CLASS JSS 2, THIRD TERM 2019/2020 LESSON NOTE FOR WEEK ONE
Topic: Simple algebra
Learning Resources:
New General Mathematics, Book 2; New Concept Mathematics Book 2.
Objectives: Students should
be able to define and identify
the following as the lesson
Class work:
progresses.
Identify constants, variables, algebraic expressions and equation in the following
I.
Algebra
expressions:
II.
Algebraic terms
(a) 2𝑥 + 5 = 10; (b) 𝑥; (c) 2𝑧 + 3𝑦 − 𝑞; (d) 20𝑧; (e) 100; (f) 2𝑥 2−2𝑥 ;
III.
Difference between
(b) (g) 3𝑤𝑥𝑦.
algebraic expressions
Home work: Study simple equation in one variable for our next class
and equations
Step I
Definition
N/B
Algebra is a mathematical representation that combine integers and letters of the
Integers are natural numbers alphabet as “constants” and “variables” respectively that often result to an algebraic
terms, expressions or equations.
. -4, -3, -2, -1,0 1,2,3,4, ….
Letters of alphabet are
Algebraic terms are a combination of constants and variables multiplied together
𝐴𝑎, 𝐵𝑏, 𝐶𝑐, … 𝑋𝑥, 𝑌𝑦, 𝑍𝑧
in an algebraic expressions or equations, (see illustration to your left). In the
Constant are all integers in an expression, 3𝑥 is a constant (3) and variable (𝑥) brought together by the
algebraic term, expression and mathematical operation (×).
equation.
Variable are all the letters of Also, (2𝑎, 𝑦, 3𝑥𝑦𝑧 𝑎𝑛𝑑 2𝑦) are algebraic terms brought together by the mathematical
3𝑥
alphabet in an algebraic term,
2
𝑦
operations (× 𝑎𝑛𝑑 ÷) with constants (2, 1,3 𝑎𝑛𝑑 3) and variables 𝑎, 𝑦, 𝑥𝑦𝑧 𝑎𝑛𝑑 𝑥
expression and equation E.g.
respectively.
3𝑥
Constant
Variable
Step II
Again, note that the constant for the "𝑦" term in the expression above is “1”.
Although we only write "𝑦". This is so because in mathematics, we don’t write "1𝑦",
we can only write 2𝑦, 3𝑦 etc.
Algebraic expression are two or more algebraic terms joined together by the
combination of all or any of the 4 basic mathematical operation (+, −,×,÷). The
expression (3𝑥 + 𝑦𝑥 + 𝑧) is a typical example of an algebraic expression.
Algebraic equation is a combination of two or more algebraic terms [(2𝑎), (𝑦),
2𝑦
(3𝑥𝑦𝑧), and (3𝑥 )] and algebraic expression [(3𝑥 + 𝑦𝑥 + 𝑧)] by the mathematical
operator (=).
Step III
Hint for class work:
𝑥 + 𝑦 = 3𝑧 + 8
Soln.
1. (𝑥 + 𝑦 = 3𝑧 + 8) is
Equating one or more of the above algebraic terms, to the algebraic expression will
an algebraic equation.
result in the algebraic equations given below.
2. (1 + 1 = 3 + 8) are
constants.
3𝑥 + 𝑦𝑥 + 𝑧 = 3𝑥𝑦𝑧 + 𝑦,
3. (𝑥 + 𝑦 = 𝑧)
are
𝐴𝑙𝑔𝑒𝑏𝑟𝑎𝑖𝑐 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛𝑠 = {3𝑥 + 𝑦𝑥 + 𝑧 = 2𝑎 + 𝑦 + 3𝑥,
variables.
3𝑥 + 𝑦𝑥 + 𝑧 = 10,
Evaluation/
Assignment
Attempt the Class work given above. See Hint in Step III.
I hope this is explicit enough? Else, your suggestion will be helpful in our next note.
“Small thing makes perfection but perfection is not a small thing” so, Study hard.
Many thanks, Stay safe.