(a) Copy and complete the table of values for the... | WAEC SSCE - General Mathematics - 2021 (Essay)

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(a) Copy and complete the table of values for the relation \(y=2x^2-x-2\) for \(4 \le x \le 4\).

x	-4	-3	-2	-2	0	1	2	3	4
y		19			-2				26

(b) Using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of \(y=2x^2-x-2\) for \(4 \le x \le 4\).

(d) Use the graph to find the: (i) roots of the equation \(2x-3r-5\ 0\); (i) range of values of \(x\) for which \(2x^2-x-2<0\).

Answer

(a) Completed table for \(y = 2x^{2} - x - 2\), \(-4 \leq x \leq 4\). Substituting each value of \(x\):

\(x=-4:\ 2(16)+4-2=34\). \(x=-3:\ 2(9)+3-2=19\). \(x=-2:\ 2(4)+2-2=8\). \(x=-1:\ 2(1)+1-2=1\). \(x=0:\ -2\). \(x=1:\ 2-1-2=-1\). \(x=2:\ 8-2-2=4\). \(x=3:\ 18-3-2=13\). \(x=4:\ 32-4-2=26\).

x	-4	-3	-2	-1	0	1	2	3	4
y	34	19	8	1	-2	-1	4	13	26

(b) Graph. Plot the nine points (2 cm to 1 unit on the x-axis, 2 cm to 5 units on the y-axis) and join with a smooth upward (minimum) parabola; its lowest point is near \(x=0.25,\ y=-2.1\).

(c) Line \(y = 2x + 3\). Plot two points, e.g. \((0,3)\) and \((2,7)\), and draw the straight line on the same axes.

(d)(i) Roots of \(2x^{2} - 3x - 5 = 0\). Where the curve meets the line, \(2x^{2}-x-2 = 2x+3\), which rearranges to \(2x^{2}-3x-5 = 0\). So the x-coordinates of the two intersection points are the required roots. From the graph \(x = -1\) and \(x = 2.5\). (Check: \(2x^2-3x-5=(2x-5)(x+1)=0\Rightarrow x=2.5,\ -1\).)

(d)(ii) Range of \(x\) for which \(2x^{2} - x - 2 < 0\). This is where the curve lies below the x-axis (\(y<0\)). The curve crosses \(y=0\) at \(x=\frac{1\pm\sqrt{17}}{4}\), i.e. \(x \approx -0.8\) and \(x \approx 1.3\). Hence \(y<0\) between them:

\[-0.8 < x < 1.3.\]

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Answer Details

(a) Completed table for \(y = 2x^{2} - x - 2\), \(-4 \leq x \leq 4\). Substituting each value of \(x\):

\(x=-4:\ 2(16)+4-2=34\). \(x=-3:\ 2(9)+3-2=19\). \(x=-2:\ 2(4)+2-2=8\). \(x=-1:\ 2(1)+1-2=1\). \(x=0:\ -2\). \(x=1:\ 2-1-2=-1\). \(x=2:\ 8-2-2=4\). \(x=3:\ 18-3-2=13\). \(x=4:\ 32-4-2=26\).

x	-4	-3	-2	-1	0	1	2	3	4
y	34	19	8	1	-2	-1	4	13	26

(b) Graph. Plot the nine points (2 cm to 1 unit on the x-axis, 2 cm to 5 units on the y-axis) and join with a smooth upward (minimum) parabola; its lowest point is near \(x=0.25,\ y=-2.1\).

(c) Line \(y = 2x + 3\). Plot two points, e.g. \((0,3)\) and \((2,7)\), and draw the straight line on the same axes.

\[-0.8 < x < 1.3.\]

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Algebraic Expressions (WAEC)

Read lesson note on Ratio, Proportions And Rates (WAEC)

Read lesson note on Graphs Of Linear And Quadratic Functions (WAEC)

Solution Of Linear Equations

Algebraic Expressions

Ratio, Proportions And Rates

Graphs Of Linear And Quadratic Functions

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(a) Copy and complete the table of values for the relation \(y=2x^2-x-2\) for \(4 \le x \le 4\). x -4 -3 -2 -2 0 1 2 3 4 y 19 -2 26 (b) Using a scale of 2 c...

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(a) Copy and complete the table of values for the relation \(y=2x^2-x-2\) for \(4 \le x \le 4\). x -4 -3 -2 -2 0 1 2 3 4 y 19 -2 26 (b) Using a scale of 2 c...

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