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BECE 2017 - MATHEMATICS [PAPER II]
THEORY QUESTIONS
a
In a class of 30 girls, 17 play football, 12 play hockey and 4 play both games.
i
Draw a Venn diagram to illustrate the given information.
ii
How many girls play:
α
one or two of the games;
β
none of the two games?
b
In the diagram, ABCD is a circle of radius 14 cm and centre O. Line BO is perpendicular to line AC. Calculate, the total area of the shaded portions.
[Take π =
a
Two consecutive odd numbers are such that seven times the smaller, subtracted from nine times the bigger, gives 144. Find the two numbers.
b
A paint manufacturing company has a machine which fills 24 tins with paint in 5 minutes.
i
How many tins will the machine fill in
α
1 minute, correct to the nearest whole number?
β
1 hour?
ii
How many hours will it take to fill 1440 tins?
c
Given that s =
a
Using a rule and a pair of compasses only, construct:
i
a triangle ABC with |BC| = 9 cm, |AC| = 8 cm and |AB| = 6 cm;
ii
the perpendicular bisector of line BC;
iii
the bisector of angle ACB.
b
Label the point of intersection of the two bisectors as Y.
c
Draw a line to join B and Y.
d
Measure:
i
|BY|;
ii
|YC|;
iii
the base angles of triangle BYC.
e
What type of triangle is BYC?
a
The table below shows the ages of students admitted in a hospital.
| Age (years) | 10 | 11 | 12 | 13 | 14 | 15 |
| Number of students | 5 | 1 | 7 | 10 | 3 | 4 |
Use the information to answer the following question:
i
What is the modal age?
ii
Calculate, correct to two decimal places, the mean age of the students.
b
Rice is sold at GH₵56.00 per bag of 50 kg. A trader bought some bags of rice and paid GH₵1,344.00.00
i
How many bags of rice did the trader buy?
ii
If the trader retailed the bags of rice at GH₵1.40 per kg, how much profit was made on 1 kg of rice?
a
Using a scale of 2 cm to 1 unit on both axes, draw on a graph sheet two perpendicular axes 0x and 0y for -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5.
i
Plot, indicating the coordinates of all perpendicular points A(2,3) and B(-3,4). Draw a straight line passing through the points A and B.
ii
Plot on the same graph sheet, indicating the coordinates of the points C(4,2) and D(-2,-3). Draw a straight line passing through the points to meet line AB.
b
Using the graphs in (a):
i
find the values of y when x = -2;
ii
measure the angle between the lines AB and CD.
a
If m =
i
values of x and y;
ii
components of m.
b
i
Solve the inequality:
ii
Illustrate the answer in b(i) on a number line.
c
In the diagram, AB is parallel to CD.
Find the value of:
i
x;
ii
y.