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ALGEBRA
Like terms:
In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions so that the result of the expression can be obtained very easily.
Expand:
In algebra, expanding can be defined as to get rid of the brackets. To expand, we need to multiply the outside numbers with the inside bracket numbers. For example:
a(b+c) = a(c+b)
=> ab + ac = ac + ab
Simplify
Simplifying an expression is just like solving the expression to make it as simple as possible. To simplify an expression, the first thing to do is to collect like terms. Then calculate the rest. For example,
3 + 4x - 2x + 5
=3 + 5 + 4x - 2x
= 8 + 2x
DIRECT AND INVERSE PROPORTIONS
Summary
Summary
Direct Proportion: y=kx for a constant k
Indirect Proportion: y = k/x for a constant k
EXPLANATION:
What is direct proportion? The alternation when a quantity goes up then the other quantity must go up too, or when a quantity goes down then the other quantity must go down too.
What is inverse proportion? The alternation when a quantity goes up then the other quantity must go down, or when a quantity goes down then the other quantity must go up.
SETS
Summary:
Sets: collection of numbers, letters, symbols, or objects, etc; which are somehow related.
Items in sets are called members or elements. They’re usually in brackets {}. They help with distinguishing between sets from lists and unrelated items.
Set Builder Notation: ‘Set Builder’ notations are used to describe the elements in a set. Set builder notations use mathematical expressions with x to describe the elements in the set.
Universal Sets: The universal set is the set of all elements under consideration
Complement of a Set: Complements of a set are elements that are not in a set. Complements are written with an apostrophe after the set. Example: x’, y’,...
Intersection: Overlapping elements that are in both sets
Union: The complete set of all elements in both sets combined
PROBABILITY
Dependant
The outcome of one event affects the outcome of another event.
Independant
The outcome of one event does not affect the outcome of another event.
Experimental
The probability of an event happening based on an actual experiment or observation.
Theoretical
The probability we expect of the total outcomes and the outcomes leading to the event.
A probability tree diagram is used to represent the probability of occurrence of events without using complicated formulas. It displays all the possible outcomes of an event. The purpose of a probability tree is that it shows all the possible outcomes of an event and calculates the probability of these outcomes. The rule for finding the probability of a particular event in a probability tree diagram occurring is to multiply the probabilities of the corresponding branches. Tree diagrams are very helpful for analysing dependent events. A tree diagram allows you to show how each possible outcome of one event affects the probabilities of the other events.
GEOMETRY
Summary:
Geometry is one of the oldest branches of mathematics. It is concerned with the properties and relations of points, lines, surfaces, solids, etc.
3D shapes
3D shapes are made up of 3 main parts: The vertex (Plural: vertices), the face, and the edge.
Surface area: Surface area is the amount of space covering the outside of a three-dimensional shape.
Volume: The amount of space a 3D object takes up.
2D shapes
2D shapes are a little more complicated. What we learned in class today was about the parts of 2D shapes.
2D SHAPES
Circumference: Area around circle
Radius: The distance from the center of the circle to the boundary of the circle.
Diameter: Line segment that goes straight across the circle, through the center. It is the longest possible line that can be drawn inside a circle and is twice the length of the radius.
Arc: Part of the circumference
Chord: A line segment going from one point of the circumference to another but does not go through the center.
Tangent: A straight line that touches the circle at a single point and does not go through the circle.
Sector: A section of the circle created by two radii.
Segment: A section of the circle created by a chord.
In triangles, the longest side of the triangle is the hypotenuse
All the angles inside a triangle add up to 180 degrees
Pythagoras Theorem:
Pythagorean theorem, a well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle) or, in algebraic notation a2 + b2 = c2.
3D SHAPES
3D SHAPES FORMULA SA - VOLUME
In geometry, 3D shapes are three-dimensional solid shapes or figures. Dimensions of 3D shapes (three-dimensional objects) are typically length, breadth, and height.
A cuboid is a three-dimensional solid shape in geometry. A cuboid is a convex polyhedron circumscribed by six rectangular faces, eight vertices, and twelve edges. A rectangular prism is another name for a cuboid. A cube is a cuboid with six square faces.
A three-dimensional shape is a pyramid. A pyramid has a polygonal base and flat triangular faces that meet at a location known as the apex. By linking the bases to an apex, a pyramid is constructed. Each edge of the base connects to the apex, forming the triangle face known as the lateral face.
A cone is a solid three-dimensional geometric object with a circular base and a sharp edge at the top known as the apex. A cone has a single face and a single vertex. A cone does not have any edges. The cone's three elements are its radius, height, and slant height.
GEOMETRIC CONSTRUCTIONS, ANGLES
COMPASS
RULER
GEOMETRIC CONSTRUCTIONS
30 degree angle
45 degree angle
60 degree angle
90 degree angle
Parallel lines:
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.
Corresponding, Alternate, and Co-interior angles:
Corresponding angles: Corresponding angles form the F shape. They have the same degree. If a line crosses parallel lines, it would form a corresponding angle.
Alternate angles: Alternate angles form the Z shape. They have the same degree. If a line crosses parallel lines, it would form an alternate angle.
Co-interior angles: Co-interior angles form the C shape. Both angles add up to 180 degrees. If a line crosses parallel lines, it would form a co-interior angle
Supplementary angles:
The two angles are said to be supplementary angles when they add up to 180°. The two angles together make a straight line. The angles are usually together.
Congruent Triangles:
Triangles are said to be congruent if the three sides and the three angles of both the angles are equal in any orientation.
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