Math Assignment - Gr11 - Foundations

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i) Pythagorean Theorem
In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides.  

The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation: c  a  b 

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. ii) Sine Ratio The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. A

hypotenuse

sin A =

=

adjacent opposite



sin B =

=

opposite adjacent 



iii) Cosine Ratio The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. A
hypotenuse adjacent opposite

cos A =

=



cos B = iv)Tangent Ratio

=

opposite adjacent 



The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent A side. hypotenuse adjacent opposite

tan A = tan B =

= =



opposite adjacent 



V) Angle of Elevation The angle of elevation, or angle of inclination, is the angle made between the horizontal and the sight line from the from the observer’s eye to some object above eye level.

vi) Angle of depression
The angle of depression is the angle made between the horizontal and the sight line from the observer’s eye to a point below eye level.

vii) Sine Law
We can define Sine Law the relationship between the length of the sides and their opposite angles in any triangle. A

b



C  a B

viii) Cosine Law The Cosine Law is the relationship between the length of the three sides and the cosine os an angle in any triangle. The cosine law (also known as the cosine formula or cosine rule) is an extension of the Pythagorean theorem: A

b





a



or equivalently,

ix) Measure of Central Tendency Definition of Measures of Central Tendency  

A measure of central tendency is a measure that tells us where the middle of a bunch of data lies. The three most common measures of central tendency are the mean, the median, and the mode.

More about Measures of Central Tendency
 



Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average. Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers. Mode: Mode is the value that occurs most frequently in a set of data.

Examples of Measures of Central Tendency


For the data 1, 2, 3, 4, 5, 5, 6, 7, 8 the measures of central tendency are Mean = Median = 5 Mode = 5

x) Variance Definition of Variance
 

Variance is a statistical measure that tells us how measured data vary from the average value of the set of data. In other words, variance is the mean of the squares of the deviations from the arithmetic mean of a data set.

More about Variance Variance is the square of the standard deviation.

Variance = xi) Standard deviation The Standard Deviation is a measure of how spreads out numbers are. The formula: it is the square root of the Variance. xii) Doubling Period The time required for each doubling in exponential growth is called doubling time The doubling time is the period of time required for a quantity to double in size or value. It is applied to population growth, inflation, resource, extraction, consumption of goods, compound interest, the volume of malignant tumors, and many other things which tend to grow over time. xiii) Half-Life Period The time it takes for a quantity to decay or be reduced to half its initial amount. So, the time required for each halving in exponential decay is called halving time. xiv) Vertex of parabola The vertex of a parabola is the highest point if the...
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