FORM ONE MATHEMATICS STUDY NOTES TOPIC 4-6.

TOPIC 4: UNITS
A unit – is defined as a symbol or sign which is assigned to a number to describe a kind of measurement made
Convertion of One Unit of Length to Another
Convert one unit of length to another
The conversion of one unit to another is done by considering the arrangement below
Example, from the above we get
Computations on Metric Units of Length
Perform computations on metric units of length
Example 1
Convert
Solution

TOPIC 5: APPROXIMATIONS
Measurements can be rounded to a certain number of significant figures.Approximation- is a process of rounding numbers to a certain degree of accuracy.A number can be rounded to a certain required place value such as to the nearest ten, hundred, and thousand
Rounding off Whole Numbers to Given Place Values
Round off whole numbers to given place values
STEPS
  • When rounding a number, stand at the digit of the required place value, then look at the next digit to the right; if it is or more, round up (i.e, increase the digit of the required place value by 1) and if it is or less, do not change the digit of the required place value
  • Replace all the remaining digits to the right of the required place value with the zeros
Example 1
The population of Tanzania in a census of 2002 was 42,850,671. Round this to the nearest
  1. million
  2. ten million
Solution
  1. The million digit is 2, since the next digit to the right is greater than 5, then we can increase 2 by 1 and put the remaining digits to the right of 2 zeros. There fore;42,850,671 ≈ 43,000,000
  2. The ten million digit is 4, since the next digit to the right is less than 5, then we do not change 4 but we put the remaining digits to the right of 4 zeros. There fore;42,850,671 ≈ 40,000,000
Decimals to a Given Number of Decimal Place
Round off decimals to a given number of decimal place
STEPS
  • When rounding a decimal, stand at the digit of the required decimal place, then look at the next digit to the right; if it is or more, round up (i.e increase the digit of the required decimal by 1) and if it is or less, do not change the digit of the required decimal place
  • Replace all the remaining digits to the right of the required decimal place with the zeros
NOTE
  • The first digit after the decimal point is the first decimal place, the second digit after the decimal point is the second decimal place e.t.c
  • Example 0.568 is the first decimal place and is the second decimal place
Example 2
Round 0.24736 to the nearest
  1. 1 decimal place
  2. 2 decimal places
  3. 3 decimal places
Solution
  1. 0.24736≈ 0.02 (1 d.p)
  2. 0.24736≈ 0.025 (2 d.p)
  3. 0.24736≈ 0.0247 (1 d.p)

The Knowledge of Rounding Off of Numbers in Computations Involving Large Numbers and Small Numbers
Use the knowledge of rounding off of numbers in computations involving large numbers and small numbers
Approximation can be used in operation to check whether a calculation is correct or not, i.e in addition, subtraction, multiplication and divisione.g 446 x 45 = 20 070
The above calculation can be checked quickly whether it is correct or not by rounding each number to 1 significant figure and then multiply i.e 400 x 50 = 20 000
Therefore, the approximation of 20 000 is close to 20 0070 is correct.Before carrying an operation, each number in a calculation is rounded to 1 significant figure
Example 5
Find the approximate value of
Example 6
A school trip of 32 people went to a tour, which costs a transport fee of 580/- each people. What was the approximate total transport cost?
Solution
32 × 580 ≈30×600 = 18 000
The approximate transport cost was 18 000/- 
TOPIC 6: GEOMETRY
Points and Lines
The Concept of a Point
Explain the concept of a point
A point – is a smallest geometric figure which gives a position of object in a plane
A line segment – is a straight line joining two points in a plane
The Concept of a Point to Draw a Line
Extend the concept of a point to draw a line
A line segment – is a straight line joining two points in a plane
A line passing through two points e.g A and B and extends without end (i.e infinitely) in both directions is denoted by
The Difference Between a Line, a Line Segment and a Ray
Distinguish between a line, a line segment and a ray
A ray - is a line starting from a point, say A and pass through a point, say B and extends without end in one direction.It is denoted by
A Circle
Draw a circle
To make a circle: Draw a curve that is "radius" away from a central point.
And so:All points are the same distance from the center.
You can draw it yourself:Put a pin in a board, put a loop of string around it, and insert a pencil into the loop. Keep the string stretched and draw the circle!
Different Parts of a Circle
Describe different parts of a circle
Theradiusof the circle is a straight line drawn from the center to theboundaryline or the circumference. The plural of the word radius isradii.
Thediameteris the line crossing the circle and passing through the center. It is the twice of the length of the radius.
Thecircumferenceof a circle is theboundaryline or theperimeterof the circle.
Anarcis a part of thecircumferencebetween two points or acontinuouspiece of a circle. The shorter arc betweenandis called theminor arc. The longer arc betweenandis called themajor arc.
Thechordis a straight line joining two points on thecircumferencepoints of a circle. The diameter is a special kind of the chord passing through the center.
Asemi-circleis an arc which is half of thecircumference.
Atangentis a straight line which touches the circle. It does not cut thecircumference. The point at which it touches, is called thepoint of contact.
 FORM ONE MATHEMATICS OTHER TOPICS
FORM ONE MATHEMATICS TOPIC 1-3.
FORM ONE MATHEMATICS STUDY NOTES TOPIC 4-6.
FORM ONE MATHEMATICS STUDY NOTES TOPIC 7-9.
FORM ONE MATHEMATICS STUDY NOTES TOPIC 10-11.

O'LEVEL MATHEMATICS NOTES 
FORM ONE MATHEMATICS STUDY NOTES

FORM TWO MATHEMATICS STUDY NOTES

FORM THREE MATHEMATICS STUDY NOTES

FORM FOUR MATHEMATICS STUDY NOTES

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