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Mathematics Term 1 Karen Bright Saragih - Coggle Diagram
Mathematics Term 1 Karen Bright Saragih
Exponent and Roots
Exponents
Exponents are used to rewrite or summarize a long multiplication problem
The part that repeats is the base while the times they are multiplied is the exponent.
Ex: 13^9
Roots
There are 2 types of roots: Square root and Cubic root
We can also find roots in fraction and rationalize the fractions they are in.
Ex: a/√b
Transformations, Congruency and Similarity, Fractions to Decimals to Percents
Transformation
Transforming is when you
change
something. There are four types of transforming which are: Translation, rotation, reflection, and Dilation.
Translation
is when you slide a figure in a fixed direction, their sizes and shape don't change, but they have different places
Rotation
is when you turn an original shape around. It can be turned clockwise or counter-clockwise.
Reflection
is when you make a similar shape to the original shape, but they are flipped.
Dilation
is when you have 2 shapes that are the same, but their sizes are different.
Congruency and Similarity
A polygon is similar if the ratios of the measures corresponding sides are equal and when the corresponding angles are congruent.
Similar figures have the
same shape
, but they don't have the
same size
Dilation (the shape getting bigger) and reduction (the shape getting smaller) are also an example when similar figures show.
Fractions to Decimals to Percents
When writing percentages to fractions, we put the percentage over 100 and simplify it if possible. (Ex: 88/100 = 22/25)
When writing percentages as a decimal, we divide the percentage with 100. (Ex: 51÷ 100 = 0.51)
When making a decimal to a percentage, we put the decimal to fraction form first then make it into a percentage. (Ex: 0.08 --> 8/100 --> 8%)
Angles and Parallel Lines
Lines
Intersecting lines is when 2 lines cross exactly at one point.
Perpendicular lines is when 2 lines meet at one point and form a 90 degree angle
Parallel Lines are lines that do not intersect but they are one as a pair
Transversal line is a line that intersects two or more lines
Vertical angles, Linear pair, Complementary angles, etc.
Vertical angles are 2 angles that are opposite angles. they are always congruent
A linear pair is also called a supplementary angle because linear pairs are 2 that form a line (180 degree angle)
Complementary angles are 2 angles that form a 90 degree angle.
Adjacent angles are angles that have a common vertex and a common side.
Angles in a circle and Trigonometry
Angles in a circle
Center angles (Angles drawn on the center point of a circle) are the double of inscribed angles (Angles drawn on the circumference of a circle)
A triangle that has a diameter will always have a 90 degree inscribed angle
Angles connected by a chord (A line) are equal
When a tangent meets the radius of a circle on the circumference, it always forms a 90 degree angle.
Whenever there is a quadrilateral in a circle, the opposite sides always total up to 180 degrees.
Trigonometry
We use Sine, Cosine, and Tangent in trigonometry
Sin = Opposite/hypotenus
Cos = Adjacent/hypotenuse
Tan = Opposite / adjacent