Page 35 - Spotlight A+ Form 4 & 5 Mathematics KSSM

Form
5 Mathematics Chapter 8 Mathematical Modeling

This situation involves the linear function because B Quadratic modeling
the first differences are a constant, that is, RM39. 1. Quadratic modeling is related to a quadratic
The first differences is the gradient, m, that is, the function. The basic equation for quadratic
rate of change of y. function is y = ax + bx + c, where a is the leading
2
Hence, y = 39x + c. coefficient, b is the center coefficient and c is the
When (0, 200), y-intercept.
200 = 39(0) + c 2. The value of the leading coefficient a can
c = 200 determine the shape of the curve of a parabola.
y = 39x + 200
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(a) When a , 0,
When x = 60, • the parabola opens downward.
y = 39(60) + 200 • the function has a maximum value known
y = 2 540 as vertex (h, k).
Thus, the membership fee to be paid for 5 years y
is RM2 540.
10
Try questions 3 & 4 in Formative Zone 8.1
(0, 6)
5
Example 6 –10 –5 0 5 10 x
The graph below shows the journey distance, –5
y km, of a helicopter for x seconds.
y (km)
(b) When a . 0,
• the parabola opens upward.
8
(2, 7) • the function has a minimum value known
6 as vertex (h, k).
4 y
2
15
x (s)
–2 0 2 4 10
–2
5
(a) Based on the graph, write the equation (0, 1)
involved. –10 –5 0 5 10 x
(b) The total journey for the helicopter to reach
the designated destination is 18 200 km. How 3. Strategies that can be proposed in the
much time is required by the helicopter to construction of a quadratic model to solve a
reach the destination?
problem:
Solution: (a) Identify the variables involved along with
y – y their units.
2
1
(a) m = ——–— (b) Identify the important information of
x – x
2 1 the situation such as the maximum point,
7 – 0
m = ———
2 – 0 minimum point and related points.
m = 3.5 (c) Identify the solution. Typically, the solution
Thus, y = 3.5x will involve the use of a table of values to
obtain the formula for the function of model
(b) y = 3.5x
18 200 = 3.5x to be solved.
x = 5 200 (d) Construct a formula for the function
CHAP. Thus, the time required by the helicopter to involved.
8 reach the destination is 5 200 seconds. (e) Solve the function using the constructed
formula.

420 8.1.2 421

C08 SpotlightA+ Mathematics F5.indd 420 03/03/2021 4:59 PM