Revision Before EST

Cross product is also known as ___ product which results in a ___.

• scalar; vector

• scalar; scalar

• vector; scalar

• vector; vector

Mathematical Induction is a technique of proving mathematical statements. Type in the correct order of the following steps.

Step __: Assume that P_n is true for some n ∈ ℤ⁺.

Step __: Prove that P_n+1 is true.

Step __: Prove that P₁ is true.

(a)  

Integration by parts is used to integrate products of two different functions. Using the acronym LIATE, we are able to select an appropriate u for differentiation and hence solve the integral. Which of the following integrals DOES NOT require integration by parts?

• 
• 
• 
• 

Which statements below are TRUE about two parallel vectors?

• The dot product is 0.

• The separating angle could be 0°.

• The separating angle could be 90°.

• The separating angle could be 180°.

• They are scalar multiple of each other, i.e. a = kb.

Choose all the correct statements about integration.
Integration can be used to ......

• to evaluate the area under a curve.

• to find the volume of revolution of a solid.

• to evaluate the area between two curves.

• to solve optimization problems.

Given the magnitude of vector p is 3 units, how can we find a new vector that is in the opposite direction of vector p and with magnitude of 20 units?

• 
• 
• 
• 

Solve the inequality given.

• x ≥ 4

• x ≤ 4

• x = 4

• No solution

We are able to construct the equation of a plane in 3-space when we are given ......

• the normal vector of the plane and a point on the plane

• 
  a point and two direction vectors on the plane

• three points on the plane

• a point on the plane and a line that is perpendicular to the plane

For inequality |4x - 6| < x + 6, the solution can be seen clearly if we draw the graphs in the same diagram. What is the solution?

• x = 0 and x = 4

• 0 < x < 4

• x < 0 or x > 4

• No solution