Key Concepts: Vectors represent magnitude and direction. Column vectors show horizontal and vertical components. Transformations include translations, reflections, rotations, and enlargements.
Section A: Vector Operations
1. Given vectors a = (3, 2) and b = (1, 4): [3]
(a) Find a + b
(b) Find 2a
(c) Find a - b
2. Calculate the magnitude of vector v = (5, 12) [2]
Section B: Transformations
3. Describe the transformation that maps: [3]
(a) Point (2, 3) to (5, 3)
(b) Point (4, 1) to (-4, 1)
(c) Point (3, 2) to (6, 4)
4. Triangle ABC has vertices A(1, 1), B(3, 1), C(2, 3). [4]
(a) Reflect in the y-axis. Give new coordinates
(b) Rotate 90° clockwise about origin. Give new coordinates
Total marks: 20
Mark Scheme
1. (a) (4, 6) [1]
(b) (6, 4) [1]
(c) (2, -2) [1]
2. |v| = √(5² + 12²) = √(25 + 144) = √169 = 13 [2]
3. (a) Translation by vector (3, 0) [1]
(b) Reflection in y-axis [1]
(c) Enlargement scale factor 2, center origin [1]
4. (a) A'(-1, 1), B'(-3, 1), C'(-2, 3) [2]
(b) A'(1, -1), B'(1, -3), C'(3, -2) [2]