Vector Analysis and Logical Reasoning

The video provides solutions to the 2021 Maths Extension 2 HSC exam, focusing on multiple choice questions. It covers topics such as vector addition, integration by parts, vector equations, contrapositive statements, evaluating true or false statements, complex numbers, curve analysis, particle motion, logic problems, and vector projections.

What is the main focus of the video tutorial?

• Physics problem-solving

• Introduction to basic mathematics

• Solutions to the 2021 Maths Extension 2 HSC exam

• Advanced calculus techniques

In question 1, which vector is equivalent to the sum of vector AB and vector CQ?

• Vector AQ

• Vector CP

• Vector AR

• Vector CR

Which method is used to solve the integral in question 2?

• Trigonometric substitution

• Partial fractions

• Integration by parts

• Substitution

What is the direction vector for the line joining points A and B in question 3?

• (2, -4, 6)

• (-6, 0, -4)

• (-2, 4, 2)

• (6, 0, 4)

What is the contrapositive of the statement: 'For all integers n, if n is a multiple of 6, then n is a multiple of 2'?

• If n is a multiple of 6, then n is not a multiple of 2

• If n is not a multiple of 2, then n is not a multiple of 6

• If n is not a multiple of 6, then n is a multiple of 2

• If n is a multiple of 2, then n is a multiple of 6

Which statement is false according to question 5?

• If a < b, then 1/a > 1/b

• If a < b, then ln(a) < ln(b)

• If a < b, then e^(-a) > e^(-b)

• If a < b, then a^3 < b^3

If 2 + i is a zero of a polynomial, what must also be a zero?

• 2 - i

• -2 + i

• -2 - i

• 2 + 2i

Which diagram best represents the curve described by the position vector R(t) = -5 cos(t) i + 5 sin(t) j + t k?

• A single loop

• A double loop

• A spiral

• A straight line

In question 8, what is required for the particle to stay on the curve?

• Velocity must increase

• Acceleration must point inwards

• Velocity must decrease

• Acceleration must point outwards

Which cards should Sam turn over to verify the statement: 'If a card is red, then it has a win on the other side'?

• Card 1 and Card 4

• Card 2 and Card 3

• Card 1 and Card 2

• Card 3 and Card 4