This comprehensive document contains a detailed summary of key concepts and topics covered in a 12th grade mathematics curriculum. It includes clear explanations, examples, and practice problems to help students understand and apply their knowledge. These notes are a valuable resource for anyone lo...
MATH NOTES FOR GRADE 12 IN A CONCISE AND
EASY TO UNDERSTAND WAY
1. Algebra:
A monomial is an expression that consists of only one term, such as 3x or 5xy^2.
A binomial is an expression that consists of two terms, such as x + y or 3a - 2b.
A trinomial is an expression that consists of three terms, such as x^2 + 3y - 4z.
A polynomial is an expression that consists of one or more terms, such as x^2 - 3x + 2 or 3x^4 +
2x^2 + 4.
The degree of a polynomial is the highest power of the variable(s) in the polynomial. For
example, the degree of x^3 + 2x^2 + 3x + 4 is 3.
A rational expression is an expression that can be written as a fraction, where the numerator
and denominator are polynomials. For example, (x^2 + 3x + 2)/(x + 1) is a rational expression.
2. Geometry:
A point is a location in space that has no size or dimension. It is represented by a dot in a
coordinate system.
A line is a straight path that extends indefinitely in two directions. It is represented by a straight
line in a coordinate system.
A plane is a flat surface that extends indefinitely in all directions. It is represented by a flat
surface in a coordinate system.
A triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is
always 180 degrees.
A quadrilateral is a polygon with four sides and four angles. The sum of the angles in a
quadrilateral is always 360 degrees.
A circle is a set of points that are all the same distance from a central point. The distance from
the center of the circle to any point on the circle is called the radius.
3. Trigonometry:
Trigonometry is the study of the relationships between the sides and angles of triangles.
The three most common trigonometric functions are sine (sin), cosine (cos), and tangent (tan).
The sine of an angle is equal to the ratio of the length of the side opposite the angle to the
length of the hypotenuse.
The cosine of an angle is equal to the ratio of the length of the side adjacent to the angle to the
length of the hypotenuse.
The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the
length of the side adjacent to the angle.
The inverse trigonometric functions (arcsin, arccos, arctan) are used to find the measure of an
angle in a right triangle given the lengths of the sides.
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