Key Concepts: A function is a relationship where each input has exactly one output. Functions can be represented as equations, tables, or graphs. Transformations of graphs involve translations, reflections, and stretches. The gradient of a line shows its steepness.
Section A: Functions and Notation
1. For the function f(x) = 3x - 5: [3]
(a) Find f(2)
(b) Find f(-1)
(c) Find f(x) = 10
2. Given g(x) = x² + 4x - 3: [2]
(a) Find g(3)
(b) Find g(0)
Section B: Graphs and Gradients
3. For the line 2x + 3y = 12: [3]
(a) Find the gradient
(b) Find the y-intercept
(c) State the x-intercept
4. A line passes through points (2, 5) and (6, 17). [3]
(a) Find the gradient
(b) Find the equation of the line
Section C: Quadratic Functions
5. For the quadratic function y = x² - 6x + 5: [4]
(a) Find the roots
(b) Find the coordinates of the vertex
(c) State the y-intercept
6. Sketch the graph of y = -(x - 3)² + 4, labeling key features. [3]
Total marks: 21
Mark Scheme
1. (a) f(2) = 3(2) - 5 = 1 [1]
(b) f(-1) = 3(-1) - 5 = -8 [1]
(c) 3x - 5 = 10, so x = 5 [1]
2. (a) g(3) = 9 + 12 - 3 = 18 [1]
(b) g(0) = 0 + 0 - 3 = -3 [1]
3. (a) Rearrange to y = -⅔x + 4, gradient = -⅔ [1]
(b) y-intercept = 4 [1]
(c) x-intercept = 6 [1]
4. (a) Gradient = (17-5)/(6-2) = 12/4 = 3 [1]
(b) y - 5 = 3(x - 2), so y = 3x - 1 [2]
5. (a) (x - 1)(x - 5) = 0, roots are 1 and 5 [2]
(b) Vertex at x = 3, y = 9 - 18 + 5 = -4; vertex is (3, -4) [1]
(c) y-intercept = 5 [1]
6. Vertex at (3, 4) [1]
Opens downward [1]
y-intercept at (0, -5), roots at (3±2, 0) = (1, 0) and (5, 0) [1]