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BECE 1997 - MATHEMATICS [PAPER II]
THEORY QUESTIONS
1
(a)
If p = 4, a = 16, b = -5 and c = 3, evaluate p2 -
(b)
Solve the inequality 5x – 3(x – 1) ≥ 39. Illustrate your answer on the number line.
(c)
If x =
(i)
x + 2y
(ii)
3x – y
Using a ruler and a pair of compasses only,
(a)
(i)
construct a triangle ABC such that |AB| = 8 cm, angle ABC = 60° and |BC| = 8 cm.
(ii)
What type of triangle is triangle ABC?
(b)
construct the bisector of angle BAC to meet |BC| at D. Measure |AD|.
(c)
construct the perpendicular bisector of |BA| to meet |AD| at O.
(d)
Using O as centre and radius OD, draw a circle to touch the three sides of the triangle.
(a)
If 2y – 5x + 10 = 0, find:
(i)
y, when x = 2;
(ii)
x, when y = 5
(b)
(i)
Using a scale of 2 cm to 1 unit on both axes, draw two perpendicular lines OX and OY on a graph sheet.
(ii)
On the same graph sheet, mark the x-axis from –5 to 5 and the y-axis from –6 to 6.
(iii)
Plot on the same graph sheet, the points A(0, -5) and B(4, 5). Join AB using a ruler.
(iv)
Find the gradient of the line AB
(v)
Measure the acute angle that the line AB makes with the x-axis, using a protractor.
(a)
The table below shows the distribution of the ages (in years) of children who were treated in a clinic in a day.
| Age (years) | 1 | 2 | 3 | 4 | 5 |
| Frequency | 6 | 4 | 2 | 3 | 5 |
Find
(i)
the mean age;
(ii)
the modal age.
(b)
Draw a bar chart for the distribution.
(a)
The volume of a cylinder is 220 cm3. The radius of the cross-section is 2.5 cm. Find the height of the cylinder.
[Take π =
(b)
Each of the interior angles of a regular polygon is 140°. How many sides does it have?