SURDS Surds are the square roots  (√) of numbers that cannot be simplified into a whole or rational number. It cannot be accurately represented in a fraction RULES OF SURDS a√c + b√c = a+b√c a√c – b√c = a-b√c a√c x b√d = ab√cd a√c ÷ b√d = a/b√c/d Addition and Subtraction of Surds ….  Read More

LOGIC Logic is the study of reasoning. It provides rules and techniques to determine the validity of arguments and propositions. Propositions: A proposition (or statement) is a declarative sentence that is either true or false, but not both. Examples: “2 + 2 = 4” (True) “The sky is green.” (False) 2. Logical Connectives: Logical connectives ….  Read More

MATRICES Matrices are the ordered rectangular array of numbers, which are used to express linear equations. A matrix has rows and columns. we can also perform the mathematical operations on matrices such as addition, subtraction, multiplication of matrix. Example Addition and Subtraction of Matrices Multiplication of Matrices The first matrix’s column count must match the ….  Read More

SIMULTANEOUS EQUATIONS – ONE LINEAR, ONE QUADRATIC LINEAR EQUATION is an equation of the form Ax + By = C in which the highest exponent or power is equal to 1 (unity). Also, where A, B, C are numerals, x and y are variables. For example, 2x + y = 6 QUADRATIC EQUATION is an ….  Read More

SPHERE AND HEMISPHERE A sphere is a three-dimensional solid where all the points lying on the surface is equidistant from the centre. A hemisphere is formed when the plane cuts the sphere into two equal halves. A sphere is a combination of the two hemispheres  

Coordinate Geometry of Straight Line distance between two points midpoint of the line joining two points    

Gradient and Intercepts of a Line Gradient of a line of the form y = mx + c, is the coefficient of x, which is represented by m and c is the intercept on the y axis. Example Find the equation of the line with gradient 4 and y-intercept -7. Solution m = 4, c ….  Read More

DIFFERENCIATION Differentiation can be defined as a derivative of a function with respect to an independent variable. Differentiation, in calculus, can be applied to measure the function per unit change in the independent variable. Let y = f(x) be a function of x. Then, the rate of change of “y” per unit change in “x” ….  Read More

Differentiation – Product and Quotient Rule If the function is the sum or difference of two functions, the derivative of the functions is the sum or difference of the individual functions, i.e., If f(x) = u(x) ± v(x) then, f'(x) = u'(x) ± v'(x) Product Rule If the function f(x) is product of two functions ….  Read More