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Practice questions for SohCahToa

Grade 10 Math: Master Essential Skills & Concepts

Solve problems that involve unit pricing and currency exchange, using proportional reasoning

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Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

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

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

Solve problems that involve parallel, perpendicular and transversal lines, and pairs of angles formed between them

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Demonstrate an understanding of angles, including acute, right, obtuse, straight and reflex, by drawing, replicating and constructing, bisecting, solving problems

Direct variation

Identifying direct variations

Inverse variation

Money related questions in linear equations

Rate of change

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Demonstrate an understanding of income, including wages, salary, contracts, commissions, piecework

Word problems of polynomials

Rectangular shape related questions in linear equations

Applications of linear relations

Applications of quadratic functions

Applications of polynomials: x^2 + bx + c

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

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Bivariate, scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Demonstrate an understanding of the International System of Units (SI) by describing the relationships of the units for length, area, volume, capacity, mass and temperature; applying strategies to convert SI units to imperial units

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

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

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

Demonstrate an understanding of the imperial system by describing the relationships of the units for length, area, volume, capacity, mass and temperature; comparing the American and British imperial units for capacity; applying strategies to convert imperial units to SI units

Angle of elevation and depression

Upper and lower bound

Upper and Lower Bound

Imperial systems

Imperial Length Conversion

Solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements

Applications of polynomials

Solve problems that involve SI and imperial area measurements of regular, composite and irregular 2-D shapes and 3-D objects, including decimal and fractional measurements, and verify the solutions

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

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

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Demonstrate an understanding of the Pythagorean theorem by identifying situations that involve right triangles, verifying the formula, applying the formula, solving problems

Bearings and direction word problems

Bearings and Direction Word Problems

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Isosceles and equilateral triangles

Demonstrate an understanding of similarity of convex polygons, including regular and irregular polygons

Similar triangles

Similar polygons

Demonstrate an understanding of primary trigonometric ratios (sine, cosine, tangent) by applying similarity to right triangles, generalizing patterns from similar right triangles, applying the primary trigonometric ratios, solving problems

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

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Parallel and perpendicular lines in linear functions

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

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

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Mathematics 10-3

math

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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)