Practice test 1
50
Time : 1 hr 15 min
1. The curve given by y = ax
3
MM :
2
+ bx + 3x + 2 passes through the point (1,2) and the gradient at
that point is 7. Find the values of a and b.
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2. The line 2x + 3y = 6 meets the y- axis at A and the x -axis at B. C is the point such that AB =
BC. CD is drawn perpendicular to AC to meet the line through A parallel to 5x + y = 7 at D.
a. Find the coordinates of A, B and
C.
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b. Write the equations of CD and AD, and hence find the coordinates of
D.
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c. Calculate the area of the triangle
ACD.
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3. In the Fig below, O is the centre of the circle containing the sector OAB. DC is a parallel arc
and BC = 3 cm.
If OC = r cm and angle AOB = ϴ rad,
a. Find the shaded area and shaded perimeter in terms of r and ϴ in simplest
from.
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b. Given that the shaded area is three- quarters of the area of the sector OAB, calculate the
value of
r.
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c. If, however, the total perimeter of the shaded area equals total perimeter of the sector OAB,
find the value of ϴ.
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