(a) Solve the inequality: \(\frac{1 + 4x}{2}\) -\(\frac{5 + 2x}{7}\) < x -2 (b) If x: y = 3: 5, find the value of \(\frac{2x^2 - y^2}{y^2 - x^2}\)

Assessment: WAEC SSCE - General Mathematics - 2019 Subject: General Mathematics

Question 1 Report

(a) Solve the inequality: \(\frac{1 + 4x}{2}\) -\(\frac{5 + 2x}{7}\) < x -2

(b) If x: y = 3: 5, find the value of \(\frac{2x^2 - y^2}{y^2 - x^2}\)

Answer

(a)

majority of the candidates multiplied through by the L.C.M which is 14 to arrive at

7(1+4x) - 2(5+2x) < 14(x - 2)

and when simplified yielded

10x < -25 x -2 $\frac{1}{2}$

(b)

it was expected that they express

x = $\frac{3 y}{5}$ or y = $\frac{5 x}{3}$

and thereafter, substitute into the given expression to have

$\frac{2 x^{2} - y^{2}}{y^{2} - x^{2}} = \frac{2 x^{2} - (\frac{5 x}{3})^{2}}{(\frac{5 x}{3})^{2} - x^{2}} = \frac{x^{(} 2 - \frac{25}{9})}{x^{2} (\frac{25}{9} - 1)} = \frac{- 7}{16}$

$\frac{2 x^{2} - y^{2}}{y^{2} - x^{2}} = \frac{2 x^{2} - (\frac{5 x}{3})^{2}}{(\frac{5 x}{3})^{2} - x^{2}} = \frac{x^{(} 2 - \frac{25}{9})}{x^{2} (\frac{25}{9} - 1)} = \frac{- 7}{16}$

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Coordinate Geometry (JAMB)

Answer Details

(a)

majority of the candidates multiplied through by the L.C.M which is 14 to arrive at

7(1+4x) - 2(5+2x) < 14(x - 2)

and when simplified yielded

10x < -25 x -2 $\frac{1}{2}$

(b)

it was expected that they express

x = $\frac{3 y}{5}$ or y = $\frac{5 x}{3}$

and thereafter, substitute into the given expression to have

$\frac{2 x^{2} - y^{2}}{y^{2} - x^{2}} = \frac{2 x^{2} - (\frac{5 x}{3})^{2}}{(\frac{5 x}{3})^{2} - x^{2}} = \frac{x^{(} 2 - \frac{25}{9})}{x^{2} (\frac{25}{9} - 1)} = \frac{- 7}{16}$

$\frac{2 x^{2} - y^{2}}{y^{2} - x^{2}} = \frac{2 x^{2} - (\frac{5 x}{3})^{2}}{(\frac{5 x}{3})^{2} - x^{2}} = \frac{x^{(} 2 - \frac{25}{9})}{x^{2} (\frac{25}{9} - 1)} = \frac{- 7}{16}$

Read lesson note on Linear Inequalities (WAEC)

Read lesson note on Coordinate Geometry (JAMB)

Linear Inequalities

Coordinate Geometry

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