Page 69 - Mathematics_Form_Two

Algebra

6. In a certain situation, a company uses (b) V = p rh
2
a special calculation formula defined
2
by ab∗= a + 2b to determine (c) I = PRT
production efficiency. Given that 100
4 (2 y∗ ∗ ) = 25, find the value of . (d) A = 1 (a bh+ )
2
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7. An operation on integers a and b is l
3
defined by ab∗= 3a + 2b, find the (e) T = 2p g
value of (3 2) 6.
* *
(f) y mx c= +
8. Given that, uv u∆= v − v u , find the Mathematics for Secondary Schools
value of 2 ∆ 3. (g) s = ut + 1 at 2
2
9. If (ab ) a= 2 + b , find the value of x
*
)
given that 4 (2 x = 25. Example 4�9
*
*
10. (a) If p q∗ = p q++ pq . Find the Given that y = mx + , c make m the
value of 2 (1 3).∗∗ subject of the formula.

(b) If ab∗= a + b 2 . Find the Solution
2
value of (2 3) 4.∗ ∗ Given the formula y = mx + . c (i)

Subtract c from both sides of equation

Transposition of formulae (i) to get y c−= mx . (ii)

A formula is an equation which shows Divide equation (ii) by x throughout to
how variables are related. For example, get m = yc−
the formula which is used to find the x

circumference, C of a circle is given by Therefore, m = yc- , provided x ≠ 0.
C = πd, where C is expressed in terms of π x
and d. In this case, C is the subject of the
formula. It is also possible to express d as Example 4�10
C
the subject of the formula, that is, d = .
p The volume, V of a cylinder with a
The procedure of expressing a formula base of radius r and height h is given
2
in different ways is called transposition by V = p rh. Make r the subject of the

of formula. The following are some formula.
examples of formulae: Solution

2
(a) A = lb Given the formula V = p rh. (i)

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 63