Form5_2011_Assignment1

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Form 5, 2011/2012 Assignment 1 Mathematics

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1. (I) When an aeroplane takes off, its ascent is in two stages. These two stages are shown in the

diagram as AB and BC.

(a) In the first stage the aeroplane climbs at an angle of 150 to the horizontal. Calculate the height it

has reached when it has covered a ground distance of 12 miles. Give your answer to the nearest

thousand feet.

(b) In the second stage the aeroplane climbs at an angle of 70 to the horizontal. At the end of its

ascent it has reached a height of 35 000 feet above the ground. Calculate the distance, to the nearest

feet, it has covered.

(c) Calculate, to the nearest feet, the total ground distance covered by the aeroplane.

(II) A surveyor wishes to measure the height of a church. Measuring the angle of elevation, she

finds that the angle increases from 300 to 350 after walking 20 meters towards the church. What is

the height of the church?


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2. (a) Expand and simplify

(b) Solve

[Hint: Use the substitution to solve for and hence, solve for ]

(c) Factorize completely

(d) Solve , giving your answers to 2 decimal places.

(e) Make the subject of the formula

3. Consider the experiment of rolling two dice and noting the two values uppermost. The score is

the sum of these two numbers.

(a) Copy and complete the above table.

(b) From your table, deduce the probability that the score:

(i) equals 12; (ii) is less than 12 (iii) equal to 7 (iv) greater than 7

(c) A second experiment is done where the score is the product of the numbers on the uppermost

face of each dice. Represent this information in tabular form as above.

(d) From your table, deduce the probability that the score:

(i) equals 36; (ii) is less than 36 (iii) is equal to 12 (iv) equal to 6


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4. The lengths, in cm, of 40 pencils were measured and the results are given below.

(a) Copy and complete the following table

Length of pencil (x cm )

Number of pencils

(Frequency)

(b) Draw a histogram which represents the information given above.

(c) Find

(i) the percentage of pencils whose length is greater than 10 cm and less than or equal to 14

cm.

(ii) the proportion of pencils whose length is at most 12 cm

(c) Represent the above information on a pie chart.

5. A factory workers basic rate is $9.35 per hour. His basic work week is 40 hours. Overtime is

paid at the rate of time and a half for work done during the week, double on Saturdays and triple on

Sundays. On a particular week he worked for a total of 60 hours. Of which, 5 hours of overtime

work was done on Saturday and 7 hours of overtime work was done on Sunday.

(a) Calculate the wages the worker will receive, assuming he did not work any overtime.

(b) Calculate his overtime pay rate for an hour worked: (i) during a week day; (ii) on Saturdays; (iii)

On Sunday.

(c) Calculate his overtime pay

(d) Calculate the total wages the worker will receive at the end of the week.

6. Construct, using compass and ruler only, the triangle ABC such that AB = 6 cm, and

. Measure and state the lengths of sides BC and AC.


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7. Data on number of brothers and sister for pupils in a class is given in the following table:

Number of Brothers and Sister Frequency

0 6

1 82 11

3 3

4 1

5 0

6 0

7 1

For this data:

(a) calculate the mean, (b) determine the median, (c) state the mode, (d) calculate the range.

8. Sarah, Jenny, Rachel and Emma each order a drink. One of them has cola, one has orange, one

has limeade and the other has water:

9. 40 teenagers belong to a youth club. They all play at least one of badminton, darts and pool. 8

teenagers play all three games. 10 teenagers play badminton and darts, 20 teenagers play darts and

pool, 12 teenagers play pool and badminton, 30 teenagers play pool, and 23 teenagers play darts.

(a) Represent the above information on a Venn diagram.

(b) How many teenagers play only badminton?

(c) How many teenagers play badminton?

(d) How many teenagers play both badminton and pool but NOT darts?

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