MATHS SUMMARIES FOR JSS
REFERENCE SUMMARIES FOR TEACHERS AND STUDENTS)
(1) THE BINARY SYSTEM
a. A number in base 2 is called a BINARY NUMBER
b. A binary number is a sum of powers of 2
c. In base 2 we have only two numbers 0 & 1 to work with
d. To express a binary number as a decimal number write the given binary number as a sum of multiples of 1, 2, 4,8,16 etc.
(2) WORD PROBLEMS AND FRACTIONS
a. You should be able to express word problems in numerical terms
b. You should be able to simplify expressions having brackets and fractions.
a. Rational numbers consist of all counting numbers, integers, and fractions (positive and negative).
b. A class of non-rational numbers includes square roots, of natural numbers which are not perfect squares.
c. An important example of a non-rational is π.
d. Approximations of square roots which are non-rational can be obtained by using trial and error method.
a. You should be able to factorize expressions of the form a2-b2. Same for a2 ± 2ab + b2.
b. You should be able to factorize quadratic expressions by completing the squares.
(5) SIMPLE EQUATIONS INVOLVING FRACTION
a. Find the L.C.M of all denominations.
b. Multiply each term in the equation by this L.C.M
c. Simplify and solve the resulting equation.
a. You should be able to solve a given system of linear equations by graphs, by elimination method or substitution method.
b. To solve by graph, we will draw the two lines of the two equations The point of intersection of the two lines or two graphs is the solution of the simultaneous equation. When the graphs coincide, then there is an infinite number of solutions.
c. The graphical method is the slowest method.
a. Direct variation: A varies directly as B can be expressed as A∞B: A∞B means A = KB Where K is constant known as the constant of the variation.
b. Inverse variation: A varies directly as B can be expressed as A ∞ 1/B i.e. A = K/B Where K is constant.
c. Joint variation: A jointly varies directly as B and inversely as the square of C; = A ∞ B/C2 OR A = KB/C2
d. Partial variation: Suppose A varies directly as B and partly as the square of C then A can be broken into two parts A1 ∞ A2 such as that A = A1 + A2 where A1 = K1B2 and A2 = K2C2. Then A = K1B1 + K2C2.
(8) CHANGE OF SUBJECT OF FORMULA
a. A formula is an equation containing two or more variables and it describes how the variables are related.
b. We solve many problem in maths by the use of formulae
c. We often need to rearrange a formula in order to make any one of the variables the subject of the formula.
d. Making a specified variable the subject of the formula simply means expressing the specified variable in terms of the other variables.
e. When values are given for other variables in a formula we can find the value of specified variables.
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