Alevel_C1C2
Alevel_C1C2
Alevel_C1C2
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8<br />
Exam-style assessment<br />
Integration<br />
1. Given that f ¢(x) = 3x 2 + 2x + 1, find f(x).<br />
When y = f(x) the values x = 2 and y = 18 satisfy the equation.<br />
Use this information to write down the equation for y in terms of x.<br />
Hence deduce the value of y when x = 3. (6)<br />
2. (a) Find ∫ (x + 1)(x2 - 1)dx (5)<br />
(b) Find<br />
∫<br />
x + 1<br />
3<br />
d x<br />
(4)<br />
x<br />
3. The gradient of a curve is given by f ¢(x) = 6x 2 - 4x and the curve passes through<br />
the point (-1, 6).<br />
Find the equation of the curve.<br />
If the curve passes through the point (3, y) find the value of y. (5)<br />
4. (a) Find ∫ td t<br />
(2)<br />
(b) Find ∫ t td t<br />
(2)<br />
Hence, or otherwise,<br />
(c) find ∫ ( 1 + t)<br />
t d t<br />
(2)<br />
5. The gradient of a curve is given by d y<br />
= ax<br />
dx<br />
Find the equation of the curve in terms of the constant a and the constant of<br />
integration c.<br />
The curve passes through the points ( 1,<br />
1 2) and (-2, 8).<br />
Determine the values of the constants and hence write down the equation of<br />
the curve. (9)<br />
© Oxford University Press 2008<br />
Core C1
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