IB Mathematics Analysis and Approaches Topic SL 3.7—circular Functions, Graphs, Composites, Transformations Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 3.7—circular Functions, Graphs, Composites, Transformations Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 3.7—circular Functions, Graphs, Composites, Transformations with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 3.7—circular Functions, Graphs, Composites, Transformations and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

SLPaper 1

Consider the equation $3\cos(2x)=1-\sin x, \qquad 0\le x<2\pi.$

Show that the equation may be written as $6\cos^2x+\sin x-4=0.$

[3]

Express $cos^{2} x$ in terms of $sin x$ , and hence obtain a quadratic equation in $sin x$ .

[2]

Solve $6 sin^{2} x - sin x - 2 = 0$ exactly for $sin x$ .

[2]

Determine all exact values of $x$ in the interval $0 \leq x < 2 π$ that satisfy the original equation.

[3]

Sketch the graphs of $y = 3 cos (2 x)$ and $y = 1 - sin x$ for $0 \leq x \leq 2 π$ , indicating approximate intersections matching the solutions from part 4.

[3]

Question 2

SLPaper 1

The depth, $h (t)$ metres, of water at the entrance to a harbour at time $t$ hours after midnight on a particular day is given by $h (t) = 8 + 4 sin (\frac{π t}{6})$ , $0 \leq t \leq 24$ .

Find the maximum depth and the minimum depth of the water.

[3]

Find the values of $t$ for which $h (t) \geq 8$

[2]

Question 3

SLPaper 1

Consider the equation $cos (2 x) = cos x$ , $0 \leq x < 2 π$ .

Show that the equation may be written as $2 cos^{2} x - cos x - 1 = 0$ .

[2]

Factor the left-hand side to obtain an equation of the form $(2 cos x + 1) (cos x - 1) = 0$ .

[2]

Find all exact values of $x$ in the interval $0 \leq x < 2 π$ that satisfy the equation.

[5]

Question 4

SLPaper 1

Consider the equation $cos (2 x) + 3 sin x = - 1$ , $0 \leq x < 2 π$ .

Show that the equation may be written as $cos^{2} x + \frac{3}{2} sin x = 0$ .

[3]

Express $cos^{2} x$ in terms of $sin x$ , and hence obtain a quadratic equation in $sin x$ .

[2]

Solve $2 sin^{2} x - 3 sin x - 2 = 0$ exactly for $sin x$ .

[2]

Determine all exact values of $x$ in the interval $0 \leq x < 2 π$ that satisfy the original equation.

[2]

Question 5

SLPaper 1

Consider the equation $2\cos(2x)=3\sin x-3, \ 0\le x<2\pi.$

Show that the equation may be written as $4\cos^2x+1-3\sin x=0.$

[3]

Express $cos^{2} x$ in terms of $sin x$ and obtain a quadratic equation in $sin x$ .

[2]

Solve $4 sin^{2} x + 3 sin x - 5 = 0$ exactly for $sin x$ .

[2]

Determine all exact values of $x$ in the interval $0 \leq x < 2 π$ that satisfy the original equation.

[3]

IB Mathematics Analysis and Approaches SL 3.7—circular Functions, Graphs, Composites, Transformations Questionbank

IB Mathematics Analysis and Approaches SL 3.7—circular Functions, Graphs, Composites, Transformations Questionbank

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IB Mathematics Analysis and Approaches SL 3.7—circular Functions, Graphs, Composites, Transformations Questionbank

IB Mathematics Analysis and Approaches SL 3.7—circular Functions, Graphs, Composites, Transformations Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 3.7—circular Functions, Graphs, Composites, Transformations Questionbank

Unlock all 19 questions with a free account