March 10, 2016 Grade 10, Introduction to Trigonometry, Math

Definition Trigonometry is the study of relationships between the sides and angles of a triangle. The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). Watch Trigonometry Video for more learn. Trigonometry The earliest known work on trigonometry was recorded in Egypt and Babylon. Early astronomers used […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

Symmetry Mathematically , when one shape becomes exactly like another if you flip, slide or turn it. It comes from a Greek word meaning ‘to measure together’ and is widely used in the study of geometry.Watch Symmetry to learn more.. For two objects, they must be the same size and shape, with one object having […]

March 10, 2016 Grade 10, Math, Polynomials

SUM OF ROOTS A quadratic equation is a second-order polynomial equation in a single variable and the second-order polynomial equation, the fundamental theorem of algebra describes that it has two solutions. These solutions may be both real, or both complex. The values of the variable satisfying the given equation are called roots of the equation. Sum of roots is […]

March 10, 2016 Grade 10, Introduction to Trigonometry, Math

TRIGONOMETRIC RATIOS OF NEGATIVE ANGLE In trigonometry negative angles go clockwise. Any function f for which the equation f (- x) = – f (x) holds true is called an odd function. A function for which the equation f (-x) = f (x) holds true is called an even function. Sine and cosine are examples of odd and even functions, respectively.Watch TRIGONOMETRIC RATIOS OF NEGATIVE ANGLE VIDEO to […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

ANGLE BETWEEN TWO LINES The point of intersection of two non-parallel lines can be found from the equations of the two lines. If two lines intersect each other, then the vertically opposite angles are equal. Intersecting lines are two lines that share exactly one point. This shared point is called the point of intersection. Watch ANGLE BETWEEN TWO […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

HOLLOW CYLINDER Cylinders are sort of prisms with circular bases. A hollow cylinder is formed by the curved surface only. Pipe, straw, tubes, flute, are examples for hollow cylinders.Watch HOLLOW CYLINDER VIDEO to learn more.. A hollow cylinder has only the curved surface, which is also called the lateral surface. The area of this surface […]

March 10, 2016 Grade 10, Math, Probability

PROBABILITY The probability of an event is its relative frequency (proportion) in the population. The greater the probability the more likely the event will occur. Probability is the science of chance behavior. Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run.Watch PROBABILITY VIDEO to learn […]

Concurrency Of The Medians Of A Triangle The medians of a triangle are concurrent and the point of concurrence, the centroid, is one-third of the distance from the opposite side to the vertex along the median.Watch Medians Of A Triangle Video to learn more. Proof: Given triangle ABC and medians AE, BD and CF. So F […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

SURFACE AREA AND VOLUME OF A CYLINDER A cylinder has circular faces at each end and a curved face. A cylinder has circular faces at each end and a curved face. A cylinder is a closed solid that has two parallel (usually circular) bases connected by a curved surface.Watch CYLINDER VOLUME AND SURFACE ARES VIDEOS […]

March 10, 2016 Areas Related to Circle, Grade 10, Math

AREA AND CIRCUMFERENCE OF A CIRCLE AND ITS SECTOR The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle. The fixed point is called the centre of the circle and the fixed distance is called the radius of the […]

Area Of The Triangle When Coordinates Of Vertices Are Given A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. To find the area of a triangle, multiply the base by the height, and then divide by 2. We can find […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

FRUSTUM OF A CONE If a plane cuts a right circular cone parallel to its base and the upper smaller cone is removed, then the remaining part of the cone containing the base is called “Frustum of the cone”.Watch FRUSTUM OF A CONE VIDEO to learn more. A frustum of a cone is the slice […]

Concurrency Of The Bisectors Of The Angles Of A Triangle Lines that contain the same point are called concurrent. Concurrence is the concept of three or more lines intersecting in a single (common) point, having a single point of intersection.Watch Angles Of A Triangle Video to learn more. Proof of Theorem: Let ABC be an […]

March 10, 2016 Grade 10, Math, Real Number

FUNDAMENTAL THEOREM OF ARITHMETIC AND REAL NUMBER A lemma is a proven statement used for proving another statement. Euclid’s Division Lemma : Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0 ≤ r < b.Watch ARITHMETIC AND REAL NUMBER VIDEO to learn more. An […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

Section Formula Consider the line joining the points A(x1,y1) and B(x2,y2). Suppose that we want to find the ratio of division of the line joining the points A and B at a point P(x,y) on it or we want to find the point of division of the line joining the points A and B in […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

VOLUME AND SURFACE AREA OF RIGHT CIRCULAR CONE If a right angled triangle is revolved about one of the side containing the right angle, the solid formed is called a right circular cone. Watch RIGHT CIRCULAR CONE VIDEO to learn more. Sector: is a part of circular region bounded by two radii and an arc. If […]

March 10, 2016 Coordinate Geometry, Grade 10, Math

VOLUME AND SURFACE AREA OF RIGHT CIRCULAR CYLINDER If a rectangle revolves about one of its sides and completes a full rotation, the solid formed is called a right circular cylinder. It is called so because, the cylinder has a circular base and its axis is at right angle to the base. The line segment […]

SCALE FACTOR When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.Watch SCALE FACTOR VIDEO to learn more.. In two similar geometric figures, the ratio of their corresponding sides is called the scale factor. To find the scale factor, locate two corresponding sides, one […]

REFLEX ANGLE Reflex angle is an angle between 180° and 360°. A full angle is therefore a reflex angle, while acute, obtuse, right, and straight angles are not.Watch REFLEX ANGLE VIDEO to learn more.. The reflex angle is the larger angle. It is more than 180° but less than 360°. Therefore, reflex Angle is an angle that lies between 180° and 360°. The […]

March 10, 2016 Constructions, Grade 10, Math

ANGLE SUBTENDED BY EQUAL ARCS The theorem states that in the equal circles , if two arcs are equal then they subtend equal angles at the centre of the circle.Watch ANGLE SUBTENDED BY EQUAL ARCS VIDEO to learn more. The angle subtended by (“hanging from”) an arc at the centre of a circle and the […]

March 10, 2016 Constructions, Grade 10, Math

EQUAL ARCS SUBTENDED EQUAL ANGLE AT THE CENTRE According to the theorem, if two arcs subtended equal angles at the centre of an equal circles or in the same circle is equal.Watch EQUAL ANGLE AT THE CENTRE VIDEO to learn more. Rotate the circle so that the arc PQ coincides with the arc AB or BA. Then the angles POQ and AOB coincide, and […]

March 9, 2016 Coordinate Geometry, Grade 10, Math

COMPLEMENTARY ANGLES Two angles are if the sum of their measures is 90o. Each angle is the of the other. Three or more angles are also not called complementary, even if their measures happen to add up to 90 degrees.Watch COMPLEMENTARY ANGLES VIDEO to learn more. Complementary angles are two angles with a sum of 90º. Three […]

March 9, 2016 Grade 10, Math, Some Applications of Trigonometry

HEIGHTS AND DISTANCES Some times we are required to find the height of a tower , tree, building and distance of a ship from light house, width of a river etc. We cannot measure them accurately , though we can find them using the knowledge of trigonometric ratio.Watch HEIGHTS AND DISTANCES VIDEO to learn more. […]

March 7, 2016 Coordinate Geometry, Grade 10, Math

SUPPLEMENTARY ANGLES Two Angles are Supplementary when they add up to 180 degrees. Together they make a straight angle. Two angles are said to be supplementary if their sum is 180o. This makes them add up to make a straight line.Watch Supplementary Angles Video to learn more. In geometry, two angles whose measures sum to […]