Page 68 - Mathematics_Form_Two

Algebra

Solution Exercise 4�1
x
Given x y = + 3 , find 5 (8 6).y. **
*
*
Start with operation in the brackets. That 1. Given that and ∆ are two
binary operations defined as
is, 5 (8 6) 5 (8 3 6)= * + ´ a (b ∆ c) = a(b – c).
**
*
=
5 26 If a = 2, b = 5 and c = 4, evaluate
*
FOR ONLINE READING ONLY
5 3 26
=+ ´ 2. In a certain business, the
the value of (a b) ∆ (a c).
*
*
Mathematics for Secondary Schools Therefore, 5 (8 6) = 83. profit calculation is defined by
5 78
= +
83
=
**
ab∗=
5(a +
2 ).b If a company uses
Example 4�7
this formula to determine its revenue
If pΔq = 2p+5q, find the value of
be the result when defined by 4 2?∗
6 ∆ 3. based on certain factors, what would
Solution 3. Evaluate each of the following by
using the defined binary operation.
From pq∆ = 2p + 5,q, it implies that,
6 ∆ 3 = (2 × 6) + (5 × 3) (a) 2 (3*4)∗ if xy∗= 3x + 6.y
= 12 + 15 (b) 5(43)∗ ∗ if pq∗= 3p − 2.q

= 27
Therefore, 6 ∆ 3 =27. (c) 95∆ if c ∆ d = c – d .
3
2

n
(d) (3 6) 6 if m n∗= mn − .
*
*
Example 4�8 m
m−n 4. An operation ∆ on integers and

If mΔn = . Calculate the value
m+ n is defined as d ∆ k = dk + 5d − 3.k
of 32∆ . Suppose a company uses this
operation to calculate a special index
Solution based on its data inputs. Find the

Given mΔn = m−n . It follows that,
m+ n index value based on the operation
32∆ .
32
−
32∆=
32+ 5. An operation ∆ is defined by
1
=
5 uv∆= uv . Find the value of 9 4.∆
v
1
Therefore, 32∆= .
5

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 62