MATH ALGEBRA.pdf

MATHEMATICS. TOPIC ALGEBRA FOR JUNIOR SECONDARY AND SENIOR SECONDARY EDUCATION.

1. ALGEBRAIC EQUATIONS

2. ALGEBRAIC EQUATIONS
•Quantities like a, b, c that have fixed values are called
constant, while quantities like x, y, z that can take
arbitrary values are called variables. An algebraic
equation is an equation containing some variables and
constants. The problem is usually to find the values of
the variables that satisfy the equation(s).
i.Multiply each term of an equation by a non-zero
constant.
ii.Subtract (or add) a constant from both sides of an
equation
iii.Subtract (or add) one equation from another

3. ALGEBRAIC EQUATIONS
•Linear Equations
•A linear equation has the form ax+b=0. where
a, b are constants and x is variable.
•To solve, subtract b from both sides to get
ax = -b
then divide both side by a to get x = -b/a
This is then the solution of the equation.

4. ALGEBRAIC EQUATIONS
•Linear Equations
•More example on the explanation of linear
equation.
•Solve 3x –12 = 0
Solution
3x-12 = 0
3x = 12
x = 12/3 = 4

5. ALGEBRAIC EQUATIONS
•Quadratic Equations
•A quadratic equation contains x
2
. it has the
form:
•A quadratic equation can be solved by
a) factorization method (b) completing squares
c) the graphical method.
d) the use of quadratic formula

6. ALGEBRAIC EQUATIONS
•Quadratic Equations
•Example; solve the equation by (a)
factorization method (b) completing squares (c) the use
of quadratic formula (d) use of graphs.
•Solution
•(a)
•

7. ALGEBRAIC EQUATIONS
•Quadratic Equations
•(b)
Add and subtract

8. ALGEBRAIC EQUATIONS
•Quadratic Equations
(c)

9. ALGEBRAIC EQUATIONS
•Quadratic Equations
•(d) For the graphical method, we draw the
graph of and note values
of x when y = 0. i.ewhere the graph meets the
x-axis.

10. ALGEBRAIC EQUATIONS
•Quadratic Equations
•From the graph, y = 0 when x = -4 or x = 2.5
•The solution of the equation is x = -4 or 2.5

11. ALGEBRAIC EQUATIONS
SimultaneousEquations
•Simultaneousequationsinvolvetwoormore
equationscontaintwoormorevariables.The
methodsofsolutionistoeliminatesomeof
thevariables.Solveforonevariableandthen
substituteitsvalueintheequations.This
methodprogressivelyreducesthenumber
variablesandeventuallyleadstoasolution(if
asolutionexists)

12. ALGEBRAIC EQUATIONS
Simultaneous Equations
Example: solve for x and y in

13. ALGEBRAIC EQUATIONS
Using elimination method, first we eliminate x
then y
Substituting this in equation(1) we get