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(a) Express 1011two in denary.
Solution
= (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20)
= (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)
= 8 + 0 + 2 + 1
= 11ten
(b) Solve the equation
⇒ \(\frac{2x\: – \: 2}{3} = \frac{3x\: + \: 3}{2}\)
Solution
The L.C.M = 6
cross multiply both sides
2(2x – 6) = 3(3x + 6)
4x – 12 = 9x + 18
collect like terms
4x – 9x = 18 + 12
-5x = 30
divide both sides by -5
⇒ \( \frac{-5x}{-5} = \frac{30}{-5} \)
x = \( \frac{30}{-5} \)
∴ x = -6
(c) Calculate the simple interest on ₦60,000.00 for 3 years at 5% per annum
Solution
Simple interest = \( \frac{Principal \: \times \: Time \: \times \: Rate}{100} \)
= \( \frac{60000 \: \times \: 3 \: \times \: 5}{100} \)
= 600 × 15
= ₦9,000
(a) Calculate the area of a rhombus whose diagonals are 8cm and 16cm long.
Solution
Area of rhombus = ½(diagonal 1 × diagonal 2)
= ½ × (16 × 8)cm
= ½ × (128)cm
= 64cm²
(b) Find the length of /DE/ in the diagram below.
Solution
ΔADE is similar to ΔABC, hence
⇒ \( \frac{DE}{5} = \frac{4}{4+2} \)
⇒ \( \frac{DE}{5} = \frac{4}{6} \)
⇒ \( \frac{DE}{5} = \frac{2}{3} \)
cross multiply
|DE| × 3 = 2 × 5
|DE| × 3 = 10
divide both sides by 3
⇒ \( \frac{|DE| \: \times \: 3}{3} = \frac{10}{3} \)
|DE| = \( \scriptsize 3 \frac{1}{3} cm \)
|DE| = \( \scriptsize 3.33 cm \)
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