Higher Manipulating and Simplifying – Diagnostic Quiz Ready to test your knowledge? Simplify \[(3p^4)^2\] \[3p^8\] \[6p^8\] \[9p^6\] \[9p^8\] Hint Which of the following is an expression for the perimeter of the rectangle? \[5x+3\] \[5x+5\] \[10x+6\] \[10x+10\] Hint Make \(x\) the subject of \(y=mx+c\). \[x=\frac{y-c}{m}\] \[x=\frac{y+c}{m}\] \[x=m(y-c)\] \[x=m(y+c)\] Hint Fully simplify \[\frac{x^2+6x}{x^2+4x-12}\] \[\frac{6x}{4x-12}\] \[\frac{3x}{2x+6}\] \[-\frac{3}{4}\] \[\frac{x}{x-2}\] Hint Simplify \[\frac{12x^6y^3}{4x^2y^9}\] \[3x^3y^3\] \[3x^4y^5\] \[\frac{3x^3}{y^3}\] \[\frac{3x^4}{y^6}\] Hint Write \(\frac{8}{2x-3} - \frac{5}{x+7}\) as a single fraction in its simplest form. \[\frac{3}{x-10}\] \[\frac{3}{2x^2+11x-21}\] \[\frac{71-2x}{2x^2+11x-21}\] \[\frac{x-10}{2x^2+4x+21}\] Hint Rohit is four times as old as Kane. Ellyse is six years younger than Rohit. Given that Kane is \(x\) years old, write an expression for the mean of their ages. \[\frac{x+2}{3}\] \[\frac{3x+2}{3}\] \[2x-2\] \[3x-2\] Hint Simplify the expression below, giving your answer in the form \(\frac{ax+b}{cx+d}\). \[\frac{3x-15}{2x+3} \div \frac{x^2-x-20}{2x^2-9x-18}\] \[\frac{3x+18}{x+4}\] \[\frac{3x-18}{x+4}\] \[\frac{3x-3}{x-4}\] \[\frac{x-3}{3x+12}\] Hint Fully simplify \[\frac{4x-3}{3x+2} \times \frac{3x-4}{2x+1} \] \[\frac{12x^2-25x+12}{6x^2+7x+2}\] \[\frac{12x^2+25x-12}{6x^2+7x+2}\] \[\frac{12x^2-25x-12}{6x^2+7x+2}\] \[\frac{12x^2+25x+12}{6x^2+7x+2}\] Hint Given that \(n\) is an integer, which of these expressions is always a multiple of 5? \[5(n+\frac{1}{2})\] \[5n+4\] \[n+5\] \[5(n+1)\] Hint Rearrange the formula below to make \(a\) the subject. \[\frac{a}{b} = \frac{3a+7}{5b-2}\] \[a=\frac{3ab+7b}{5b-2}\] \[a=\frac{7b}{2b-2}\] \[a=\frac{7}{2}-\frac{7b}{2}\] \[a=\frac{7}{2b-2}\] Hint Given \(n\) is an integer, which pair of expressions represent two, consecutive numbers. \(n + 1\) and \(n - 1\) \(2n + 1\) and \(2n - 1\) \(2n\) and \(2(n +1)\) \(n\) and \(n+1\) Hint Fully simplify \[\frac{15x+6}{3x^2+18}\] \[\frac{5x+2}{x^2+6}\] \[\frac{5x}{12}\] \[\frac{5x+2}{x+6}\] \[\frac{1}{x+3}\] Hint Rearrange the formula below to make \(u\) the subject. \[v^2=u^2+2as\] \[u^2=v^2+2as\] \[u^2=v^2-2as\] \[u=\sqrt{v^2-2as}\] \[u=\sqrt{v^2+2as}\] Hint Write the expression below as a fraction in its simplest form. \[\frac{3}{2a+5} + \frac{7}{3a+4}\] \[\frac{10}{5a+9)}\] \[\frac{23a+47}{(2a+5)(3a+4)}\] \[\frac{10}{(2a+5)(3a+4)}\] \[\frac{23a+47}{5a+9}\] Hint Time is Up! Time's up More?