Adv - 10M/C (Camb)

What will an investment of $50 000 be worth in 5 years if it is invested at 6% p. a. with interest compounded monthly?

• $51 262.56

• $66 911.28

• $67 442.51

• $71 589.42

Which statement is true at the point 𝑃 on the curve 𝑦 = 𝑓(𝑥)?

• 𝑦 ′ and 𝑦 ′′ are both positive

• 𝑦 ′ and 𝑦 ′′ are both negative

• 𝑦 ′ is positive and

  𝑦 ′′ is negative

• 𝑦 ′ is negative and

  𝑦 ′′ is positive

The results of an English examination were normally distributed. The mean and standard deviation were 63 and 16 respectively. If Peter’s 𝑧-score was −1.5, what was his actual examination mark?

• 39

• 42

• 47

• 57

The line ℓ has equation 𝑥 + 2𝑦 + 3 = 0. If 𝑚 is the gradient of ℓ and 𝜃 is the acute angle between ℓ and the 𝑥-axis, then which statement is true?

• 𝑚 > 0 and 𝜃 > 45°

• 𝑚 > 0 and 𝜃 < 45°

• 𝑚 < 0 and 𝜃 > 45°

• 𝑚 < 0 and 𝜃 < 45°

If 𝐹(𝑥) is a primitive of 𝑓(𝑥), which statement is true?

Which expression is equal to sin 𝑥 sec 𝑥 ?

Consider the point 𝑃(𝑎, 𝑓(𝑎)) on the curve 𝑦 = 𝑓(𝑥). If 𝑓 ′ (𝑎) = 0 and 𝑓′(𝑥) is positive on both sides of 𝑃, which statement best describes 𝑃?

• 𝑃 is a point of inflection

• 𝑃 is a horizontal point of inflection

• 𝑃 is a minimum turning point

• 𝑃 is a maximum turning point

The displacement-time graph of a particle moving in a straight line is shown.

The displacement is measured in metres and the time elapsed is in seconds.

What is the velocity of the particle?

• 20 ms^-1

• 20 ms^-1

• 45 ms^-1

• 3 ms^-1