قراءة كتاب A Review of Algebra
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and subtraction of fractions.
Multiplication and division of fractions.
Law of signs in division, changing signs of factors, etc.
Complex fractions.
Simultaneous Equations
Solved by
- addition or subtraction.
- substitution.
- comparison.
Graphical representation.
Involution
Law of signs.
Binomial theorem laws.
Expansion of
- monomials and fractions.
- binomials.
- trinomials.
Law of signs.
Evolution of monomials and fractions.
Square root of algebraic expressions.
Square root of arithmetical numbers.
Optional
- Cube root of algebraic expressions.
- Cube root of arithmetical numbers.
Theory of Exponents
Proofs: 
Meaning of
- fractional exponent.
- zero exponent.
- negative exponent.
Four rules
- To multiply quantities having the same base, add exponents.
- To divide quantities having the same base, subtract exponents.
- To raise to a power, multiply exponents.
- To extract a root, divide the exponent of the power by the index of the root.
Radicals
Radical in its simplest form.
Transformation of radicals
- Fraction under the radical sign.
- Reduction to an entire surd.
- Changing to surds of different order.
- Reduction to simplest form.
Addition and subtraction of radicals.
Multiplication and division of radicals
Rationalization
- Monomial denominator.
- Binomial denominator.
- Trinomial denominator.
Square root of a binomial surd.
Radical equations. Always check results to avoid extraneous roots.
Quadratic Equations
Pure. 
Affected. 
Methods of solving
- Completing the square.
- Formula. Developed from
- Factoring.
Equations in the quadratic form.
Properties of quadratics
- Then
- Discriminant,
and its discussion. - Nature or character of the roots.
Case I.
One equation linear.
The other quadratic.
Case II.
Both equations homogeneous and of the second degree.
Case III.
Any two of the quantities 
etc., given.
Case IV.
Both equations symmetrical or symmetrical except for sign. Usually one equation of high degree, the other of the first degree.
Case V. Special Devices
I. Solve for a compound unknown, like 
etc., first.
II. Divide the equations, member by member.
III. Eliminate the quadratic terms.
Proportionals
- mean,
- third,
- fourth.
Theorems
- Product
