OCR Further Additional Pure AS Specimen — Question 2 5 marks

Exam BoardOCR
ModuleFurther Additional Pure AS (Further Additional Pure AS)
SessionSpecimen
Marks5
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Mark schemeDownload PDF ↗
TopicVector Product and Surfaces
TypeArea of parallelogram using vector product
DifficultyStandard +0.3 This is a straightforward application of the vector product formula for area. Students need to find two adjacent side vectors (AB and AD), compute their cross product, and find its magnitude. While it involves Further Maths content (vector product), the question is computationally routine with no conceptual challenges beyond direct formula application.
Spec1.10c Magnitude and direction: of vectors4.04g Vector product: a x b perpendicular vector
2 The points \(A ( 1,2,2 ) , B ( 8,2,5 ) , C ( - 3,6,5 )\) and \(D ( - 10,6,2 )\) are the vertices of parallelogram \(A B C D\). Determine the area of \(A B C D\).
Question 2:
AnswerMarks
2Area(cid:32) (b(cid:16)a)(cid:117)(c(cid:16)a)
(cid:167)7(cid:183) (cid:167)(cid:16)4(cid:183)
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:32) 0 (cid:117) 4
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
3 3
(cid:169) (cid:185) (cid:169) (cid:185)
(cid:167)(cid:16)12(cid:183)
(cid:168) (cid:184)
(cid:32) (cid:16)33
(cid:168) (cid:184)
(cid:168) (cid:184)
28
(cid:169) (cid:185)
AnswerMarks
(cid:32) 2017 (cid:11)(cid:32)44.9...(cid:12)M1
A1
M1
A1FT
B1FT
AnswerMarks
[5]1.2
1.1
1.1a
1.1
AnswerMarks
1.1Use of formula with attempted
substitution
Two correct vectors
Attempt at vector product soi
For vector product FT their vectors
AnswerMarks
FT their vector productBC
OR using formula
M1A1FT for
(cid:167)a b (cid:16)a b (cid:183) (cid:167)(cid:16)12(cid:183)
2 3 3 2
(cid:168) (cid:184) (cid:168) (cid:184)
a b (cid:16)ba (cid:32) (cid:16)33
(cid:168) 3 1 1 3 (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:169)a 1 b 2 (cid:16)a 2 b 1(cid:185) (cid:169) 28(cid:185)
Question 2:
2 | Area(cid:32) (b(cid:16)a)(cid:117)(c(cid:16)a)
(cid:167)7(cid:183) (cid:167)(cid:16)4(cid:183)
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:32) 0 (cid:117) 4
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
3 3
(cid:169) (cid:185) (cid:169) (cid:185)
(cid:167)(cid:16)12(cid:183)
(cid:168) (cid:184)
(cid:32) (cid:16)33
(cid:168) (cid:184)
(cid:168) (cid:184)
28
(cid:169) (cid:185)
(cid:32) 2017 (cid:11)(cid:32)44.9...(cid:12) | M1
A1
M1
A1FT
B1FT
[5] | 1.2
1.1
1.1a
1.1
1.1 | Use of formula with attempted
substitution
Two correct vectors
Attempt at vector product soi
For vector product FT their vectors
FT their vector product | BC
OR using formula
M1A1FT for
(cid:167)a b (cid:16)a b (cid:183) (cid:167)(cid:16)12(cid:183)
2 3 3 2
(cid:168) (cid:184) (cid:168) (cid:184)
a b (cid:16)ba (cid:32) (cid:16)33
(cid:168) 3 1 1 3 (cid:184) (cid:168) (cid:184)
(cid:168) (cid:184) (cid:168) (cid:184)
(cid:169)a 1 b 2 (cid:16)a 2 b 1(cid:185) (cid:169) 28(cid:185)
2 The points $A ( 1,2,2 ) , B ( 8,2,5 ) , C ( - 3,6,5 )$ and $D ( - 10,6,2 )$ are the vertices of parallelogram $A B C D$.

Determine the area of $A B C D$.

\hfill \mbox{\textit{OCR Further Additional Pure AS  Q2 [5]}}
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