CMTS questions.docx

**Vector** Multiple Choice Questions. Question 1 Point A(3,4) and point B(-2,5) lie on a cartesian plane. Find [\$\\overrightarrow{\\text{AB}}\$]{.math.inline}. A. [\$\\overrightarrow{\\text{AB}} = i + 9j\$]{.math.inline} B. [\$\\overrightarrow{\\text{AB}} = - i - 9j\$]{.math.inline} C. [\$\\ov...

**Vector** Multiple Choice Questions. Question 1 Point A(3,4) and point B(-2,5) lie on a cartesian plane. Find [\$\\overrightarrow{\\text{AB}}\$]{.math.inline}. A. [\$\\overrightarrow{\\text{AB}} = i + 9j\$]{.math.inline} B. [\$\\overrightarrow{\\text{AB}} = - i - 9j\$]{.math.inline} C. [\$\\overrightarrow{\\text{AB}} = - 5i + j\$]{.math.inline} D. [\$\\overrightarrow{\\text{AB}} = 5i - j\$]{.math.inline} Question 3 Point A(6,2) and point B(-4,3) lie on a cartesian plane. It is given that [\$3\\overrightarrow{\\text{OA}} = \\overrightarrow{\\text{OB}} - 6\\overrightarrow{\\text{OC}}\$]{.math.inline}. Find [\$\\overrightarrow{\\text{OC}}\$]{.math.inline}. A. [\$\\overrightarrow{\\text{OC}} = - \\frac{11}{3}i - \\frac{1}{2}j\$]{.math.inline} B. [\$\\overrightarrow{\\text{OC}} = - \\frac{11}{3}i - 9j\$]{.math.inline} C. [\$\\overrightarrow{\\text{OC}} = \\frac{11}{3}i + \\frac{1}{2}j\$]{.math.inline} D. [\$\\overrightarrow{\\text{OC}} = \\frac{11}{3}i + 9j\$]{.math.inline} Question 4 Point D(-3,8) and point E(5,-6) lie on a cartesian plane. Find [\$\\overrightarrow{\\text{DE}}\$]{.math.inline}. A. [\$\\left\| \\overrightarrow{\\text{DE}} \\right\| = 3\\sqrt{281}\$]{.math.inline} B. [\$\\left\| \\overrightarrow{\\text{DE}} \\right\| = \\sqrt{260}\$]{.math.inline} C.[\$\\ \\left\| \\overrightarrow{\\text{DE}} \\right\| = \\sqrt{8}\$]{.math.inline} D. [\$\\left\| \\overrightarrow{\\text{DE}} \\right\| = 2\\sqrt{481}\$]{.math.inline} Question 5 Question 6 Question 7 Question 8 Question 9 Question 10 **Matrix** Multiple Choice Questions. Question 1 It is given that 3 matrices, [\$A = \\begin{bmatrix} 2 & 4 \\\\ \\end{bmatrix}\\ ,\\ \\ B = \\begin{bmatrix} 8 \\\\ 5 \\\\ 2 \\\\ \\end{bmatrix}\\ \\ ,\\ C = \\begin{bmatrix} 4 & 6 & 3 \\\\ 1 & 2 & 1 \\\\ \\end{bmatrix}\$]{.math.inline}. Determine The order of each matrix and the element. A. The order of A is [1 × 2 ]{.math.inline}, B is [2 × 3]{.math.inline} and C is [2 × 3]{.math.inline} B. The order of A is [2 × 1 ]{.math.inline}, B is [3 × 2]{.math.inline} and C is [2 × 3]{.math.inline} C. The order of A is [1 × 2 ]{.math.inline}, B is [2 × 3]{.math.inline} and C is [3 × 2]{.math.inline} D. The order of A is [2 × 1 ]{.math.inline}, B is [3 × 2]{.math.inline} and C is [3 × 2]{.math.inline} Question 2 Given matrix, [\$D = \\begin{bmatrix} 2 & 6 & 9 \\\\ 1 & 5 & 8 \\\\ 3 & 4 & 7 \\\\ \\end{bmatrix}\$]{.math.inline}, identify the elements of [*d*~12~]{.math.inline}, [*d*~23~]{.math.inline} and [*d*~31~]{.math.inline}. Answer: [*d*~12~ = 5]{.math.inline}, [*d*~23~ = 8]{.math.inline} and [*d*~31~ = 3]{.math.inline}. Question 3 Given matrix, [\$E = \\begin{bmatrix} 2 & 8 \\\\ 3 & 7 \\\\ \\end{bmatrix}\$]{.math.inline} and [\$F = \\begin{bmatrix} 1 & 4 \\\\ 5 & - 1 \\\\ \\end{bmatrix}\$]{.math.inline}. Find E+F matrix. Answer: [\$E + F = \\begin{bmatrix} 3 & 4 \\\\ 8 & 6 \\\\ \\end{bmatrix}\$]{.math.inline} Question 4 Given matrix, [\$E = \\begin{bmatrix} 2 & 8 \\\\ 3 & 7 \\\\ \\end{bmatrix}\$]{.math.inline} and [\$F = \\begin{bmatrix} 1 & 4 \\\\ 5 & - 1 \\\\ \\end{bmatrix}\$]{.math.inline}. Find 2E-4F matrix. Answer: [\$2E - 4F = 2\\begin{bmatrix} 2 & 8 \\\\ 3 & 7 \\\\ \\end{bmatrix} - 3\\begin{bmatrix} 1 & 4 \\\\ 5 & - 1 \\\\ \\end{bmatrix} = \\begin{bmatrix} 2\\left( 2 \\right) - 3(1) & 2\\left( 8 \\right) - 3\\left( 4 \\right) \\\\ 2\\left( 3 \\right) - 3\\left( 5 \\right) & 2\\left( 7 \\right) - 3\\left( - 1 \\right) \\\\ \\end{bmatrix} = \\begin{bmatrix} 1 & 4 \\\\ 14 & 11 \\\\ \\end{bmatrix}\$]{.math.inline} Question 5 Given matrix, [\$G = \\begin{bmatrix} 2 & 8 \\\\ 3 & 7 \\\\ \\end{bmatrix}\$]{.math.inline} and [\$H = \\begin{bmatrix} x + 3 & y - 4 \\\\ 3 & 7 \\\\ \\end{bmatrix}\$]{.math.inline}. Find value of [*x*]{.math.inline} and [*y*]{.math.inline}. Answer: [2 = *x* + 3 , *x* =  − 1    , 8 = *y* − 4  , *y* = 12 ]{.math.inline} **Absolute value/ inequalities** Multiple Choice Questions. Question 1 Solve the inequalities [2 − *x* \ 9]{.math.inline} B. [*x* \  − 9]{.math.inline} D. [*x* \>  − 5]{.math.inline} Question 2 Solve the inequalities [\$- \\frac{x}{5} \< 10\$]{.math.inline}. A. [*x* \> 50]{.math.inline} B. [*x* \  − 50]{.math.inline} D. [*x* \