OCR Further Pure Core 2 2019 June — Question 4 5 marks

Exam BoardOCR
ModuleFurther Pure Core 2 (Further Pure Core 2)
Year2019
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors: Lines & Planes
TypeLine intersection with line
DifficultyStandard +0.3 This is a standard Further Maths line intersection problem requiring students to equate parametric forms and solve simultaneous equations. While it involves more algebraic manipulation than a typical A-level question, it's a routine textbook exercise for FM students with no novel insight required, placing it slightly above average difficulty.
Spec4.04h Shortest distances: between parallel lines and between skew lines
+ \lambda \left( \begin{array} { r } - 2
4
- 2 \end{array} \right)
& l _ { 2 } : \mathbf { r } = \left( \begin{array} { l } 4
3
1 \end{array} \right)
Question 4:
AnswerMarks Guidance
4(a) 1 0
A= 
k 1
1 02  2  2
A=  = = 
k 11 2k+1 9
1 0 2 1 02 2
� � � �== � �= � �
k 𝑘𝑘 = 4 1 s o A 1  2𝑘𝑘+ 1 9
AnswerMarks
4 1B1
M1
A1
AnswerMarks
[3]1.2
1.1
AnswerMarks
1.1Correct form of A seen
Correctly multiplying object
vector into their A to find image
AnswerMarks
and equating to given imagetheir A must have at least 1
unknown element
AnswerMarks
(b)detA = 1 – 0 = 1
The determinant is the area scale factor so a
AnswerMarks
determinant of 1 leaves the area unchangedB1
B1
AnswerMarks
[2]1.1
2.4Correctly finding determinant
Convincing explanation. Must
include both ideas.
Question 4:
4 | (a) | 1 0
A= 
k 1
1 02  2  2
A=  = = 
k 11 2k+1 9
1 0 2 1 02 2
� � � �== � �= � �
k 𝑘𝑘 = 4 1 s o A 1  2𝑘𝑘+ 1 9
4 1 | B1
M1
A1
[3] | 1.2
1.1
1.1 | Correct form of A seen
Correctly multiplying object
vector into their A to find image
and equating to given image | their A must have at least 1
unknown element
(b) | detA = 1 – 0 = 1
The determinant is the area scale factor so a
determinant of 1 leaves the area unchanged | B1
B1
[2] | 1.1
2.4 | Correctly finding determinant
Convincing explanation. Must
include both ideas.
+ \lambda \left( \begin{array} { r } 
- 2 \\
4 \\
- 2
\end{array} \right) \\
& l _ { 2 } : \mathbf { r } = \left( \begin{array} { l } 
4 \\
3 \\
1
\end{array} \right)

\hfill \mbox{\textit{OCR Further Pure Core 2 2019 Q4 [5]}}
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Q1 7 Q2 8 Q3 5 Q4 5 Q5 11 Q6 6 Q7 7 Q8 8 Q9 11 Q10 7