Mathematical Concepts and Problem Solving

The video tutorial covers various Canadian exam questions, focusing on graphing functions, identifying invariant points, solving trigonometric equations, applying exponent and logarithm laws, combinatorics, geometry, and calculating decibels. Each section provides detailed explanations and problem-solving techniques to help students understand and solve complex mathematical problems.

What is the correct interpretation of (f times g) of x?

• f(g(x))

• f(x) * g(x)

• f(x) + g(x)

• f(x) - g(x)

How do you determine the range of a function graphically?

• By finding the x-intercepts

• By determining the symmetry

• By calculating the slope

• By identifying the highest and lowest y-values

What does 'invariant points' mean in the context of graph transformations?

• Points that are added

• Points that are deleted

• Points that remain unchanged

• Points that change position

How many invariant points are there for a graph where y = √f(x)?

• Zero

• Two

• Four

• Six

What is the first step in solving a trigonometric equation involving cos²x?

• Replace cos²x with 1 + sin²x

• Replace cos²x with tan²x

• Replace cos²x with sin²x

• Replace cos²x with 1 - sin²x

What is the correct formula for tan 2θ?

• tan θ + tan θ

• 2 tan θ / (1 - tan²θ)

• 1 - tan²θ

• tan²θ - 1

What is the exponent law for a^b raised to the power c?

• a^(b*c)

• a^(b-c)

• a^(b/c)

• a^(b+c)

What is the common error when expanding (a + b)³?

• Ignoring the cross terms

• Multiplying a and b directly

• Adding a and b directly

• Subtracting a from b

How many ways can three girls be arranged?

• 3

• 6

• 9

• 12

What is the formula for arc length in a circle?

• radius / θ

• θ / radius

• radius + θ

• θ * radius