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5.21F Vectors: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Write down the vector from point P to point Q. P has position vector (2, 3) and Q has position vector (5, 1).

(Total for Question 1 is 1 mark)

Calculate 3 times the vector (1, -2).

(Total for Question 2 is 1 mark)

A = (4, 0) and B = (-1, 3). Work out A + B.

(Total for Question 3 is 2 marks)

Vector u = (2, 5). Vector v = (6, -1). Work out 2u - v.

(Total for Question 4 is 2 marks)

In a square grid, point A has position vector (1, 2) and point B has position vector (4, 5).

a) Find the vector AB. (2 marks)

b) Give the position vector of the point C which is 1/3 of the way from A to B. Give your answer as a coordinate pair. (3 marks)

(a)Find the vector AB.(2)

(b)Give the position vector of point C which is 1/3 of the way from A to B.(3)

(Total for Question 5 is 5 marks)

Point X has position vector (0, 0). Point Y has position vector (0, 6). Point Z has position vector (8, 6).

Work out the vector ZX and state its components. (3 marks)

(Total for Question 6 is 3 marks)

On a diagram, P is at (2, 1) and Q is at (5, 4). The vector PQ is k times the vector (1, 1).

a) Find PQ. (2 marks)

b) Hence find k. (3 marks)

(a)Find PQ.(2)

(b)Hence find k where PQ = k(1, 1).(3)

(Total for Question 7 is 5 marks)

The vector a = (2, -1) and the vector b = ( -1, 2 ).

a) Find a + b. (2 marks)

b) Find 2a + 3b. (3 marks)

(a)Find a + b.(2)

(b)Find 2a + 3b.(3)

(Total for Question 8 is 5 marks)

Points A, B and C have position vectors a = (1, 0), b = (4, 0) and c = (7, 0).

a) Write down the vectors AB and BC. (2 marks)

b) Show that B is the midpoint of AC by using vectors. Give clear working. (3 marks)

c) Hence or otherwise, write AC as a multiple of AB. (4 marks)

(a)Write down AB and BC.(2)

(b)Show that B is the midpoint of AC using vectors.(3)

(c)Hence or otherwise, write AC as a multiple of AB.(4)

(Total for Question 9 is 9 marks)

On a diagram, O is the origin. Point M has position vector m = (3, 2). Point N has position vector n = ( -1, 4 ).

a) Find the vector MN. (2 marks)

b) Express MN in the form p m + q n, where p and q are scalars. Show full working. (5 marks)

(a)Find MN.(2)

(b)Express MN in the form p m + q n, where p and q are scalars. Show full working.(5)

(Total for Question 10 is 7 marks)

Mark scheme · 5.21F Vectors: Foundation Tier Practice

Question 1

B1 vector PQ = (3, -2) cao
Answer: (3, -2)

Question 2

B1 3(1, -2) = (3, -6) cao
Answer: (3, -6)

Question 3

M1 add components: (4 + -1, 0 + 3) or correct method shown
A1 (3, 3) cao
Answer: (3, 3)

Question 4

M1 calculate 2u = (4, 10) and subtract v or show component method
A1 ( -2, 11) cao
Answer: (-2, 11)

Question 5

(a) M1 subtract components: (4 - 1, 5 - 2) or equivalent
(a) A1 (3, 3) cao
(a) Answer: (3, 3)
(b) M1 use A + (1/3)AB or calculate fraction of difference
(b) M1 compute coordinates: (1 + 1, 2 + 1) shown or equivalent
(b) A1 (2, 3) cao
(b) Answer: (2, 3)

Question 6

M1 use ZX = X - Z or show correct subtraction of components
M1 compute components: (0 - 8, 0 - 6) or shown method
A1 (-8, -6) cao
Answer: (-8, -6)

Question 7

(a) M1 compute PQ = Q - P = (5 - 2, 4 - 1) or show subtraction
(a) A1 (3, 3) cao
(a) Answer: (3, 3)
(b) M1 equate components: (3,3) = (k, k) or show method
(b) M1 solve k = 3 from one component or show both give same
(b) A1 k = 3 cao
(b) Answer: 3

Question 8

(a) M1 add components: (2 + -1, -1 + 2)
(a) A1 (1, 1) cao
(a) Answer: (1, 1)
(b) M1 calculate 2a = (4, -2) and 3b = (-3, 6) or show component multiplication
(b) M1 add results to get (1, 4) or show addition
(b) A1 (1, 4) cao
(b) Answer: (1, 4)

Question 9

(a) M1 AB = b - a = (3, 0) or BC = c - b = (3, 0) shown
(a) A1 AB = (3, 0) and BC = (3, 0) cao
(a) Answer: AB = (3, 0), BC = (3, 0)
(b) M1 show AC = c - a = (6, 0) or equivalent
(b) M1 show that AB = 1/2 AC or that A + 1/2 AC = B
(b) A1 state B is midpoint cao
(b) Answer: AC = (6, 0), AB = (3, 0) = 1/2 AC so B is midpoint
(c) M1 relate AC and AB using components or scalar k with AC = k AB
(c) M1 substitute numbers to get (6,0) = k(3,0) or equivalent
(c) A1 k = 2 cao
(c) A1 AC = 2 AB cao
(c) Answer: AC = 2 AB

Question 10

(a) M1 compute MN = n - m or show subtraction
(a) A1 (-4, 2) cao
(a) Answer: (-4, 2)
(b) M1 set up equation p(3,2) + q(-1,4) = (-4,2) or equivalent
(b) M1 equate components and form linear system: 3p - q = -4 and 2p + 4q = 2
(b) M1 solve the system correctly, e.g. substitute q = 3p + 4 into the second equation
(b) A1 p = -1 cao
(b) A1 q = 1 cao
(b) Answer: MN = -m + n (p = -1, q = 1)

Vectors: Foundation Tier Practice - Worksheets, Questions and Revision