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Higher Maths

www.maths4scotland.co.uk. Higher Maths. Strategies. The Wave Function. Click to start. Maths4Scotland Higher. The following questions are on. The Wave Function. Non-calculator questions will be indicated.

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Higher Maths

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  1. www.maths4scotland.co.uk Higher Maths Strategies The Wave Function Click to start

  2. Maths4Scotland Higher The following questions are on The Wave Function Non-calculator questions will be indicated You will need a pencil, paper, ruler and rubber. Click to continue

  3. Hint Maths4Scotland Higher • Part of the graph of y = 2sin x + 5cos x is shown • in the diagram. • Express y = 2sin x + 5cos x in the form k sin (x + a) • where k > 0 and 0  a  360 • b) Find the coordinates of the minimum turning point P. Expand ksin(x + a): Equate coefficients: Square and add a is in 1st quadrant (sin and cos are +) Dividing: Put together: Minimum when: P has coords. Previous Next Quit Quit

  4. Hint Maths4Scotland Higher • Write sin x - cos x in the form k sin (x - a) stating the values of k and a where • k > 0 and 0  a  2 • b) Sketch the graph of sin x - cos x for 0  a  2 showing clearly the graph’s • maximum and minimum values and where it cuts the x-axis and the y-axis. Expand ksin(x - a): Equate coefficients: Square and add a is in 1st quadrant (sin and cos are +) Dividing: Put together: Sketch Graph Previous Next Quit Quit Table of exact values

  5. Express in the form Hint Maths4Scotland Higher Expand kcos(x + a): Equate coefficients: Square and add a is in 1st quadrant (sin and cos are +) Dividing: Put together: Previous Next Quit Quit

  6. Find the maximum value of and the value of x for which it occurs in the interval 0 x  2. Hint Maths4Scotland Higher Express as Rcos(x - a): Equate coefficients: Square and add a is in 4th quadrant (sin is - and cos is +) Dividing: Put together: Max value: when Previous Next Quit Quit Table of exact values

  7. Express in the form Hint Maths4Scotland Higher Expand ksin(x - a): Equate coefficients: Square and add a is in 1st quadrant (sin and cos are both +) Dividing: Put together: Previous Next Quit Quit

  8. The diagram shows an incomplete graph of Find the coordinates of the maximum stationary point. Hint Maths4Scotland Higher Max for sine occurs Sine takes values between 1 and -1 Max value of sine function: Max value of function: 3 Coordinates of max s.p. Previous Next Quit Quit

  9. a) Express f (x) in the form b) Hence solve algebraically Hint Maths4Scotland Higher Expand kcos(x - a): Equate coefficients: Square and add a is in 1st quadrant (sin and cos are both + ) Dividing: Put together: Solve equation. Cosine +, so 1st & 4th quadrants Previous Next Quit Quit

  10. Hint Maths4Scotland Higher Solve the simultaneous equations where k > 0 and 0 x 360 Use tan A = sin A / cos A Divide Find acute angle Sine and cosine are both + in original equations Determine quadrant(s) Solution must be in 1st quadrant State solution Previous Next Quit Quit

  11. Hint Maths4Scotland Higher Solve the equation in the interval 0 x 360. Use Rcos(x - a): Equate coefficients: Square and add a is in 2nd quadrant (sin + and cos - ) Dividing: Put together: Solve equation. Cosine +, so 1st & 4th quadrants Previous Next Quit Quit

  12. Maths4Scotland Higher You have completed all 9 questions in this presentation Previous Quit Quit Back to start

  13. Maths4Scotland Higher Table of exact values Return

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