Menjelang Sambutan Ulangtahun Kemerdekaan

Effective Study Skills
Students often fail to secure good grades despite studying for hours. This is because they have never studied effectively. Unless you know how to make your study hours effective, you cannot get the expected results. Here we will give you some glimpses of effective study skills.

• A study is called effective if you can remember and recall the major segments of the syllabus that you have read. Do not try to cram chapters that you fail to understand. You will never be able to remember them. The easiest thing to do is to seek the assistance of your classmates or the teachers to understand the confusing portions.
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  You have to decide what is most important to you. Make your schedule to address those important needs. You should never compromise with your priorities. Never try to finish too many things at a time. Study all the subjects on a regular basis while allotting some time for revisions. Keep yourself motivated. It is better to know the theme of the chapter that you are planning to study. Reading it line by line will then help you understand it better.
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  Effective study skills also stress on reading methods. You will see that there are some words that have fonts in bold or italics; you should pay special attention to these. You can also try to find whether the current text refers to any other works of the author that you have read earlier.
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  Effective study skills include listening to the explanations given by teachers. You should read and understand the notes that you have taken in the classroom. Following these aforesaid effective study skills will save you disappointments and help you get the desired results.
  
  

Solid Geometry

Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes are cubes, rectangular solids, prisms, cylinders, spheres, cones and pyramids.

Cubes
A cube is a three-dimensional figure with six matching square sides.

The figure above shows a cube.

The dotted lines indicate edges hidden from your view.

If s is the length of one of its sides,

the Volume of the cube = s x s x s.

Since the cube has six square-shape sides,

the Surface area of a cube = 6 x s x s

Cuboid

In a cuboid, the length, width and height may be of different lengths.

The volume of the above cuboid would be the product of the length, width and height that is
Volume of rectangular solid = lwh
Surface area of rectangular solid = 2(lw + wh + lh)

Prisms
A prism is a solid that has two congruent parallel bases that are polygons. The polygons form the bases of the prism and the length of the edge joining the two bases is called the height.

A rectangular solid is a prism with a rectangle-shaped base.
The volume of a prism is given by the product of the area of its base and its height.

Cylinders
A cylinder is a solid with two congruent circles joined by a curved surface.
In the above figure, the radius of the circular base is r and the height is h.

The volume of the cylinder is the area of the base × height.

Spheres
A sphere is a solid with all its points the same distance from the center.

Cones

A circular cone has a circular base, which is connected by a curved surface to its vertex. A cone is called a right circular cone, if the line from the vertex of the cone to the center of its base is perpendicular to the base.

Pyramids
A pyramid is a solid with a polygon base and connected by triangular faces to its vertex. A pyramid is a regular pyramid if its base is a regular polygon and the triangular faces are all congruent isosceles triangles.

Symmetry / Reflection

• A plane figure is symmetrical about a line if it is divided into two identical (coincident) parts by that line. The line is called its line (or axis) of symmetry.
• A plane figure is symmetrical about a point if every line segment joining two points of the figure and passing through the point is bisected at that point. The point is called its point (or center) of symmetry.
• A plane figure has a rotational symmetry if on rotation through some angle ( 180°) about a point it looks the same as it did in its starting position.
• If A° ( 180°) is the smallest angle through which a figure can be rotated and still looks the same, then it has a rotational symmetry of order 360/A.
• The reflection (or image) of a point P in a line AB is a point P' such that AB is the perpendicular bisector of the line segment PP'.
  To find the reflection (or image) of a point P in a line ABFrom P, draw PM perpendicular to AB and produce PM to P' such that MP'= MP, then P' is the reflection (or image) of P in the line AB.
• The reflection of the point P (x, y) in the x-axis is the point P'(x, -y).
• The reflection of the point P (x, y) in the y-axis is the point P'(-x, y).
• If a point P (x, y) is rotated through 180° (clockwise or anti-clockwise) about the origin to the point P', then co-ordinates of P' are (-x,-y).
• If a point P (x, y) is rotated through 90° clockwise about the origin to the point P', then co-ordinates of P' are (y,-x).
• If a point P (x, y) is rotated through 90° anti-clockwise about the origin to the point P', then co-ordinates of P' are (-y,x).