Literal quadratic equations Practice Questions (Grade 9)

Warm-upeasy

Given $a^{2} + b^{2} = c^{2}$ , for all positive values of $a$ , $b$ , and $c$ , which equation correctly solves for $a$ ?

Subtract $b^{2}$ from both sides: $a^{2} = c^{2} - b^{2}$ . Take the positive square root: $a = \sqrt{c^{2} - b^{2}}$ .

Mid-gameeasy

Given $a^{2} + b^{2} = c^{2}$ , for all positive values of $a$ , $b$ , and $c$ , which equation correctly solves for $b$ ?

Subtract $a^{2}$ from both sides: $b^{2} = c^{2} - a^{2}$ . Take the positive square root: $b = \sqrt{c^{2} - a^{2}}$ .

Mid-gameeasy

Given $I = mr^{2}$ , for all positive values of $I$ , $m$ , and $r$ , which equation correctly solves for $r$ ?

Divide both sides by $m$ : $r^{2} = \dfrac{I}{m}$ . Take the positive square root: $r = \sqrt{\dfrac{I}{m}}$ .

Mid-gamemedium

Given $E = \dfrac{1}{2}mv^{2} + E_{0}$ , for all positive values of $E$ , $m$ , $v$ , and $E_{0}$ , which equation correctly solves for $v$ ?

Subtract $E_{0}$ from both sides: $E - E_{0} = \dfrac{1}{2}mv^{2}$ . Multiply both sides by $2$ : $2(E - E_{0}) = mv^{2}$ . Divide by $m$ : $v^{2} = \dfrac{2(E - E_{0})}{m}$ . Take the positive square root: $v = \sqrt{\dfrac{2(E - E_{0})}{m}}$ .

Mid-gamemedium

Given $V = \pi r^{2} h$ , for all positive values of $V$ , $r$ , and $h$ , which equation correctly solves for $r$ ?

Divide both sides by $\pi h$ : $r^{2} = \dfrac{V}{\pi h}$ . Take the positive square root: $r = \sqrt{\dfrac{V}{\pi h}}$ .

Mid-gamemedium

Given $A = 4\pi r^{2}$ , for all positive values of $A$ and $r$ , which equation correctly solves for $r$ ?

Divide both sides by $4\pi$ : $r^{2} = \dfrac{A}{4\pi}$ . Take the positive square root: $r = \sqrt{\dfrac{A}{4\pi}}$ .

Mid-gamemedium

Given $d = \dfrac{1}{2}gt^{2}$ , for all positive values of $d$ , $g$ , and $t$ , which equation correctly solves for $t$ ?

Multiply both sides by $2$ : $2d = gt^{2}$ . Divide by $g$ : $t^{2} = \dfrac{2d}{g}$ . Take the positive square root: $t = \sqrt{\dfrac{2d}{g}}$ .

Buzzer beatermedium

Given $P = \dfrac{k}{r^{2}}$ , for all positive values of $k$ , $r$ , and $P$ , which equation correctly solves for $r$ ?

Multiply both sides by $r^{2}$ : $Pr^{2} = k$ . Divide by $P$ : $r^{2} = \dfrac{k}{P}$ . Take the positive square root: $r = \sqrt{\dfrac{k}{P}}$ .

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