← Practice

AS91578 Differentiation

Trigonometric functions, including reciprocal

AAchieved

  1. 1The height of a section of a roller-coaster track in Rotorua is modelled by h = 25 + 12 sin(x/10), where x is the horizontal distance travelled in metres and h is the height above the ground in metres. Find the gradient of the track when x = 20.Free
  2. 2On an Auckland harbour crane, the length of cable from the jib to a load 12 m below it is L = 12/cos θ metres, where θ is the angle in radians that the cable makes with the vertical. Find dL/dθ when θ = π/6.Free
  3. 3Differentiate y = tan(3x). Find dy/dx.Free
  4. 4A Achieved question, in the pass🔒 Pass
  5. 5A Achieved question, in the pass🔒 Pass
  6. 6A Achieved question, in the pass🔒 Pass
  7. 7A Achieved question, in the pass🔒 Pass

MMerit

  1. 8A Merit question, in the pass🔒 Pass
  2. 9A Merit question, in the pass🔒 Pass
  3. 10A Merit question, in the pass🔒 Pass
  4. 11A Merit question, in the pass🔒 Pass

EExcellence

  1. 12A Excellence question, in the pass🔒 Pass
  2. 13A Excellence question, in the pass🔒 Pass