Vector geometric proofs: GCSE and IGCSE Maths Practice
Vectors
Vector geometric proofs
19 self-marking GCSE and IGCSE practice questions on Vector geometric proofs, written specifically for AQA, Pearson, OCR, Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Instant marking with full worked solutions on every question.
A few of the 19 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 13 marksGrade 7-8
OABC is a parallelogram, where OA=a and OC=c
What are the common mistakes in Vector geometric proofs?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Finds the required length but does not go on to compare it to AB
Correctly found CD but never compared it to AB to identify the scalar factor and state the ratio
Finds OM and ON but does not go on to compare them
Correctly found both OM and ON but never compared them to check whether M and N are actually the same point
Applies the given fraction to the wrong vector in a vector-geometry problem
Applied the 1/3 scale factor to OA instead of to AB, mixing up which vector the ratio AX:AB refers to
Quick answers about Vector geometric proofs
How many Vector geometric proofs practice questions are there?
There are 19 self-marking GCSE and IGCSE Maths questions on Vector geometric proofs, written for AQA, Pearson, OCR, Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Higher and Extended tier. Each one is marked instantly and has a full worked solution.
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No. You can start practising Vector geometric proofs straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
.
X
is the point on
AB
such that
AX=31AB
.
Find
OX
in terms of
a
and
c
, giving your answer in its simplest form.
Show the worked solution
Since OABC is a parallelogram, AB is equal and parallel to OC, so AB=c. M1
AX=31AB=31c
OX=OA+AX=a+31c
Question 24 marksGrade 7-8
OABC is a kite, where OA=a and OC=c, and B is the point such that OB=2a+2c. M is the midpoint of OB and N is the midpoint of AC.
Prove that M and N are not the same point, and find the relationship between OM and ON.
Show the worked solution
OM=21OB=21(2a+2c)=a+c
Question 34 marksGrade 8-9
O, A and B are points such that OA=a and OB=b. C is the point such that OC=3a, and D is the point such that OD=3b. M is the midpoint of AB and N is the midpoint of CD.
Prove that O, M and N are collinear.
Question 44 marksGrade 8-9
OABC is a trapezium with OA parallel to CB, where OA=a, OC=c, and CB=2a. M is the midpoint of OC and N is the midpoint of AB.
Prove that MN is parallel to OA.
Question 55 marksGrade 8-9
OABC is a quadrilateral, where OA=a, OB=b, and BC=ka, where k is a positive integer.
M is the point on OA such that OM:MA=1:1.
N is the point on BC such that BN:NC=1:1.
(a) Express MN in terms of k, a and b.
(b) Find the value of k for which MN is parallel to OB.
Question 65 marksGrade 9
OAN, OMB and APB are straight lines. AN = 2OA. M is the midpoint of OB.
OA = a, OB = b. AP = k·AB, where k is a scalar quantity.
Given that MPN is a straight line, find the value of k.
AC=OC−OA=c−a, so ON=OA+21AC=a+21(c−a)=21a+21c. M2
Comparing, OM=a+c=2(21a+21c)=2ON. A1
Since OM=ON (in fact OM is twice ON, so M is further from O than N is), M and N are not the same point - this kite's diagonal OB does not bisect the other diagonal AC at its midpoint. B1