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BECE 2008 - MATHEMATICS [PAPER II]
THEORY QUESTIONS
(a)
E and F are subsets of the universal set U such that
U = {natural numbers less than 15}
E = {even numbers between 1 and 15} and
F = {multiples of 4 between 9 and 15}
(i)
List the elements of U, E and F.
(ii)
Draw a Venn diagram to show the sets U, E and F.
(b)
In a school,
(c)
A typist charges 28 Gp for the first five sheets and 8 Gp for each additional sheet she types. How much will she earn, if she types 36 sheets?
(a)
The diagram AEBCD shows the shape of Mr. Awuah's garden, which is made up of a rectangular portion ABCD and a triangular portion AEB.
|AB| = |DC| = 90 m, |AD| = |BC| = 70 m, |AE| = 48.5 m and |EB| = 50 m. The height of the triangle is 20 m.
Find
(i)
area of ABCD;
(ii)
area of AEB;
(iii)
total area of the garden;
(iv)
perimeter of the garden.
(b)
Find the value of x if
(a)
A traffic survey gave the results shown in the table below.
| Vehicle | Car | Lorry | Bus | Bicycle |
| Frequency | 15 | 12 | 8 | 25 |
(i)
Represent the information on a pie chart.
(ii)
What percentage of the vehicles were lorries?
(b)
Akosua was granted a loan of GH₵ 96.00. The interest rate was 24% per annum.
Calculate the
(i)
interest at the end of the year
(ii)
total amount she had to pay at the end of the year
(iii)
amount she still owes, if Akosua was able to pay only GH₵ 60.00 at the end of the year.
(a)
Copy and complete the table of values for the relation y1 = 2x + 5 and y2 = 3 - 2x for x from -4 to 3.
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y1 = 2x + 5 | -3 | 3 | 7 | 11 | ||||
| y2 = 3 - 2x | 11 | 9 | 5 |
(b)
(i)
Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y-axis, draw two perpendicular axes 0X and 0Y on a graph sheet.
(ii)
On the same graph sheet draw the graphs of the relation y1 = 2x + 5
and y2 = 3 - 2x
(c)
Find the coordinates of the point where y1 and y2 meet.
(d)
The vectors p =
Find the vector r.
(a)
Using a ruler and a pair of compasses only,
(i)
construct triangle ABC with sides |AB| = 7 cm, |BC| = 8 cm and |AC| = 9 cm;
(ii)
draw the perpendicular bisectors of the three sides;
(iii)
locate the point of the intersection, O, of the perpendicular bisector;
(iv)
with center O and radius OA, draw a circle to pass through the vertices of the triangle.
(b)
Measure and write down the radius of the circle you have drawn in (a)(iv).
(c)
Find the product of (2x - 3) and (x -1).
(a)
The marks obtained by 20 pupils in a test were as follows:
| 4 | 8 | 7 | 6 | 2 |
| 1 | 7 | 4 | 3 | 7 |
| 6 | 4 | 7 | 5 | 2 |
| 7 | 5 | 4 | 8 | 3 |
(i)
Construct a frequency distribution table for this data.
(ii)
What is the mode of the distribution?
(iii)
Calculate the mean mark.
(iv)
What percentage of the pupils passed, if the pass mark is 6?
(v)
What is the probability that a pupil selected at random scored not more than 5 marks?
(b)
Simplify 7