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Practice questions for SohCahToa

Demonstrate an understanding of factors of whole numbers

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Prime factorization

Number properties: Prime or Composite

Number properties: Prime?

Prime factors – Word Problem

Greatest common factors (GCF)

Greatest Common Factor 2 Numbers

Greatest Common Factor 2 Numbers – Word Problem

Least common multiple (LCM)

Lowest Common Multiple - 2 Numbers – Word Problem

Lowest Common Multiple 2 Numbers

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Demonstrate an understanding of irrational numbers

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting radicals to mixed radicals

Converting radicals to entire radicals

Demonstrate an understanding of powers with integral and rational exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Demonstrate an understanding of multiplication of polynomial expressions

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Demonstrate an understanding of common factors and trinomial factoring

Factoring polynomials: ax^2 + bx + c

Factoring Polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Find the difference of squares

Word problems of polynomials

Common factors of polynomials

Factoring polynomials by grouping

Factoring polynomials: x^2 + bx + c

Interpret and explain the relationships among data, graphs and situations

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Solve problems involving systems of linear equations in two variables

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Demonstrate an understanding of relations and functions

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

Demonstrate an understanding of slope

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Rate of change

Describe and represent linear relations

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Determine the characteristics of the graphs of linear relations

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Parallel and perpendicular lines in linear functions

Relate linear relations expressed in various forms

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Applications of linear relations

Applications of linear equations

Solving systems of linear equations by elimination

Determine the equation of a linear relation

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Solving systems of linear equations by substitution

Solve problems involving distance between two points and midpoint of a line segment

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Use tangent ratio to calculate angles and sides (Tan = o / a)

Represent a linear function using function notation

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Number Relations and Functions 10

Algebra and Number

Relations and Functions

math

Ex. 1

- Hi! Welcome to this question right here. So this one here you can use whatever you like. Sohcahtoa, you can use sin, cos, tangent as long as you can find the length from b to c, which is from here to here. Okay? 
So how do we know the length from there to there? We only know the angle over here is 22 and this angle here is 15. But if you look in a different way you can actually see there's one right triangle right here. So you can actually find the length from a to b because you kind of know this side's 80 and if you know this angle right here, maybe you can find the length a to b. Then if you look at a bigger scale, if I can just go ahead and treat this big triangle right here, because I know this whole thing right here is 22 plus 15, I can also figure out the a to c. Then I can take the a to c, subtract the a to b and I'll get the b to c. Okay? Kind of weird. Let's actually do it step by step. So let's actually find the length a to b first. So here is my length a to b. So here we go. To find the length a to b, you have to visualize your triangle as actually just this part right here. So you're trying to find the opposite side from this angle 22. This is the opposite, this is the adjacent. So you're going to use tangent. So for the length a to b, I will be using tangent of 22 degrees and the opposite will be the one I'm looking for which is the length a to b divided by the 80 degrees which is the adjacent which is over here. So I'm going to go ahead and calculate that. I've got tangent 22 times 80. Tangent 22 times 80. I'm just gonna write down 32.3. And let's call that centimeters for now. So what about a to c? If you're doing a to c, then you have to look at the triangle like this. Look at it like this. These two angles right here is just 22 plus 15. Twenty-two plus 15, we get 37, right. So from this angle you're looking for the opposite side and you have the adjacent 80 again. So it will just be tangent once again. Using the tangent 37, using these two triangles together is equal to the length of a to c divided by 80 again. So I'm going to go tangent 37 and I'm going to multiply it by 80. A little bit of cross multiplying. I get myself a 60.3 centimeters. So if I know from here to here it's 63 centimeters. So from here to here the blue line is 63 in total and the a to b over here is just 32 roughly, then what will be my b to c? 
Well, just subtract the difference and that's it, right? 
So it just goes 63.2 minus 32.2. . . are they all 0.3s? My bad. All 0.3s. So three and threes are gone. So 63.3-- oh, it's actually 60. I'm really sorry all those mistakes right here. So this is actually 60.3, okay. So, 60.3 minus 32.3 I get myself 28, okay. Sorry about all those scribbles. The final answer should be just 28 centimeters if that was centimeters. Okay? Thanks for watching!

Ex. 2

SOHCAHTOA is actually a memory aid to memorize how to calculate sine, cosine and <a href="[[glossary.html|{"keyword":"Tangent (in Trigonometry)"}]]">tangent</a> of an angle. SOH: sine = opposite over hypotenuse; CAH = adjacent over hypotenuse; and TOA = opposite over adjacent. Besides using them separately, the sine, cosine, and tangent ratios can be used together to solve trigonometry problems.

Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Use tangent ratio to calculate angles and sides (Tan =  \(  \frac{o}{a}\)  )

ASTC rule in trigonometry (All Students Take Calculus)