## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | IB Standard |

The acceleration, \(a\) ms^{-2} , of an object at time \(t\) seconds is given by

The object is at rest when \(t=1\).

Find the velocity of the object when \(t=7\).

## 2. | IB Analysis and Approaches |

Given that \( \frac{dy}{dx} = \sin(x + \frac{\pi}{3})\) and \(y = 5\) when \(x = \frac{8\pi}{3}\), find \(y\) in terms of \(x\).

## 3. | A-Level |

(a) Using a suitable substitution, or otherwise, find

$$ \int \frac{x}{(3x^2 - 5)^2} dx$$(b) Solve the differential equation below giving your answer in the form \(y = f(x)\). It is given that given that y = \( \frac{1}{2} \) when x = 0.

$$ \frac{dy}{dx} = \frac{2xy^3}{(3x^2 - 5)^2}$$## 4. | IB Analysis and Approaches |

Find \(f(x)\) if:

$$ f'(x) = \frac{12x}{\sqrt{3x^2+4}}$$given that \(f(0) = 10 \)

## 5. | IB Analysis and Approaches |

Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \).

(a) Find an expression for the first derivative \(f'(x) \).

The graph of \(f\) has exactly one maximum point at P.

(b) Find the x-coordinate of P.

The graph of \(f\) has exactly one point of inflection at Q.

(c) Find the x-coordinate of Q.

(d) The region enclosed by the graph of \(f\), the x-axis, and the vertical lines through P and Q has an area of one square unit, find the value of \(k\).

If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.