# Math Guide

Introduction:

Algebrais the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. The part of algebra called elementary algebra is often partof the curriculum in secondary education and introduces the concept of variables representing numbers.

## Sample problem for practice grade 9 algebra:

Practice grade 9 algebra Problem 1:

-6x +5 +12x -6

Solution:

-6x +5 +12x -6

Combine the x terms and the numbers

-6x + 12x +5 -6

Practice grade 9 algebra Problem 2:

2(x-9) + 6(-x +2) +4x

Solution:

2(x-9) + 6(-x +2) +4x

2x -18 -6x +12 +4x

Combine the x terms and constant terms

2x – 6 x + 4x -18 +12

-4 x + 4x -18 +12

=0x -6

Practice grade 9 algebra Problem 3:

3x2 +12 +9 x -20 +6x2 –x

Solution:

3x2 +12 + 9 x -20 +6x2 –x

Combine the x2 terms, x terms and Constant terms

3x2 + 6x2 +9x -x + 12 – 20

Practice grade 9 algebra Problem 4:

1.2(x -9) -2.3(x +4)

Solution:

1.2(x -9) -2.3(x +4)

1.2x – 10.8 -2.3x -9.2

Combine the x terms and Constants.

Practice grade 9 algebra Problem 5:

x2 + 8x +b     find b

Solution:

x2 + 8x +b (This can be represented as ( a + b )2 = a2+b2+2ab)

x2 + 2 . 4 .x +b

b = 42 = 16

Practice grade 9 algebra Problem 6:

x y2 / x y2

Solution:

xy2 / x2y

X .y. y / x .x. y

Practice grade 9 algebra Problem 7:

Factor the polynomial x2 + 5x + 6

Solution:

x2 + 5x + 6

We have to factor. So we can split the 5x as 2x +3 x

x2 +2x +3x +6

X (x +2) + 3 (x +2)