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Basic formal algebra |
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CONTENTS |
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| Elementary processes of algebra |
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Workout |
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40 slides |
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| Basic algebra |
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Library |
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-1 questions |
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Once you have registered, you can work through the slides one by one.
The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account.
blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.
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SAMPLE FROM THE WORKOUT |
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SLIDE 1 - QUESTION 1 |
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SLIDE 2 - SOLUTION |
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SAMPLE FROM THE LIBRARY |
| Showing American English version |
QUESTION [difficulty 0.1] |
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SOLUTION |
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DEPENDENCIES |
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CONCEPTS |
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LEV. |
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Calculator: inputting numbers in standard form
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620.3 |
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Elementary linear equations
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620.5 |
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Fractions in answers
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620.7 |
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Removing brackets
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620.9 |
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Equation
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621.1 |
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Expression
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621.1 |
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Term
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621.1 |
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Coefficient
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621.1 |
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Collecting like terms
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621.4 |
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Products and exponents
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621.6 |
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Expand and collect
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621.8 |
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Method of substitution
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622.0 |
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Factorising
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622.3 |
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Factorise and solve
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622.5 |
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Cancelling down
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622.8 |
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Bring all terms to the left or to the right
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623.2 |
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Tidying up an equation
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623.3 |
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Multi-step linear equation
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623.4 |
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Cross-multiply and solve
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623.6 |
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Harder factorising
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623.8 |
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RAW CONTENT OF THE WORKOUT |
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| To make use of this chapter, please first register. Then you can work through the slides one by one. |
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| What is provided here is the raw text of the workout. Most of the information is contained in the image files, which are not included with this text. The text may appear deceptively short. (The content overall of blacksacademy.net is vast.) Any in-line questions appear as a question mark [?]. This text is provided only as an indication of the overall quantity of material contained in the chapter. To use the material you must sign-in or create an account. |
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SLIDE 1
Substitution into an algebraic expression
? Evaluate when
? Evaluate
when
? Evaluate when
SLIDE 2
? Evaluate when
? Evaluate
when
? Evaluate when
SLIDE 3
Inputting numbers in standard form
? Evaluate when
? Evaluate when and
? Evaluate when , , and
SLIDE 4
? Evaluate when
? Evaluate when and
? Evaluate when , , and
SLIDE 5
Elementary linear equations
Solve
? ?
? ?
? ?
SLIDE 6
? ?
? ?
? ?
SLIDE 7
Getting used to fractions in answers
Solve
? ?
? ?
SLIDE 8
? ?
? ?
SLIDE 9
Removing brackets
? ?
? ?
? ?
SLIDE 10
?
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?
SLIDE 11
Equation
Expression ,
Term
Coefficient
Variable
SLIDE 12
Identify the equation, expressions, terms, coefficients and variables in
SLIDE 13
Equation
Expressions
Terms
Coefficients
Variables
SLIDE 14
Collecting like terms
Simplify
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SLIDE 15
?
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SLIDE 16
Products and exponents
Simplify
? ?
? ?
? ?
SLIDE 17
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SLIDE 18
Expand and collect
Remove the brackets and simplify
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SLIDE 19
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SLIDE 20
Method of substitution
? ?
From ?
Substitute in ?
SLIDE 21
In each case find x by the method of substitution
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SLIDE 22
? ?
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SLIDE 23
Factorizing
Factorize the following
? ?
? ?
? ?
SLIDE 24
? ?
? ?
? ?
SLIDE 25
Factorize and solve
If and , what is the value of y?
Solution
SLIDE 26
? If and , what is the value of x?
? If and , what is the value
of z?
? and . Find the value of p.
SLIDE 27
? If and , what is the value of x?
? If and , what is the value
of z?
? and . Find the value of p.
SLIDE 28
Cancelling down
Cancel down
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? ?
SLIDE 29
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SLIDE 30
Example
If , then
Find
? when
? when
? when
SLIDE 31
? When ,
? When ,
? When ,
SLIDE 32
Bringing all terms to the left or right
? Bring all terms to the left
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SLIDE 33
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Remark
In the last question, both the two last lines are correct. It is customary to “tidy-up” an equation at the end by making the coefficient of the term with largest exponent positive.
SLIDE 34
Multi-step linear equations
Solve the following linear equations
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SLIDE 35
? ?
? ?
SLIDE 36
Cross-multiply and solve
Solve
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SLIDE 37
? ?
? ?
SLIDE 38
Example
What does the above become if you substitute into and substitute into ?
Solution
Harder factorizing
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