Quiz 15 of 20

2016 JSCE Mathematics Theory Questions Paper 3

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(a) Express 1011two in denary
1011two = 1x123 +0x22+1x21+1x2o
=  1x8+0+1x2+1x1
= 8+2+1
= 11two
(b) \(\frac{2x-2}{3}=\frac{3x+3}{2}\)
find the L.C.M of both sides
\(\frac{\left ( 2x-6 \right )}{3}=3\frac{\left ( 3x+6 \right )}{2}\)
cross multiply both side
2(2x -6) = 3(3x+6)
4x -12 = 9x + 18
collect like terms
4x -9x = 18+12
-5x = 30
x = -30
\(x=\frac{-30}{5}\)
x =-6
(c) Simple interest \(\frac{Principal x Time x Rate}{100}\)
\(\frac{60000 x 3 x 5}{100}\)
=  600 x 15
= N9000

(a)

Area of rhombus

= \(\frac{1}{2}\)(diagonal 1 x diagonal 2)

=  \(\frac{1}{2}\) x (16 x 8)cm

= \(\frac{1}{2}\) (128) km2

= 64cm2

(b)

Clearly  ADE is similar to ABC hence

\(\frac{DE}{5}=\frac{4}{4+2}\)

\(\frac{DE}{5}=\frac{4}{6}\)

\(\frac{DE}{5}=\frac{2}{3}\)

cross multiply

DE x 3 =  2x 5

DE x 3 = 10

Divide both side by 3

\(\frac{DE}{3}=\frac{10}{3}\)

DE = \(\frac{31}{3}\)

DE = 3.33cm

(a) Express 1011two in denary
1011two = 1x123 +0x22+1x21+1x2o
=  1x8+0+1x2+1x1
= 8+2+1
= 11two
(b) \(\frac{2x-2}{3}=\frac{3x+3}{2}\)
find the L.C.M of both sides
\(\frac{\left ( 2x-6 \right )}{3}=3\frac{\left ( 3x+6 \right )}{2}\)
cross multiply both side
2(2x -6) = 3(3x+6)
4x -12 = 9x + 18
collect like terms
4x -9x = 18+12
-5x = 30
x = -30
\(x=\frac{-30}{5}\)
x =-6
(c) Simple interest \(\frac{Principal x Time x Rate}{100}\)
\(\frac{60000 x 3 x 5}{100}\)
=  600 x 15
= N9000

(a)

Area of rhombus

= \(\frac{1}{2}\)(diagonal 1 x diagonal 2)

=  \(\frac{1}{2}\) x (16 x 8)cm

= \(\frac{1}{2}\) (128) km2

= 64cm2

(b)

Clearly  ADE is similar to ABC hence

\(\frac{DE}{5}=\frac{4}{4+2}\)

\(\frac{DE}{5}=\frac{4}{6}\)

\(\frac{DE}{5}=\frac{2}{3}\)

cross multiply

DE x 3 =  2x 5

DE x 3 = 10

Divide both side by 3

\(\frac{DE}{3}=\frac{10}{3}\)

DE = \(\frac{31}{3}\)

DE = 3.33cm