\begin{questions} \Question[3] Evaluate \(2m(m-3n)\) when: \begin{multicols}{3} \begin{parts} \part \(m=3,n=5\) \begin{solutionordottedlines}[2cm] \(2 \cdot 3(3-3 \cdot 5) = 6(3-15) = 6(-12) = -72\) \end{solutionordottedlines} \part \(m=-3, n=-2\) \begin{solutionordottedlines}[2cm] \(2 \cdot (-3)(-3-3 \cdot (-2)) = -6(-3+6) = -6 \cdot 3 = -18\) \end{solutionordottedlines} \part \(m=\frac{1}{3}, n=\frac{1}{2}\) \begin{solutionordottedlines}[2cm] \(2 \cdot \frac{1}{3}\left(\frac{1}{3}-3 \cdot \frac{1}{2}\right) = \frac{2}{3}\left(\frac{1}{3}-\frac{3}{2}\right) = \frac{2}{3}\left(\frac{2-9}{6}\right) = \frac{2}{3} \cdot \frac{-7}{6} = -\frac{7}{9}\) \end{solutionordottedlines} \end{parts} \end{multicols} \Question[1] Evaluate \(\frac{p+2q}{3r}\) when \(p = 7, q = -2, r = 2\) \begin{solutionordottedlines}[2cm] \(\frac{7+2(-2)}{3 \cdot 2} = \frac{7-4}{6} = \frac{3}{6} = \frac{1}{2}\) \end{solutionordottedlines} \Question[1] Evaluate \(\frac{x+y}{3}\) when \(x = -6, y = -5\) \begin{solutionordottedlines}[2cm] \(\frac{-6-5}{3} = \frac{-11}{3}\) \end{solutionordottedlines} \Question[3] Fill in the missing term: \begin{multicols}{3} \begin{parts} \part \(2a+\dotfill=7a\) \begin{solutionordottedlines}[2cm] \(2a+5a=7a\) \end{solutionordottedlines} \part \(5m^2-\dotfill = -6m^2n\) \begin{solutionordottedlines}[2cm] \(5m^2-11m^2n = -6m^2n\) \end{solutionordottedlines} \part \(-6lm+\dotfill=lm\) \begin{solutionordottedlines}[2cm] \(-6lm+7lm=lm\) \end{solutionordottedlines} \end{parts} \end{multicols} \Question[6] Simplify by collecting like terms: \begin{multicols}{3} \begin{parts} \part \(9a^2+5a^2-12a^2\) \begin{solutionordottedlines}[2cm] \(9a^2+5a^2-12a^2 = 2a^2\) \end{solutionordottedlines} \part \(14a^2d-10a^2d-6a^2d\) \begin{solutionordottedlines}[2cm] \(14a^2d-10a^2d-6a^2d = -2a^2d\) \end{solutionordottedlines} \part \(17m^2-14m^2+8m^2\) \begin{solutionordottedlines}[2cm] \(17m^2-14m^2+8m^2 = 11m^2\) \end{solutionordottedlines} \part \(-4x^2+3x^2-3y-7y\) \begin{solutionordottedlines}[2cm] \(-4x^2+3x^2-3y-7y = -x^2-10y\) \end{solutionordottedlines} \part \(7x^3+6x^2-4y^3-x^2\) \begin{solutionordottedlines}[2cm] \(7x^3+6x^2-4y^3-x^2 = 7x^3+5x^2-4y^3\) \end{solutionordottedlines} \part \(-3ab^2+4a^2b-5ab^2+a^2b\) \begin{solutionordottedlines}[2cm] \(-3ab^2+4a^2b-5ab^2+a^2b = -8ab^2+5a^2b\) \end{solutionordottedlines} \end{parts} \end{multicols} \Question[12] Simplify \begin{multicols}{4} \begin{parts} \part \(4a\times 3b\) \begin{solutionordottedlines}[2cm] \(4a \times 3b = 12ab\) \end{solutionordottedlines} \part \(-2p \times(-3q)\) \begin{solutionordottedlines}[2cm] \(-2p \times(-3q) = 6pq\) \end{solutionordottedlines} \part \(27y \div 3\) \begin{solutionordottedlines}[2cm] \(27y \div 3 = 9y\) \end{solutionordottedlines} \part \(3 \times 12t \div 9\) \begin{solutionordottedlines}[2cm] \(3 \times 12t \div 9 = 4t\) \end{solutionordottedlines} \part \(24x\div 8 \times 3\) \begin{solutionordottedlines}[2cm] \(24x\div 8 \times 3 = 9x\) \end{solutionordottedlines} \part \(-\frac{12m}{18}\) \begin{solutionordottedlines}[2cm] \(-\frac{12m}{18} = -\frac{2}{3}m\) \end{solutionordottedlines} \part \(\frac{12ab}{4a}\) \begin{solutionordottedlines}[2cm] \(\frac{12ab}{4a} = 3b\) \end{solutionordottedlines} \part \(\frac{3x}{5}\times\frac{2}{3}\) \begin{solutionordottedlines}[2cm] \(\frac{3x}{5}\times\frac{2}{3} = \frac{2x}{5}\) \end{solutionordottedlines} \part \(\frac{2}{5a}\times\frac{1}{4a}\) \begin{solutionordottedlines}[2cm] \(\frac{2}{5a}\times\frac{1}{4a} = \frac{2}{20a^2} = \frac{1}{10a^2}\) \end{solutionordottedlines} \part \(\frac{3x}{5}\div\frac{3}{4}\) \begin{solutionordottedlines}[2cm] \(\frac{3x}{5}\div\frac{3}{4} = \frac{3x}{5} \times \frac{4}{3} = \frac{4x}{5}\) \end{solutionordottedlines} \part \(\frac{9y}{2}\div 18\) \begin{solutionordottedlines}[2cm] \(\frac{9y}{2}\div 18 = \frac{9y}{2} \times \frac{1}{18} = \frac{y}{4}\) \end{solutionordottedlines} \part \(\frac{5p}{6}\div(-\frac{10p}{3})\) \begin{solutionordottedlines}[2cm] \(\frac{5p}{6}\div(-\frac{10p}{3}) = \frac{5p}{6} \times \frac{-3}{10p} = -\frac{1}{4}\) \end{solutionordottedlines} \end{parts} \end{multicols} \Question[4] Fill in the missing boxes. Each box contains the product of the 2 boxes below it. \begin{multicols}{2} \begin{centering} \begin{parts} \part \begin{centering} \begin{tikzpicture} \draw (0,0) rectangle (1,1); \draw (1,0) rectangle (2,1); \draw (2,0) rectangle (3,1); \draw (0.5,1) rectangle (1.5,2); \draw (1.5,1) rectangle (2.5,2); \draw (1,2) rectangle (2,3); \node at (0.5,0.5) {$2a$}; \node at (1.5,0.5) {$4b$}; \node at (2.5,0.5) {$5a$}; \node at (1,1.5) {$8ab$}; \node at (2,1.5) {$20ab$}; \node at (1.5,2.5) {$160a^2b$}; \end{tikzpicture} \end{centering} \part \begin{centering} \begin{tikzpicture} \draw (0,0) rectangle (1,1); \draw (1,0) rectangle (2,1); \draw (2,0) rectangle (3,1); \draw (0.5,1) rectangle (1.5,2); \draw (1.5,1) rectangle (2.5,2); \draw (1,2) rectangle (2,3); \node at (1,1.5) {$24a$}; \node at (1.5,2.5) {$48a^2b$}; \node at (2.5,0.5) {$2b$}; \node at (0.5,0.5) {$12a$}; \node at (1.5,0.5) {$2a$}; \node at (2,1.5) {$4ab$}; \end{tikzpicture} \end{centering} \end{parts} \end{centering} \end{multicols} \Question[8] Expand: \begin{multicols}{4} \begin{parts} \part \(b(b+7)\) \begin{solutionordottedlines}[2cm] \(b(b+7) = b^2+7b\) \end{solutionordottedlines} \part \(4h(5h-7)\) \begin{solutionordottedlines}[2cm] \(4h(5h-7) = 20h^2-28h\) \end{solutionordottedlines} \part \(-k(5k-4)\) \begin{solutionordottedlines}[2cm] \(-k(5k-4) = -5k^2+4k\) \end{solutionordottedlines} \part \(-4x(3x-5)\) \begin{solutionordottedlines}[2cm] \(-4x(3x-5) = -12x^2+20x\) \end{solutionordottedlines} \part \(4c(2c-d)\) \begin{solutionordottedlines}[2cm] \(4c(2c-d) = 8c^2-4cd\) \end{solutionordottedlines} \part \(-3x(2x+5y)\) \begin{solutionordottedlines}[2cm] \(-3x(2x+5y) = -6x^2-15xy\) \end{solutionordottedlines} \part \(3p(2-5pq)\) \begin{solutionordottedlines}[2cm] \(3p(2-5pq) = 6p-15p^2q\) \end{solutionordottedlines} \part \(-10b(3a-7b)\) \begin{solutionordottedlines}[2cm] \(-10b(3a-7b) = -30ab+70b^2\) \end{solutionordottedlines} \end{parts} \end{multicols} \Question[6] Expand and collect like terms \begin{multicols}{3} \begin{parts} \part \(\frac{1}{4}(x+2)+\frac{x}{3}\) \begin{solutionordottedlines}[2cm] \(\frac{1}{4}(x+2)+\frac{x}{3} = \frac{1}{4}x+\frac{1}{2}+\frac{x}{3} = \frac{7}{12}x+\frac{1}{2}\) \end{solutionordottedlines} \part \(\frac{3}{7}(3x+5)+\frac{x}{3}\) \begin{solutionordottedlines}[2cm] \(\frac{3}{7}(3x+5)+\frac{x}{3} = \frac{9}{7}x+\frac{15}{7}+\frac{x}{3} = \frac{37}{21}x+\frac{15}{7}\) \end{solutionordottedlines} \part \(-\frac{1}{2}(3x+2)-\frac{2x}{5}\) \begin{solutionordottedlines}[2cm] \(-\frac{1}{2}(3x+2)-\frac{2x}{5} = -\frac{3}{2}x-1-\frac{2x}{5} = -\frac{19}{10}x-1\) \end{solutionordottedlines} \part \(2p(3p+1)-5(p+1)\) \begin{solutionordottedlines}[2cm] \(2p(3p+1)-5(p+1) = 6p^2+2p-5p-5 = 6p^2-3p-5\) \end{solutionordottedlines} \part \(2p(3p+1)-4(2p+1)\) \begin{solutionordottedlines}[2cm] \(2p(3p+1)-4(2p+1) = 6p^2+2p-8p-4 = 6p^2-6p-4\) \end{solutionordottedlines} \part \(4z(4z-2)-z(z+2)\) \begin{solutionordottedlines}[2cm] \(4z(4z-2)-z(z+2) = 16z^2-8z-z^2-2z = 15z^2-10z\) \end{solutionordottedlines} \end{parts} \end{multicols} \Question[8] Expand: \begin{multicols}{4} \begin{parts} \part \((x-6)(x-4)\) \begin{solutionordottedlines}[2cm] \((x-6)(x-4) = x^2-4x-6x+24 = x^2-10x+24\) \end{solutionordottedlines} \part \((4x+1)(3x-1)\) \begin{solutionordottedlines}[2cm] \((4x+1)(3x-1) = 12x^2-4x+3x-1 = 12x^2-x-1\) \end{solutionordottedlines} \part \((4x+3)(2x-1)\) \begin{solutionordottedlines}[2cm] \((4x+3)(2x-1) = 8x^2-4x+6x-3 = 8x^2+2x-3\) \end{solutionordottedlines} \part \((x-4)(2x+5)\) \begin{solutionordottedlines}[2cm] \((x-4)(2x+5) = 2x^2+5x-8x-20 = 2x^2-3x-20\) \end{solutionordottedlines} \part \((x+3)(x+3)\) \begin{solutionordottedlines}[2cm] \((x+3)(x+3) = x^2+3x+3x+9 = x^2+6x+9\) \end{solutionordottedlines} \part \((2x-5)(x+3)\) \begin{solutionordottedlines}[2cm] \((2x-5)(x+3) = 2x^2+6x-5x-15 = 2x^2+x-15\) \end{solutionordottedlines} \part \((