7.2.2 Algebraic Formulae, PT3 Practice

Posted on March 6, 2018 by user

Question 6:

$Given 2 a b = 3 a - \frac{b^{2}}{2} . Express a in terms of b .$

Solution:

$\begin{array}{l} 2 a b = 3 a - \frac{b^{2}}{2} \\ 3 a - 2 a b = \frac{b^{2}}{2} \\ a (3 - 2 b) = \frac{b^{2}}{2} \\ a = \frac{b^{2}}{2 (3 - 2 b)} \end{array}$

Question 7:

$Given a = \frac{\sqrt{b + 1}}{a} . Express b in terms of a .$

Solution:

$\begin{array}{l} a = \frac{\sqrt{b + 1}}{a} \\ \sqrt{b + 1} = a^{2} \\ {[{(b + 1)}^{\frac{1}{2}}]}^{2} = {(a^{2})}^{2} \\ b + 1 = a^{4} \\ b = a^{4} - 1 \end{array}$

Question 8:

$\begin{array}{l} Given x = \frac{5 w}{2 w - y} . \\ (i) Express w in terms of x and y . \\ (ii) Find the value of w when x = 10 and y = 15. \end{array}$

Solution:

$\begin{array}{l} (i) \\ x = \frac{5 w}{2 w - y} \\ 2 w x - x y = 5 w \\ 2 w x - 5 w = x y \\ w (2 x - 5) = x y \\ w = \frac{x y}{2 x - 5} \\ (ii) \\ w = \frac{(10) (15)}{2 (10) - 5} \\ = \frac{150}{15} \\ = 10 \end{array}$

Question 9:
Azmin is h years old. His father is twice his brother’s age. If Azmin is 3 years older than his brother, write a formula for the sum (S) of their age.

Solution:
Azmin’s age = h
Azmin’s brother’s age = h – 3
Azmin’s father’s age = (h – 3) × 2 = 2h – 6

Therefore, the sum (S) of their age
S = h + (h – 3) + (2h – 6)
S = h + h – 3 + 2h – 6
S = 4h – 9

Question 10:
Mei Ling is 12 years older than Ali. In the next four years, Raju will be two times older than Ali. If h represents Ali’s age, write the algebraic expressions that represent the total of their ages, in terms of h, in four years time.

Solution:
Ali’s age in the next four years = h + 4
Mei Ling’s age = (h + 4) + 12 = h + 16
Raju’s age = (h + 4) × 2 = 2h + 8

Therefore, the total (S) of their age
S = (h + 4) + (h + 16) + (2h + 8)
S = 4h + 28

7.2.1 Algebraic Formulae, PT3 Practice

Posted on March 4, 2018 by user

7.2.1 Algebraic Formulae, PT3 Practice

Question 1:

Given m²+ 7 = k, express m in terms of k.

Solution:

$\begin{array}{l} m^{2} + 7 = k \\ m^{2} = k - 7 \\ m = \sqrt{k - 7} \end{array}$

Question 2:

Given 5km = mn – 2k, express k in terms of m and n.

Solution:

$\begin{array}{l} 5 k m = m n - 2 k \\ 5 k m + 2 k = m n \\ k (5 m + 2) = m n \\ k = \frac{m n}{5 m + 2} \end{array}$

Question 3:

Given

$2 k - \frac{m}{2 n} = m$ , express m in terms of k and n.

Solution:

$\begin{array}{l} 2 k - \frac{m}{2 n} = m \\ - m - \frac{m}{2 n} = - 2 k \\ m + \frac{m}{2 n} = 2 k \\ \frac{2 n m + m}{2 n} = 2 k \\ \frac{m (2 n + 1)}{2 n} = 2 k \\ m = \frac{4 k n}{2 n + 1} \end{array}$

Question 4:

Given

$\frac{4 m}{\sqrt{T} - k} = \frac{3 h}{m}$ , express T in terms of h and m.

Solution:

$\begin{array}{l} \frac{4 m}{\sqrt{T} - k} = \frac{3 h}{m} \\ 4 m^{2} = 3 h \sqrt{T} - 3 h k \\ 3 h \sqrt{T} = 4 m^{2} + 3 h k \\ \sqrt{T} = \frac{4 m^{2} + 3 h k}{3 h} \\ T = {(\frac{4 m^{2} + 3 h k}{3 h})}^{2} \leftarrow Square both sides \end{array}$

Question 5:

Given

$\sqrt{\frac{8 s - 3 h}{4}} = 2$ , express s in terms of h.

Solution:

$\begin{array}{l} \sqrt{\frac{8 s - 3 h}{4}} = 2 \\ \frac{8 s - 3 h}{4} = 4 \leftarrow Square both sides \\ 8 s - 3 h = 16 \\ 8 s = 16 + 3 h \\ s = \frac{16 + 3 h}{8} \\ s = 2 + \frac{3 h}{8} \end{array}$

7.1 Algebraic Formulae

Posted on March 1, 2018 by user

7.1 Algebraic Formulae

7.1.1 Variables and Constant

1. A variable is a quantity without a fixed value.

2. A constant is a quantity with a fixed value.

7.1.2 Concept of Formulae

1. An algebraic formula is an equation which shows the relationship between several variables and/ or constant.

2. The subject of an algebraic formula is a linear variable expressed in terms of the other variables.

Example 1:

$Express x in terms of y, if y = \frac{2 - 3 x}{x} .$

Solution:

$\begin{array}{l} y = \frac{2 - 3 x}{x} \\ x y = 2 - 3 x \\ x y + 3 x = 2 \\ x (y + 3) = 2 \\ x = \frac{2}{y + 3} \end{array}$

Example 2:

$Given that s = \frac{p^{2} - q^{2}}{2 u}, make p the subject of the formula .$

Solution:

$\begin{array}{l} s = \frac{p^{2} - q^{2}}{2 r} \\ 2 r s = p^{2} - q^{2} \\ p^{2} = 2 r s + q^{2} \\ p = \sqrt{2 r s + q^{2}} \end{array}$