Mathematics for IGCSE & O level - Vectors (Section 5)

• 1

  Given vector v = [x, y], which statement is correct?

  回答

  A

  C

  D
• 2

  A vector's direction is best described by:

  回答

  (C)

  An angle or orientation
• 3

  In the context of vector geometry, what does the term 'parallel' mean regarding two vectors?

  回答

  (C)

  The vectors lie in the same plane and never intersect.
• 4

  If a translation moves a point from (1, 2) to (4, 6), what is the translation vector?

  回答

  (A)

  [3, 4]
• 5

  The magnitude of the vector [3, 4] is:

  回答

  (B)

  5
• 6

  In the context of vectors, which of the following are correct?

  回答

  A

  C

  D
• 7

  Which of the following is true about finding the magnitude of a vector?

  回答

  (D)

  The magnitude is found by squaring both components and then taking the square root of their sum
• 8

  When a vector is multiplied by a scalar, what aspect(s) of the vector change(s)?

  回答

  A

  B
• 9

  Which of the following are true concerning vectors?

  回答

  A

  B

  C
• 10

  If vector a = [2,3], and vector b = [4,1], what is the vector 3a + 2b?

  回答

  (A)

  [14,11]
• 11

  If A is the point (3, -1) and B is the point (0, 2), what is the magnitude of vector AB?

  回答

  (B)

  √13
• 12

  If a translation is described by the vector [-2, 1], what operation is performed on the x and y coordinates?

  回答

  (A)

  Subtract 2 from x, add 1 to y.
• 13

  Which operation changes only the magnitude of a vector and not its direction?

  回答

  (B)

  Scalar multiplication with a positive scalar
• 14

  Given vector a = [3, -1] and vector b = [-2, 2], then -a + b is:

  回答

  (B)

  [-1, 1]
• 15

  In a parallelogram ABCD, if AB = a and AD = b, then AC equals:

  回答

  (C)

  a + b
• 16

  Which of the following is equivalent to the vector -v?

  回答

  (A)

  v multiplied by -1
• 17

  How is the vector AB defined in terms of position vectors?

  回答

  (B)

  OB - OA
• 18

  What type of transformation is described by the vector [0, 4]?

  回答

  (C)

  A translation 4 units up
• 19

  If vector a = [2, 0] and b = [0, 3], then 2a + b is:

  回答

  (A)

  [4, 3]
• 20

  Which of the following are characteristics of a vector?

  回答

  A

  B
• 21

  If AB = CD and CD = EF, what is the relationship between AB and EF?

  回答

  (A)

  AB = EF
• 22

  Given vector u = [2, -1], and vector v = [-1, 3], what is the result of u + v?

  回答

  (A)

  [1, 2]
• 23

  Given the vectors a = [1, 0] and b = [0, 1], what is the magnitude of a + b?

  回答

  (C)

  √2
• 24

  What is the result when you add the vectors [2, 3] and [-1, 1]?

  回答

  (B)

  [1, 4]
• 25

  If a is a vector and k is a scalar, what is the effect of multiplying the vector a by the scalar k?

  回答

  A

  B
• 26

  What does a position vector in the context of vectors describe?

  回答

  (B)

  The position of a point relative to the origin
• 27

  Which geometric transformation is represented by a vector?

  回答

  (D)

  Translation
• 28

  Which is the result of a - a, where a is a vector?

  回答

  (A)

  The zero vector
• 29

  If point A is at (1, 2) and it is translated by the vector [2, 3], what are the new coordinates of A?

  回答

  (A)

  (3, 5)
• 30

  If AB = [2, 5] and AC = [1, 1], then BC is equal to:

  回答

  (B)

  [-1, -4]
• 31

  Given vector a = [3, -2], which of the following vectors is equal to -2a?

  回答

  (B)

  [-6, 4]
• 32

  The top number in a column vector tells you how the shape moves ______, or in the y-direction.

  回答

  (A)

  Left or right
• 33

  What geometric shape can represent the vector sum of three vectors, where the endpoint of one vector is the start point of the next?

  回答

  (B)

  A triangle
• 34

  In the column vector, [3, -1], the shape moves ______, and ______.

  回答

  (B)

  3 units right, 1 unit down
• 35

  Which of the following statements correctly defines a unit vector?

  回答

  (B)

  A vector with a magnitude of 1 and a defined direction.
• 36

  If you translate a point with coordinates (x, y) using the vector [a, b], what are the new coordinates of the point?

  回答

  (A)

  (x + a, y + b)
• 37

  If vector AB = [6, 8], what is the magnitude of the vector -AB?

  回答

  (A)

  10
• 38

  Which of the following represents the zero vector?

  回答

  (C)

  [0, 0]
• 39

  If a vector 'v' is [2, 3], which is the result of -1/2 v?

  回答

  (C)

  [-1, 1.5]
• 40

  Given points A(1, 2) and B(4, 6), what is the vector from A to B in component form?

  回答

  (C)

  [3, 4]
• 41

  Which statement is true about vectors?

  回答

  A

  B
• 42

  What geometric figure does the addition of two vectors, represented by the sides, define?

  回答

  (B)

  A triangle
• 43

  In column vector notation, which component indicates the horizontal direction and magnitude of movement?

  回答

  (A)

  The top number
• 44

  When adding two column vectors, you _______ the corresponding components.

  回答

  (C)

  add
• 45

  Given vector a = [5, 12], what is its magnitude?

  回答

  (B)

  13
• 46

  What is a zero vector?

  回答

  (C)

  A vector with a magnitude of 0 and no direction.
• 47

  If vector a = [4, 3], then what is the unit vector of a?

  回答

  (B)

  [4/5, 3/5]
• 48

  Which of the following statements are true regarding vector geometry?

  回答

  A

  C

  D
• 49

  If vector a = [5, -1] and vector b = [-2, 3], which of these represents the resultant vector of a + b?

  回答

  (B)

  [7, -4]