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Trigonometry and logarithms: lesson checks flashcards

This deck has 9 check-yourself questions and 5 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Years 12–13 · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• A triangle has sides 5 cm and 7 cm meeting at an angle of 60°. Without a calculator, find the exact length of the third side and the exact area.Check
• Solve tan x = √3 for 0 ≤ x < 360°, giving exact answers.Check
• The small-angle approximations work in degrees too.Spot the error
• An arc of length 10 cm subtends an angle θ at the centre of a circle of radius 8 cm. Find θ and the area of the sector.Check
• arcsin x means 1 over sin x.Spot the error
• Given that cosec θ = 3 with θ acute, find cot θ and cos θ exactly.Check
• Express 5 cos θ − 12 sin θ in the form R cos (θ + α) with R > 0 and 0 < α < π/2, and write down the minimum value of the expression.Check
• A bigger amplitude means a faster oscillation.Spot the error
• A buoy's height above mean sea level is modelled by y = 1.2 sin (0.8t), in metres and seconds. Find the amplitude, the period, and the first time the buoy is 0.6 m above mean level.Check
• Exponential growth means growing very fast.Spot the error
• For the curve y = e^3x, write down the gradient function, the gradient at x = 0, and the y-intercept.Check
• Express log 4 + log 25 as a single logarithm and evaluate it, then solve e^3x = 40 to 3 significant figures.Check
• A straight line on a log graph means the data is linear.Spot the error
• The model y = 4 × 2^x is to be drawn as a straight line. State what should be plotted, and give the line's gradient and intercept.Check

The lessons these cards come from

• Compound angles and the harmonic form
• Exponential functions and e
• Log graphs and exponential models
• Logarithms and their laws
• Radians, arcs and small angles
• Reciprocal and inverse trigonometric functions
• Triangles and the sine and cosine rules
• Trigonometric graphs and equations
• Trigonometric modelling

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