Formula Sheet

. Formula Sheet 4 CXC Area and Perimeter Formula Trigonometric Formula Perimeter = distance around the outside (add all sides). Opposite – side opposite to angle Adjacent –side beside (adjacent) to angle Hypotenuse- longest side sin cos tan opposite hypotenus adjacent hypotenus opposite adjacent θ θ θ = = = hyp θ c adj hyp a opp b Remember: works only on right angle triangles Pythagorean Theorem Triples: 3,4,5 5,12,13 8,15,17 C is the hypotenuse, a and b are the other sides. Remember: works only on right angle triangles Coordinate Geometry Formula Distance Formula: Midpoint Formula: Gradient Formula: Parallel lines have equal slope. Perpendicular lines have negative reciprocal gradients. Volume and Surface Area Equation of a line Slope-Intercept Method: y mx c = + Point-Gradient Method:.

. Angle Information Parallel lines Complementary angles - two angles whose sum is 90. Supplementary angles - two angles whose sum is 180. Corresponding angles are equal. 1= 5, 2= 6, 3= 7, 4= 8 Alternate Interior angles are equal. 3= 6, 4= 5 Alternate Exterior angles are equal. 1= 8, 2= 7 Same side interior angles are supplementary. m 3+m 5=180, m 4+m 6=180 General Triangle Information Sum of angles of triangle = 180. Measure of exterior angle of triangle = the sum of the two non-adjacent interior angles. The sum of any two sides of a triangle is greater than the third side. Solving triangles c b a B A C Sine rule sin sin sin a b c A B C = = or c C sin b B sin a A sin = = Used when any two sides and their corresponding angles are involved to find one missing side or angle. Cosine rule 2 2 2 2 2 2 2 2 2 2 cos 2 cos 2 cos a b c bc A b a c ac B c a b ab C = + − × = + − × = + − × Polygons Sum of Interior Angles: Sum of Exterior Angles: Each Interior Angle (regular poly): Each Exterior Angle (regular poly): Quadratic Formula.

. Used when three sides and an angle between them are given to find the other side Heron’s Formula Area of a triangle given only the length of the sides ( )( )( ) 2 A s s a s b s c a b c where s = − − − + + = Capital letters represent Angles Common letters represent sides If 2 0 ax bx c + + = then 2 4 2 b b ac x a − ± − = Circle Facts Tangent 5. Radius to tangent is 90o at point of contact. 6. The tangents to a circle from an external point T are equal in length. 7. Angle between tangent to circle and chord at the point of contact is eqaual to the to the angle in the alternet segment 2. 1a. O 4. 3. 6. 5. T 7. radius diameter segment Sector Diameter = 2× radius Area of circle = πr2 Circumference of circle = 2πr or πd Length of arc = 2πr × 360 θ Area of sector = πr2 × 360 θ Angles in circles �� � �� � − �� � �� � × = − = θ θ π sin 2 1 360 sec 2 2 r r triangle of Area tor of Area Segment of Area T B A D E.

. 1b. 1c. 1d. 1. a,b,c,d Angle at the center in twice angle at the circumference. 2. Angle formed on the diameter in 90o 3. Angles in the same segment are equal 4. opposite angles in a cyclic Quadrilateral are supplimentary( add up to 180o) Matrices Transformational Matrices Adding or subtracting matrices a b e f a e b f c d g h c g d h ± ± � � � � � � ± = � ÷ � ÷ � ÷ ± ± � � � � � � Multiplying Matrices a b e f ae bg af bh c d g h ce dg cf dh + + � � � � � � × = � ÷ � ÷ � ÷ + + � � � � � � Determinant of 2×2 Matrix If a b A c d A ad cb � � = � ÷ � � = − A singular matrices has a determinant of 0 Adjoint of 2×2 matrix int a b A c d d b A adjo c a � � = � ÷ � � − � � = � ÷ − � � Inverse of 2×2 matrix REFLECTION Multiply matrices by each point to get reflection in x- axis y- axis y=x y=-x �� � � �� � �− 1 0 0 1 �� � � �� � � −1 0 0 1 �� � � �� � � 0 1 1 0 �� � � �� � � − − 0 1 1 0 TRANSLATION Movement of x in x direction and y in ydirection add matrix �� � � �� � � y x to eack point to get its image. ROTATION Multiply by matrices to get rotation of -degrees clockwise ϴ about origin (0,0) �� � � �� � � − θ θ θ θ θ cos sin sin cos R �� � � �� � � − 0 1 1 0 R90 �� � � �� � � − − 1 0 0 1 R180 �� � � �� � � − 0 1 1 0 R270 Enlargment Multiply each point by scale factor K to get the image of the point for an enlargment from the origin. Sets.

. . 1. 1. 1 adjoint. 1. a b A c d. A A A. or. d b A ad bc c a.

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. . . Shape Volume Surface Area. Cube. 1. l. l. l×l×l=l3 6l2.