Page 39 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Differentiation

SPM PRACTICE
SPM PRACTICE

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2
Paper 1 13. Given that y = px + qx and
dy
d y
2
 
2
= 4
– 32y where p and q are
3x – 1
dx
dx
2
lim
1. Find the value of x : 0 x + 2 . constants, find the possible values of
2. Find the value of lim 3 + 11x – 4x 2 . p and q.
x : 3 x – 3 14. Find the gradient function for the curve
dy y = (x + x )(2 – x) and hence, find the
2
3. Find dx for y = 2 – x using the first
2
principles. equation of the tangent at x = 1.
15. Find the gradient function for the curve
dy 2 3
4. Find dx for y = – + 1 using the first y = (x + 2) 2 and hence, find the equation
x
principles. of the normal at x = –1.
d 1 16. The gradient of tangent to the curve

5. Find  (8x – x) . a
4
2
dx 4 y = 2 – bx – 1 at point (–1, –2) is 4.
x
6. Find the first derivative for y = (1 – x) 3 Find the values of a and b.
with respect to x. x + 2 17. The equation of a curve is
3x y = x – 3x + 5. Find the coordinates
3
2
7. Find f ʹ(x) for f(x) = .
x – 2 of the points on the curve such that the
dy 2(x – 7) tangent at the points are parallel to the
8. Given the value of dx for y = x x-axis.
is 7 when x = k. Find the possible 11
2 18. Given y = 2x + is the equation of
2
values of k. the tangent to a curve y = –2x + 8x + 1
2
9. Find f ʹ(–3) for f (x) = (4 – 2x) (x + 3). at point (h, k). Find the value of h and
2
2
of k.
d y
2
10. Find for each of the following. 19. Given that the curve y = ax + bx has a
3
dx 2
(a) y = 1 – 2 stationary point at (2, 4), find the values
x
x 2 4 of a and b.
5 – x
Form 5 11. Given y = 2x 1 , show that 20. The sum of two numbers x and y is 10.
–
(b) y =
3x
2
The product of the square of x and y is P.
Find the value of x so that P is maximum.
d y x 21. A ball is thrown upwards from a
dy
2
2x + 3 = 0. building. After t seconds, the height,
dx 2 dx
s meter from the initial point is given by
12. Given y = x , show that s = 15t – 5t .
4
2
4y d y – dy 2 = 0. (a) When will the ball reach its
2
   
3 dx 2 dx maximum height?
(b) State the maximum height.
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