Question 1
Which lines on the graph below show the vectors:
\begin{pmatrix}1\\3\end{pmatrix} from A
\begin{pmatrix}2\\-1\end{pmatrix} from B
\begin{pmatrix}-4\\-5\end{pmatrix} from C
ANSWER: Multiple Choice (Type 2)
A: D, H, F
B: D, J, F
C: E, J, G
D: E, H, G
Answer: A
Workings:
The vector from point A travels 1 to the right and 3 up, giving vector D.
The vector from point B travels 2 to the right and 1 down, giving vector H.
The vector from point C travels 4 to the left and 5 down, giving vector F.
Marks = 3
Question 2
Given the vectors:
\textbf{a} = \begin{pmatrix}2\\3\end{pmatrix} \textbf{b} = \begin{pmatrix}1\\5\end{pmatrix}Which lines on the graph below show the vectors:
2\textbf{a}\\ \textbf{a} + \textbf{b}\\ 4\textbf{a} - 2\textbf{b}
ANSWER: Multiple Choice (Type 1):
A: B, C, E
B: A, D, F
C: C, D, F
D: A, B, E
Answer: A
Workings:
2\textbf{a} is shown by vector C.
\textbf{a} + \textbf{b} is shown by vector B.
4\textbf{a} - 2\textbf{b} is shown by vector E.
Marks = 3
Question 3
Given the following vectors:
\textbf{a} = \begin{pmatrix}2\\5\end{pmatrix} \textbf{b} = \begin{pmatrix}10\\-4\end{pmatrix} \textbf{c} = \begin{pmatrix}-3\\-7\end{pmatrix}
Write the following expressions as a single column vector;
3(a):
\textbf{a} + \textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}12\\1\end{pmatrix}
B: \begin{pmatrix}10\\7\end{pmatrix}
C: \begin{pmatrix}4\\9\end{pmatrix}
D: \begin{pmatrix}8\\1\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}2\\5\end{pmatrix} + \begin{pmatrix}10\\-4\end{pmatrix} = \begin{pmatrix}2+10\\5-4\end{pmatrix} = \begin{pmatrix}12\\1\end{pmatrix}
Marks = 1
3(b):
\textbf{c} + \textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}7\\-11\end{pmatrix}
B: \begin{pmatrix}5\\-8\end{pmatrix}
C: \begin{pmatrix}10\\-5\end{pmatrix}
D: \begin{pmatrix}6\\-2\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}-3\\-7\end{pmatrix}+\begin{pmatrix}10\\-4\end{pmatrix}=\begin{pmatrix}-3+10\\-7-4\end{pmatrix}=\begin{pmatrix}7\\-11\end{pmatrix}
Marks = 1
3(c):
-\textbf{c}-\textbf{a}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}1\\2\end{pmatrix}
B: \begin{pmatrix}4\\3\end{pmatrix}
C: \begin{pmatrix} -3\\-2\end{pmatrix}
D: \begin{pmatrix}-2\\-4\end{pmatrix}
Answer: A
Workings:
-\begin{pmatrix}-3\\-7\end{pmatrix}-\begin{pmatrix}2\\5\end{pmatrix}=\begin{pmatrix}3-2\\7-5\end{pmatrix}=\begin{pmatrix}1\\2\end{pmatrix}
Marks = 1
Question 4
Given the following vectors
\textbf{a} = \begin{pmatrix}3\\1\end{pmatrix} \textbf{b} = \begin{pmatrix}5\\-2\end{pmatrix} \textbf{c} = \begin{pmatrix}2\\7\end{pmatrix}
Write the following expressions as a single column vector;
4(a):
\textbf{a} + \textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}8\\-1\end{pmatrix}
B: \begin{pmatrix}7\\5\end{pmatrix}
C: \begin{pmatrix}5\\8\end{pmatrix}
D: \begin{pmatrix}6\\2\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}3\\1\end{pmatrix}+\begin{pmatrix}5\\-2\end{pmatrix}=\begin{pmatrix}8\\-1\end{pmatrix}
Marks = 1
4(b):
2\textbf{c} + \textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}9\\12\end{pmatrix}
B: \begin{pmatrix}11\\0\end{pmatrix}
C: \begin{pmatrix}8\\9\end{pmatrix}
D: \begin{pmatrix}13\\-3\end{pmatrix}[/latex]
Answer: A
Workings:
\begin{pmatrix}4\\14\end{pmatrix}+\begin{pmatrix}5\\-2\end{pmatrix}=\begin{pmatrix}9\\12\end{pmatrix}
Marks = 1
4(c):
3\textbf{c} - 2\textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}-4\\25\end{pmatrix}
B: \begin{pmatrix}0\\19\end{pmatrix}
C: \begin{pmatrix}9\\-8\end{pmatrix}
D: \begin{pmatrix}5\\-4\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}6\\21\end{pmatrix}-\begin{pmatrix}10\\-4\end{pmatrix}=\begin{pmatrix}-4\\25\end{pmatrix}
Marks = 1
4(d):
2\textbf{a} - \textbf{c}ANSWER: Multiple choice (Type 2)
A: \begin{pmatrix}4\\-5\end{pmatrix}
B: \begin{pmatrix}1\\4\end{pmatrix}
C: \begin{pmatrix}8\\-11\end{pmatrix}
D: \begin{pmatrix}7\\-5\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}6\\2\end{pmatrix}-\begin{pmatrix}2\\7\end{pmatrix}=\begin{pmatrix}4\\-5\end{pmatrix}
Marks = 1
Question 5
Given the following vectors:
\textbf{a} = \begin{pmatrix}5\\-1\end{pmatrix} \textbf{b} = \begin{pmatrix}8\\-4\end{pmatrix} \textbf{c} = \begin{pmatrix}1\\5\end{pmatrix}
Write the following vectors as a single column vector;
5(a):
\textbf{a} - \textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}-3\\3\end{pmatrix}
B: \begin{pmatrix}4\\-6\end{pmatrix}
C: \begin{pmatrix}7\\-9\end{pmatrix}
D: \begin{pmatrix}3\\-5\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}5\\-1\end{pmatrix}-\begin{pmatrix}8\\-4\end{pmatrix}-\begin{pmatrix}5\\-1\end{pmatrix}=\begin{pmatrix}5\\7\end{pmatrix}
Marks = 1
5(b):
2\textbf{c} +\textbf{b} - \textbf{a}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}5\\7\end{pmatrix}
B: \begin{pmatrix}3\\7\end{pmatrix}
C: \begin{pmatrix}20\\-14\end{pmatrix}
D: \begin{pmatrix}-1\\13\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}2\\10\end{pmatrix}+\begin{pmatrix}8\\-4\end{pmatrix}-\begin{pmatrix}5\\-1\end{pmatrix}=\begin{pmatrix}5\\7\end{pmatrix}
Marks = 1
5(c):
3\textbf{c} + \textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}11\\11\end{pmatrix}
B: \begin{pmatrix}16\\2\end{pmatrix}
C: \begin{pmatrix}29\\-13\end{pmatrix}
D: \begin{pmatrix}25\\-7\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}3\\15\end{pmatrix}+\begin{pmatrix}8\\-4\end{pmatrix}=\begin{pmatrix}11\\11\end{pmatrix}
Marks = 1
5(d):
2\textbf{a}-\dfrac{1}{2}\textbf{b}ANSWER: Multiple Choice (Type 2)
A: \begin{pmatrix}6\\0\end{pmatrix}
B: \begin{pmatrix}15\\-11\end{pmatrix}
C: \begin{pmatrix}-1\\9\end{pmatrix}
D: \begin{pmatrix}13\\-7\end{pmatrix}
Answer: A
Workings:
\begin{pmatrix}10\\-2\end{pmatrix}-\begin{pmatrix}4\\-2\end{pmatrix}=\begin{pmatrix}6\\0\end{pmatrix}
Marks = 1
Question 6
Three vectors are listed below with some numbers missing.
\textbf{a} = \begin{pmatrix}3\\2\end{pmatrix} \textbf{b} = \begin{pmatrix}x\\y\end{pmatrix} \textbf{c} = \begin{pmatrix}1\\z\end{pmatrix}
Use the following calculations.
\textbf{a} + \textbf{b} = \begin{pmatrix}3\\0\end{pmatrix}\\ 2\textbf{c} + \textbf{b} = \begin{pmatrix}2\\2\end{pmatrix}Find the value of x, y and z.
ANSWER: Multiple Answers (Type 1)
Answer: x = 0, y = -2, z = 2
Workings:
\begin{pmatrix}3\\2\end{pmatrix}+\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}3\\0\end{pmatrix}\\
x=0, y=-2
\begin{pmatrix}2\\2z\end{pmatrix}+\begin{pmatrix}0\\-2\end{pmatrix}=\begin{pmatrix}2\\2\end{pmatrix}
z=2
Marks = 2