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The Witch's Magic
Sequencing
High 11
Math

Pre-Calculus Honors: Chapter 8

Jocelyn Romay
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Question 1

Multiple Choice

Find the dot product of v = 2i + 2j and w = i + 2j.

  • 2
  • 4
  • 6
  • 8

Question 2

Multiple Choice

If v = 3i + 4j, what is the magnitude of v?

  • 5
  • 7
  • 6
  • 8

Question 3

Multiple Choice

Find the angle between v = 2i + j and w = -i - 2j.

  • 0 degrees
  • 45 degrees
  • 90 degrees
  • 180 degrees

Question 4

Multiple Choice

Are the vectors v = 3i + 4j and w = 4i + 3j parallel, orthogonal, or neither?

  • Parallel
  • Orthogonal
  • Neither
  • Cannot be determined

Question 5

Multiple Choice

Are the vectors v = 2i + 2j and w = i + 2j parallel, orthogonal, or neither?

  • Parallel
  • Orthogonal
  • Neither
  • Cannot be determined

Question 6

Multiple Choice

What is the vector projection of u = (-2, 4) onto v = (1, 1)?

  • (1, 1)
  • (2, 2)
  • (1, -1)
  • (0, 0)

Question 7

Multiple Choice

How can vector u = (11, 3) be resolved into components parallel and orthogonal to v = (-3, -2)?

  • u₁ = (0, 0), u₂ = (11, 3)
  • u₁ = (9, 6), u₂ = (2, -3)
  • u₁ = (-9, -6), u₂ = (20, 9)
  • u₁ = (-11, -3), u₂ = (0, 0)

Question 8

Multiple Choice

Find the work done by the force F = -4 + 20j in moving an object from P(0, 10) to Q(5,25).

  • 100 units
  • 120 units
  • 140 units
  • 160 units

Question 9

Multiple Choice

A force F = 4i - 7j moves an object 4 ft along the x-axis. What is the work done if the force unit is pounds?

  • 16 ft-lb
  • 28 ft-lb
  • 32 ft-lb
  • 44 ft-lb

Question 10

Multiple Choice

Find the weight of a car on a driveway inclined at 10° if a force of 490 lb is needed to prevent it from rolling down.

  • 2800 lb
  • 2900 lb
  • 3000 lb
  • 3100 lb

Question 11

Multiple Choice

Determine the angle of inclination for a plane if a 200 lb package requires 80 lb force to prevent sliding.

  • 22°
  • 24°
  • 26°
  • 28°

Question 12

Multiple Choice

A car weighing 2500 lb is driven 300 ft on a road inclined at 12°. Calculate the work done against gravity.

  • 88800 ft-lb
  • 90000 ft-lb
  • 92000 ft-lb
  • 84000 ft-lb

Question 13

Short Answer

Graph r=5

  • radius 5

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