JAMB Mathematics Past Questions & Answers - Page 6

Using Pythagoras theorem

⇒ \((20\sqrt2)2 = x^2 + x^2\)

⇒ 800 = \(2x^2\)

⇒ 400 = \(x^2\)

⇒ x = \(\sqrt400\) = 20 cm

∴ Area of a square = \(x^2 = 20^2 = 400 cm^2\)

∴ Perimeter of a square = 4x = 4 x 20 = 80 cm

Volume of the composite solid = Volume of A + Volume of B

Volume of a cuboid = length x breadth x height

Volume of A = 6 x 26 x 8 = 1248 cm\(^3\)

Volume of B = 6 x 10 x 22 = 1320 cm\(^3\)

∴ Volume of the composite solid = 1248 + 1320 = 2568 cm\(^3\)

Total possible outcome = 6 x 6 = 36

Required outcome = 15

∴ Pr(E) = \(\frac{15}{36} = \frac{5}{12}\)

An exterior angle of a n-sided regular polygon = \(\frac{360}{n}\)

For (n - 1) sided regular polygon = \(\frac{360}{n - 1}\)

For (n + 2) sided regular polygon = \(\frac{360}{n + 1}\)

⇒ \(\frac{360}{n - 1} - \frac{360}{n + 2}\) = 6 9Given)

⇒ \(\frac{360(n + 2) - 360(n - 1)}{(n - 1)(n + 2)}\)

⇒ \(\frac{360n + 720 - 360n + 360}{(n - 1)(n + 2)}\)

⇒ \(\frac{1080}{(n - 1)(n + 2)} = \frac{6}{1}\)

⇒ 1080 = 6 (n - 1)(n + 2)

⇒ 180 = (n - 1)(n + 2)

⇒ 180 = n\(^2\)+ 2n - n - 2

⇒ 180 = n\(^2\) + n - 2

⇒ n\(^2\)b+ n - 2 - 180 = 0

⇒ n\(^2\) + n - 182 = 0

⇒ n\(^2\) + 14n - 13n - 182 = 0

⇒ n (n + 14) - 13 (n + 14) = 0

⇒ (n - 13) (n + 14) = 0

⇒ n - 13 = 0 or n + 14 = 0

⇒ n = 13 or n = -14

∴ n = 13 (We can't have a negative number of side)

% error = \(\frac{Error}{Actual Value}\) x 100%

Student's Value = 18mL

Actual Value = 18.4mL

Error = 18.4 - 18 = 0.4

∴ % error = \(\frac{0.4}{18.4}\) x 100% = 2.17%