Paper 3 (Non-Calculator) Vectors

1 Examiner s use only Team Leader s use onlySurname Initial(s)Signature Centre over Candidate No. Paper Reference(s)1380/3 HEdexcel GCSEM athematics (Linear) 1380 Paper 3 (Non-Calculator)VectorsPast Paper QuestionsArranged by TopicMaterials required for examination Items included with question papersRuler graduated in centimetres and Nilmillimetres, protractor, compasses,pen, HB pencil, Paper may be to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initials and signature. Check that you have the correct question ALL the questions. Write your answers in the spaces provided in this question must NOT write on the formulae page. Anything you write on the formulae page will gain NO credit. If you need more space to complete your answer to any question, use additional answer for CandidatesThe marks for individual questions and the parts of questions are shown in round brackets: (2).

2 There are 26 questions in this question Paper . The total mark for this Paper is are 24 pages in this question Paper . Any blank pages are must not be to CandidatesShow all stages in any steadily through the Paper . Do not spend too long on one you cannot answer a question, leave it and attempt the next at the end to those you have left more free papers at: by Peter Bland*N34730A0124* Paper Reference13803 HLeave blank1. OPT is a triangle. M is the midpoint of OP. OT = a TP = b (a) Express OM in terms of a and b. OM = .. (2) (b) Express TM in terms of a and b. Give your answer in its simplest form. TM = .. (2)Q1(Total 4 marks)Diagram NOTaccurately drawnMPOTabLots more free past papers at blank2. OAB is a triangle. OA = a OB = b (a) Find the vector AB in terms of a and =.

3 (1) P is the point on AB such that AP : PB = 3 : 2 (b) Show that OP=15(2a + 3b)(3)Q2(Total 4 marks)AaODiagram NOTaccurately drawn PBbLots more free past papers at blank3. OAB is a triangle. OA = a, OB = b (a) Find the vector AB in terms of a and = ..(1) P is the point on AB so that AP : PB = 2 : 1 (b) Find the vector OP in terms of a and b. Give your answer in its simplest = ..(3)Q3(Total 4 marks)ADiagram NOTaccurately drawn aP O BbLots more free past papers at blank4. OABC is a parallelogram. M is the midpoint of CB. N is the midpoint of AB. (a) Find, in terms of a and/or c, the Vectors (i).

4 (ii) ..(2) (b) Show that CA is parallel to MN.(2)Q4(Total 4 marks)Diagram NOT accurately drawnOBNCcaMAOAOC==acMB, more free past papers at blank5. = 2a + bOX = 4a + 3bOY (a) Express the vectorX Y in terms of a and b Give your answer in its simplest form..(2)Y4a+ 3bO2a+bXDiagram NOTaccurately drawnLots more free past papers at blank XYZ is a straight line. XY : YZ = 2 : 3 (b) Express the vectorOZ in terms of a and b Give your answer in its simplest form..(3)Q5(Total 5 marks)ZY4a+ 3bO2a+bXDiagram NOTaccurately drawnLots more free past papers at blank6. Diagram NOT accurately drawn ABCD is a parallelogram.

5 AB is parallel to DC. AD is parallel to BC. AB = p AD = q (a) Express, in terms of p and q (i) AC (i) .. (ii) BD (ii) ..(2) Diagram NOT accurately drawn AC and BD are diagonals of parallelogram ABCD. AC and BD intersect at T. (b) Express AT in terms of p and q..(1)(Total 3 marks)A p B q D C A p B q T D C Q6 Lots more free past papers at blank7.

6 OPT is a triangle. M is the midpoint of OP. OT = a TP = b (a) Express OM in terms of a and b. OM = .. (2) (b) Express TM in terms of a and b. Give your answer in its simplest form. TM = .. (2)Q7(Total 4 marks)Diagram NOTaccurately drawnMPOTabLots more free past papers at OAB is a 2aOB= 3b (a) Find AB in terms of a and ..(1) P is the point on AB such that AP : PB= 2 : 3 (b) Show that OP is parallel to the vector a+b.(3)Q8(Total 4 marks)DiagramNOTaccurately drawnLots more free past papers at