Recommended Algebra topics to be taught for 9th grade classes

 

1) Algebraic terminology constant, parameter, term, variable, function, equation, expression ,formula, identity.

2)Important algebraic identities and their geometric representations.

3)Moving variables and terms to the other side.

4) 1 variable equations with constant coefficients and their root.

5)1 variable equation with parameterized coefficients and their root.

6)Expansion(multiplication) of terms and simplification of the result.

7)Factorization(opposite of expansion).

8)Basic multivariable function.

8a)Properties of MOD  for integer number divisions.

9)Substituting numbers for variables of a function and simplifying the results(evaluation of functions).

10)Substituting a function for variables of another function(evaluation of functions).

11)System of 2 equations and 2 unknown with constant coefficients and generalized solution

12) System of 2 equations and 2 unknown with parameterized coefficients.

13)Some examples of 2 equations and unknown in our daily life

14)System of 2 equations and 2 unknown with no answer.

15)Simple linear absolute value equations.

16)Properties of equalized fractions.16a

17)Fraction topics

18)Inequalities.

19)Moving terms to the other side in inequalities.

20)Arithmetic operations on inequalities.

21)Comparing inequalities.

22)More than one inequality at once and inequalities with radicals.

23)Radicals and fractional powers.

24)Using identities to evaluate functions with radical and daily life.

25)Rationalization of fractions with radicals.

26)Simplifying fractions with radicals.

27)Nested fractions.

28)Solve for a particular variable in a multi variable equation or identity .

29)Solving quadratic equations, and related topics(delta/discriminant, roots(x1,x2) ) .

30)Factorization of quadratic equations.

31)Maximum, minimum, axis of symmetry, axis intersection points and graphs of Quadratic functions.

32)Fractional equations.

33)Converting quadratic equation to fractional equation.

34)Quadratic equations with parameterized coefficients.

35)Properties of sum, product, difference  of quadratic equations roots.

36)Properties of sum of powers of quadratic equations(x1n +x2n)  roots

37)Systems of 3 equations and 3 unknown

16a)Fraction topics

Common fractions              

 Fractions as division        

 Proper and improper fractions      

 Placing fractions on a number line               

 Equal fractions and simplifying     

 Comparing fractions        

 Adding and subtracting fractions

 Multiplying fractions        

 Reciprocals         

 Dividing fractions             

 Evaluating fractions using a calculator       

               

 

 

 

 

 

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Recommended Algebra topics to be taught for 10th grade classes

Systems of 3 equations and 3 unknown.

Logarithms and their properties.

Sum of arithmetic and geometric series.

Convergent geometric series.

Basic fractional series and their sums.

Basic trigonometric functions and their properties.

Inverse functions.

Composite functions.

Binomial expansion.

Synthetic division of polynomials.

Equation of lines in Cartesian systems; parallel and perpendicular lines