# Mock Exam Paper A P1 (Old format) Ordinary Level

**PRE-LEAVING CERTIFICATE EXAMINATION, 2011**

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**MATHEMATICS – ORDINARY LEVEL **

**PAPER I (300 marks)**

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**Duration: ** hours

Attempt **SIX** **QUESTIONS**. (50 marks each)

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**Warning: Marks will be lost if all necessary work is not clearly shown.**

**Answers should include the appropriate units of measurement, **

**where relevant.**

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**Q.1 (a)** The speedometer of a bus shows a speed 5% greater than the actual speed the bus is

travelling. At what speed is the bus travelling if the speedometer shows 52*km/hr*.

**(b)** A tanker delivered heating oil to a hotel. Before the delivery the tanker had 11360 litres of oil and after the delivery it had 7160 litres.

Calculate the cost of the oil delivered if 1 liter costs 20.5 cent.

When VAT was added to the cost of the oil, the bill amounted to €1041.81.

Calculate the rate of VAT added.

**(c) (i)** The length and width of a rectangular playing field are in the ratio 9:5, respectively.

If the length of the field is 22.5*m*, find its width.

**(ii)** A sum of money was invested for 7 years at compound interest. If it amounted to €5000

at the end how much was invested? Give your answer correct to the nearest euro.

**Q.2 (a)** Find the solution set of

**(b)** Solve for *x* and *y*,

**(c)** Solve each of the following for *p*,

**(i)**

**(ii)**

**Q.3 (a)** Given that

calculate the value of *y* when .

**(b)** If is a root of the equation , where .

**(i)** Write down the second root.

**(ii)** Find the value of *b* and *c*.

**(iii)** Hence, or otherwise, find the point *p*. Where *p* is the point of intersection

between the equation and the *y*-axis.

** (c)** **(i)** Write as a single fraction, where .

**(ii)** Hence, or otherwise, find the two solutions for *x*,

, where, .

Give your answers correct to two decimal places.

**Q.4 (a)** Let , where .

Plot *z* and on an Argand diagram.

** (b)** Given .

**(i)** Calculate .

**(ii)** Express in the form , where .

**(c)** *a *and *b* are real numbers such that:

- Find the value of
*a*and*b*. - Verify that is a root of the equation...