and range
   • The inverse of a relation
   • Graphs of relations and inequalities
   • Summary

   What is a relation? In everyday life we speak of relations between people, such as "is the mother of". In mathematics, a relation is a rule that links elements of one set to elements of another set (or of the same set). A relation is written as a set of ordered pairs (x, y), where x is related to y. The order matters:…

2. 2. Functions

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   • What is a function?
   • Function notation, domain and range
   • Inverse functions
   • Graphs of quadratic functions
   • Step, absolute value and piecewise functions
   • Summary

   What is a function? A function is a special relation in which every element of the domain is related to exactly one element of the range . The relation {(1, 4), (2, 5), (3, 4)} is a function: each x has one y (two x-values may share a y). The relation {(1, 4), (1, 6)} is not a function, because 1 is related to two…

3. 3. Statistics

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   • Grouped data: classes, boundaries and class marks
   • The mean of grouped data
   • The median and mode of grouped data
   • Cumulative frequency, the ogive and quartiles
   • Summary

   Grouped data In Form Two you found the mean, median and mode of simple data. When there are many values, data are grouped into classes. In Form Three we learn to calculate the measures of central tendency for grouped data and to use cumulative frequency . Class limits and boundaries For the class 20–29, the class…

4. 4. Rates and Variations

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   • Rates
   • Exchange rates
   • Direct and inverse variation
   • Joint and partial variation
   • Summary

   Rates A rate compares two quantities of different kinds , such as distance and time (speed in km/h), money and mass (price per kg), or volume and time (litres per minute). For example, a pump that fills 1,800 litres in 45 minutes works at a rate of 1,800 ÷ 45 = 40 litres per minute. Exchange rates are rates used to…

5. 5. Sequence and Series

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   • Sequences, series and the nth term
   • Arithmetic progressions
   • The sum of an arithmetic series
   • Geometric progressions and their sums
   • Applications: savings, interest, growth and depreciation
   • Summary

   Sequences and series A sequence is a list of numbers that follow a pattern, such as 2, 5, 8, 11, … Each number is a term ; the first term is written a or T 1 , and the nth term T n . A series is the sum of the terms of a sequence: 2 + 5 + 8 + 11. The sum of the first n terms is written S n . Arithmetic progression (AP)…

6. 6. Circles

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   • Parts of a circle, arcs and sectors
   • Chord properties
   • Angle properties of a circle
   • Cyclic quadrilaterals
   • Tangents to a circle
   • Summary

   Parts of a circle A circle is the set of all points in a plane that are the same distance from a fixed point, the centre . That distance is the radius . A chord joins two points on the circle; the longest chord, through the centre, is the diameter . Part of the circumference is an arc . A chord divides the circle into…

7. 7. The Earth as a Sphere

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   • The earth as a sphere: great and small circles
   • Latitude and longitude
   • Distances along great circles
   • Distances along parallels of latitude
   • Longitude and time
   • Summary

   The earth as a sphere For calculations we treat the earth as a sphere with radius about 6,370 km . It rotates about an axis through the North Pole and the South Pole . Great circles and small circles A great circle is a circle on the earth's surface whose centre is the centre of the earth; it divides the earth into two…

8. 8. Accounts

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   • Accounts and the accounting equation
   • Double entry, the ledger and the cash account
   • The trial balance
   • The trading, profit and loss account
   • The balance sheet
   • Summary

   Why keep accounts? Every business, from a small duka to a large company, needs records of its money and goods. Book-keeping is the recording of business transactions in a systematic way. Accounts are the summaries prepared from these records to show whether the business made a profit or a loss and what it owns and…