Page 41 - Ranger SPM 2022 - Additional Mathematics

Additional Mathematics SPM Chapter 2 Differentiation
4. The normal to the curve y = x + cx at 9. The cost of making x units of handicrafts
3
1

point (2, d) has a gradient of . Find is RM  1 x + 50x + 50 and will be sold
2
2 2
(a) the value of c and of d, for RM 80 – x each. Find
1


(b) the equation of the tangent to the 4
Penerbitan Pelangi Sdn Bhd. All Rights Reserved.
curve at x = –1. (a) the profit function, P from the sale
5. An open cuboid with a square base has of x units of handicrafts,
a volume of 750 cm . The prices per (b) the value of x so that the profit
3
cm of a piece of iron sheet to make function is maximum and hence,
2
the sides and the base are RM2 and find the maximum profit.
RM3 respectively. Find the dimensions 10. The diagram shows the water in a
of the cuboid so that the price to make hemispheric bowl of radius 8 cm.
the cuboid is minimum. Hence, find the 8 cm
minimum price to make 50 of similar
cuboids.
6. Given that the equation of a curve is
y = 6 . h cm
x 2
(a) Find dy when x = 3.
dx
(b) Hence, find the approximate value for Given that the rate of change of height
HOTS
6 of water in the bowl is 0.2 cm/s. HOTS
3.01 2 correct to 4 significant figures. (a) Express the surface area of the water,
A cm , in the bowl in terms of h.
2
7. An empty cone with base radius of (b) Hence, find the rate of change of the
10 cm and height of 10 cm is being surface area of the water in terms of
filled with water at a rate of 4π cm /s. π when h = 5 cm.
3
HOTS
Find the rate of change of HOTS 11. The diagram below shows a piece of
(a) the height at 18 seconds, brick which is rectangular in shape.
(b) the surface area of the water at The total surface area of the brick is
18 seconds.
2
HOTS
300 cm . HOTS
8. The diagram below shows a mold with
length 5 m and its cross section is an x cm h cm
HOTS
equilateral triangle. HOTS
Form 5 80 cm (a) Show that h = 50 – 2x .
2x cm
x
3
3
Water is poured into the mold at a rate (b) If the volume of the brick is V cm ,
express V in terms of x.
of 1003 cm /s. Find (c) If the value of x of the above brick
3
(a) the rate of change of height of the can be changed, find the maximum
water in the mold at 25 minutes, volume of the brick. Prove that the
(b) the volume of the water at that time. volume of the brick is maximum.

194

02 Ranger Mate Tambahan Tg5.indd 194 25/02/2022 9:23 AM