# 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

$$a=\frac1t+4sin3t, (t\ge1)$$

The object is at rest when $$t=1$$.

Find the velocity of the object when $$t=7$$.

### 2.

IB Standard

Very accurate equipment was used to measure the movement of a particle which moved in a straight line for 3 seconds. Its velocity, $$v$$ ms-1 , at time $$t$$ seconds, is given by:

$$v=(t^2-5)^3$$

(a) Find the velocity of the particle when $$t=2$$.

(b) Find the value of t for which the particle is at rest.

(c) Find the total distance the particle travels during the first three seconds.

(d) Show that the acceleration of the particle is given by $$a=6t(t^2-5)^2$$

(e) Find all possible values of t for which the velocity and acceleration are both positive or both negative.

### 3.

IB Standard

Pob and Wie are travelling from Bangkok to Khon Kaen.

Pob travels at a velocity given by $$V_P=50-t^2$$, where t is in seconds and the velocity is in ms-1.

Wie's displacement from Bangkok in metres is given by $$S_W=2t^2+70$$.

When $$t=0$$, both vehicles are at the same point.

Find Pob's displacement from Bangkok when $$t=5$$.

### 4.

IB Standard

Make a sketch of a graph showing the velocity (in $$ms^{-1}$$) against time of a particle travelling for six seconds according to the equation:

$$v=e^{\sin t}-1$$

(a) Find the point at which the graph crosses the $$t$$ axis.

(b) How far does the particle travel during these first six seconds?

### 5.

IB Standard

A particle P moves along a straight line. The velocity $$v$$ in metres per second of P after $$t$$ seconds is given by $$v(t) = 3\sin{t} - 8t^{\cos{t}}, 0 \le t \le 7$$.

(a) Find the initial velocity of P.

(b) Find the maximum speed of P.

(c) Write down the number of times that the acceleration of P is 0 ms-2.

(d) Find the acceleration of P at a time of 5 seconds.

(e) Find the total distance travelled by P.

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.

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