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Practice questions for SohCahToa

Grade 11 Math: Master Advanced Concepts & Skills

Solve problems that involve the application of rates

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Direct variation

Identifying direct variations

Inverse variation

Joint and combined variation

Rate of change

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

Metric Area Conversion M/CM to Inch

Solve problems that involve quadratic equations

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands (limited to square roots)

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Solve problems that involve radical equations (limited to square roots or cube roots)

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Demonstrate an understanding of normal distribution, including standard deviation and z-scores

Introduction to quadratic functions

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Interpret statistical data, using confidence intervals, confidence levels, margin of error

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

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Determine the number of combinations of n different elements taken r at a time to solve problems

Combinations

Problems involving both permutations and combinations

Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers)

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

Research and give a presentation on a historical event or an area of interest that involves mathematics

Making a confidence interval

Null hypothesis and alternative hypothesis

Proving claims

Solve problems that involve scale diagrams, using proportional reasoning

Introduction to bearings

Bearings and direction word problems

Bearings and Direction Word Problems

Angle of elevation and depression

Enlargements and reductions with scale factors

Scale diagrams

Demonstrate an understanding of the relationships among scale factors, areas, surface areas and volumes of similar 2-D shapes and 3-D objects

Similar triangles

Similar polygons

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

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Derive proofs that involve the properties of angles and triangles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems that involve properties of angles and triangles

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

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

Combination of SohCahToa questions

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

Classifying triangles

Isosceles and equilateral triangles

Pairs of lines and angles

Solve problems that involve the cosine law and the sine law, excluding the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Analyze and prove conjectures, using inductive and deductive reasoning, to solve problems

Conditional probability

Probability involving permutations and combinations

Law of total probability

Law of Total Probability

Probability of a randomly selected employee meeting a sales target

Probability of a randomly selected driver being involved in an accident

Probability of a randomly selected customer making a purchase

Probability of a randomly selected person being overweight

Analyze the characteristics of quadratic functions, including vertex, intercepts, domain and range, axis of symmetry

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Operations with radicals

Operations with Radicals

Evaluating and simplifying radicals

Converting radicals to mixed radicals

Converting radicals to entire radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Rationalize the denominator

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Mathematics 20-2

math

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Ex. 1

<p>- 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?<br />
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?<br />
Well, just subtract the difference and that's it, right?<br />
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!</p>


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. 