5 Mark Question

Question 15 Marks

Find the products given below and case verify the result for a = 1, b = 2 and c = 3.
$\Big(\frac{1}{4}\text{abc}\Big)\times(-6\text{b}^2\text{c})\times\Big(-\frac{1}{3}\text{c}^3\Big)$

Answer

$\Big(\frac{1}{4}\text{abc}\Big)\times(-6\text{b}^2\text{c})\times\Big(-\frac{1}{3}\text{c}^3\Big)$
$=\frac{1}{4}\times(-6)\times\Big(-\frac{1}{3}\Big)\text{a}\times \text{b}\times \text{b}^2\times \text{c}\times\text{c}\times \text{c}^3$
$=\frac{1}{2}\text{a}\times\text{b} ^{1+2}\times \text{c}^{1+1+3}$
$=\frac{1}{2}\text{ab}^3\text{c}^5$
Verification:
$\text{L.H.S}=\Big(\frac{1}{4}\text{abc}\Big)\times(-6\text{b}^2\text{c})\Big(-\frac{1}{3}\text{c}^3\Big)$
$=\Big[\frac{1}{4}(1)(2)(3)\Big]\times[-6(2)^2\times3]\Big[-\frac{1}{3}(3)^3\Big]$
$=\Big(\frac{3}{2}\Big)\times(-72)\times (-9)$
$=\frac{3\times648}{2}=3\times 324$
$=972$
$\text{R.H.S}=\frac{1}{2}\text{ab}^3\text{c}^5$
$=\frac{1}{2}\times1\times(2)^3\times(3)^5$
$=\frac{1}{2}\times8\times243$
$=4\times243$
$=972$
$\therefore \text{L.H.S}= \text{R.H.S}$

View full question & answer→

Question 25 Marks

Find the products given below and case verify the result for a = 1, b = 2 and c = 3.
$\Big(\frac{-4}{7}\text{a}^2\text{b}\Big)\times\Big(\frac{-2}{3}\text{b}^2\text{c}\Big)\times\Big(\frac{-7}{6}\text{c}^2\text{a}\Big)$

Answer

$\Big(\frac{-4}{7}\text{a}^2\text{b}\Big)\times\Big(\frac{-2}{3}\text{b}^2\text{c}\Big)\times\Big(\frac{-7}{6}\text{c}^2\text{a}\Big)$$=\Big(\frac{-4}{7}\Big)\times\Big(\frac{-2}{3}\Big)\times \Big(\frac{-7}{6}\Big)\text{a}^2\times \text{a}\times \text{b}\times \text{b}^2\times \text{c}\times \text{c}^2$
$=\frac{-4}{9}\text{a}^3\text{b}^3\text{c}^3$
Verification:
$\text{L.H.S}$
$\Big(\frac{-4}{7}\text{a}^2\text{b}\Big)\times\Big(\frac{-2}{3}\text{b}^2\text{c}\Big)\times \Big(-\frac{7}{6}\text{c}^2\text{a}\Big)$
$\Big[\frac{-4}{7}(1)^2(2)\Big]\times \Big[\frac{-2}{3}(2)^2\times3\Big]\times\Big[\frac{-7}{6}(3)^2\times1\Big]$
$\Big[\frac{-4}{7}\times 1\times2\Big]\times \Big[\frac{-2}{3}\times 4\times3\Big]\times\Big[\frac{-7}{6}\times 9\Big]$
$=\Big(\frac{-8}{7}\Big)\times(-8)\times\Big(-\frac{21}{2}\Big)$
$=-\Big[\frac{8}{7}\times 8\times\frac{21}{2}\Big]$
$=-96$
$\text{R.H.S}$
$=\frac{-4}{9}\text{a}^3\text{b}^3\text{c}^3$
$=\frac{-4}{9}(1)^3\times (2)^3\times(3)^3$
$=\frac{-4}{9}\times1\times 8\times27$
$=-96$
$\therefore \text{L.H.S}=\text{R.H.S}$

View full question & answer→

Question 35 Marks

Find the products given below and case verify the result for a = 1, b = 2 and c = 3.
$\Big(\frac{2}{5}\text{a}^2\text{b}\Big)\times (-15\text{b}^2\text{ac})\times\Big(-\frac{1}{2}\text{c}^2\Big)$

Answer

$\Big(\frac{2}{5}\text{a}^2\text{b}\Big)\times (-15\text{b}^2\text{ac})\times\Big(-\frac{1}{2}\text{c}^2\Big)$
$=\frac{2}{5}\times (-15)\times \Big(-\frac{1}{2}\Big)\text{a}^2\times\text{a}\times \text{b}\times\text{b}^2\times \text{c}\times\text{c}^2$
$=3\text{a}^{2+1}\times \text{b}^{1+2}\times \text{c}^{1+2}$
$=3\text{a}^3\text{b}^3\text{c}^3$
Verification:
$=\Big(\frac{2}{5}\text{a}^2\text{b}\Big)\times (-15\text{b}^2\text{ac})\Big(-\frac{1}{2}\text{c}^2\Big)$
$=\frac{2}{5}(1)^2(2)\times (-15)\times(2)^2\times 1\times3\times\Big(-\frac{1}{2}(3)^2\Big)$
$=\Big(\frac{2}{5}\times1\times2\Big)\times(-15\times4\times3)\times\Big(-\frac{1}{2}\times9\Big)$
$=\frac{4}{5}\times(-180)\times\Big(-\frac{9}{2}\Big)$
$=\frac{360\times9}{5}=72\times9$
$=648$
$\text{R.H.S}=3\text{a}^3\text{b}^3\text{c}^3$
$=3(1)^3(2)^3(3)^3$
$=3\times1\times8\times27$
$=81\times8 $
$=648$
$\therefore \text{L.H.S}=\text{R.H.S}$

View full question & answer→

Question 45 Marks

Find the products given below and case verify the result for a = 1, b = 2 and c = 3.
$\Big(\frac{4}{9} \text{abc}^3\Big)\times \Big(\frac{-27}{5} \text{a}^3 \text{b}^2\Big)\times(-8 \text{b}^3 \text{c})$

Answer

$\Big(\frac{4}{9} \text{abc}^3\Big)\times \Big(\frac{-27}{5} \text{a}^3 \text{b}^2\Big)\times(-8 \text{b}^3 \text{c})$
$=\frac{4}{9}\times\Big(\frac{-27}{5}\Big)(-8)\text{a}\times\text{a}^3\times\text{b}\times\text{b}^2\times\text{b}^3\times \text{c}^3\times \text{c}$
$=\frac{96}{5}\text{a}^4\text{b}^6\text{c}^4$
Verification:
$\text{L.H.S}=\Big(\frac{4}{9}\text{abc}^3\Big)\times \Big(\frac{-27}{5}\text{a}^3\text{b}^2\Big)\times (-8\text{b}^3\text{c})$
$=\Big[\frac{4}{9}\times1\times2\times(3)^3\Big]\times\Big[\frac{-27}{5}(1)^3(2)^2\Big]\\\times[-8\times(2)^3\times3]$
$=\Big[\frac{4}{9}\times1\times2\times27\Big]\times\Big[\frac{-27}{5}1\times4\Big]\times[-8\times8\times3]$
$=(24)\times\Big(\frac{-108}{5}\Big)\times(-192)$
$=\frac{497664}{5}$
$\text{R.H.S}=\frac{96}{5}(\text{a}^4\text{b}^6\text{c}^4)$
$=\frac{96}{5}(1)^4(2)^6(3)^4$
$=\frac{96}{5}\times 1\times 64\times81$
$=\frac{497664}{5}$
$\therefore\text{L.H.S}=\text{R.H.S}$

View full question & answer→

Question 55 Marks

Find the products:
Multiply $-\frac{2}{3}\text{a}^2\text{b by }\frac{6}{5}\text{a}^3\text{b}^2$ and verify your result for a = 2 and b = 3.

Answer

$\frac{-2}{3}\text{a}^2\text{b}\times \frac{6}{5}\text{a}^3\text{b}^2$ $=\frac{-2}{3}\times \frac{6}{5}\text{a}^2\times \text{a}^3\times \text{b}\times \text{b}^2$ $=\frac{-4}{5}\text{a}^{2+3}\text{b}^{1+2}$ $=\frac{-4}{5}\text{a}^5\text{b}^3$Verification:
Now if a = 2, b = 3, then $-\frac{2}{3}\text{a}^2\text{b}=\frac{-2}{3}\times (2)^2\times 3$ $=\frac{-2}{3}\times 4\times 3$ $=-8$ $\frac{6}{5}\text{a}^3\text{b}^2=\frac{6}{5}\times (2)^3\times (3)^2$ $=\frac{6}{5}\times 2\times 2\times 2\times 3\times 3$ $=\frac{6}{5}\times 8\times 9=\frac{432}{5}$ $\therefore \text{L.H.S} = -8 \times \frac{432}{5}$ $=\frac{-3456}{5}$ $\text{R.H.S}=\frac{-4}{5}\text{a}^5\text{b}^3=\frac{-4}{5}(2)^5(3)^3$ $=\frac{-4}{5}(2\times2\times2\times2\times2)\times3\times3\times3$ $=\frac{-4}{5}\times32\times27$ $=\frac{-4\times864}{5}=\frac{-3456}{5}$ $\therefore \frac{-3456}{5}=\frac{-3456}{5}$ $\text{L.H.S.}= \text{R.H.S}$

View full question & answer→

Question 65 Marks

Find the products:
Multiply $-\frac{8}{21}\text{x}^2\text{y}^3\text{ by }-\frac{7}{16}\text{xy}^2$ and varify you result for x = 3 and y = 2.

Answer

$-\frac{8}{21}\text{x}^2\text{y}^3\times\frac{-7}{16}\text{xy}^2$
$=\frac{-8}{21}\times \frac{-7}{16}\text{x}^2\times \text{x}\times \text{y}^3\times \text{y}^2$
$=\frac{-1}{3}\times \frac{-1}{2}\times \text{x}^{2+1}\times \text{y}^{3+2}$
$=\frac{1}{6}\text{x}^3\text{y}^5$
Verification: x = 3, y = 2
$\text{L.H.S} =-\frac{8}{21}\text{x}^2\text{y}^3\times \frac{-7}{16}\text{xy}^2$
$=\frac{-8}{21}(3)^2(2)^3\times \frac{-7}{16}(3)(2)^2$
$=\frac{-8}{21}\times9\times 8\times\frac{-7}{16}\times 3\times 4$
$=\frac{-8}{21}\times \frac{-7}{16}\times 9\times 8\times 3\times 4$
$=\frac{-1}{3}\times \frac{-1}{2}\times72\times12 $
$=12\times12=144$
$\text{R.H.S}=\frac{1}{6}\text{x}^3\text{y}^5$
$=\frac{1}{6}\times(3)^3(2)^5$
$=\frac{1}{6}\times 27\times 32$
$=9\times 16=144$
$\therefore\text{L.H.S}= \text{R.H.S}$

View full question & answer→

Maths 5 Mark Question

Test yourself on this topic