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BECE 2003 - MATHEMATICS [PAPER II]
THEORY QUESTIONS
ξ = {1, 2, 3, 4, ...,18}
A = {Prime numbers}
B= {Odd numbers greater than 3}
(a)
If A and B are subsets of the Universal set, ξ, list the members of A and B.
(b)
Find the set
(i)
A ∩ B;
(ii)
A ∪ B.
(c)
(i)
Illustrate ξ, A and B on a Venn diagram.
(ii)
Shade the region for prime factors of 18 on the Venn diagram.
(a)
If 2n – 5m + 10 = 0, find
(i)
m, when n = 2;
(ii)
n, when m = 5.
(b)
Simplify
(c)
A number of sweets were shared among 8 children and each child received 30. If 12 children shared the same number of sweets, how many will each receive?
The table shows the distribution of the ages (in years) of children in a nursery school.
| Age (years) | 1 | 2 | 3 | 4 | 5 |
| Number of children | 6 | 4 | 2 | 3 | 5 |
(a)
Find
(i)
the modal age
(ii)
the mean age
(b)
Draw a bar chart for the distribution.
(c)
What is the probability that a child chosen at random from the school is 4 years old?
(a)
If p =
Find p + 2q + r.
(b)
Find the solution set of the inequality x -
(c)
A rectangular sheet of metal has length 44 cm and breadth 10 cm. It is folded to form a cylinder with the breadth becoming the height.
Calculate
(i)
the radius of the cylinder formed;
(ii)
the volume of the cylinder.
[Take π =
(a)
Using a pair of compasses and ruler only,
(i)
Construct the triangle ABC with |AB| = 8 cm, |BC| = 8cm and |AC| = 7cm.
(ii)
Bisect angle ABC and let the bisector meet AC at D. Produce |BD| to P such that |BD| = |DP|. Join AP and CP.
(b)
Measure
(i)
angle ADB;
(ii)
|AP|.
(c)
What kind of quadrilateral is ABCP?