IB Maths AI HL Topic 5: Calculus questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1Hard6 marks

A cart moves along a straight track. Figure 1 shows its signed acceleration, $a$ during the first $4$ seconds. At $t=0$ the cart has velocity $4\text{ m s}^{-1}$ in the positive direction.

(a)

Find an expression for the cart’s velocity, $v$ in terms of $t$ for $0\leq t\leq4$

[2]

(b)

Find the total distance travelled by the cart during the first $4$ seconds. Write down a suitable expression before evaluating it with your GDC, and give your answer to 3 significant figures.

[4]

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