14.1- Introduction
Demonstrate familiarity with Cartesian coordinates in two dimensions14.2- Equation of a straight line
• find the gradient of a straight line
• calculate the gradient of a straight line from the coordinates of two
points on it
• calculate the length and the coordinates of the midpoint of a
line segment from the coordinates of its end points
• interpret and obtain the equation of a straight line graph in the form
y = mx + c
• determine the equation of a straight line parallel to a given line
• find the gradient of parallel and perpendicular lines
Question 1 : Find the equation of a line parallel to y = 4x – 1 that passes through (0, –3) ?
Question 2 : find the gradient of a line perpendicular to y = 3x + 1 ?
Question 3 : Find the equation of a line perpendicular to one passing through the coordinates (1, 3) and (–2, –9) ?
Question : A (0, 2) and B (6, 5) are points on the straight line ABCD.
AB = BC = CD ; calculate the coordinates of D ?
14.3- Linear and Quadratic Functions
Identify and interpret gradients and intercepts of linear functions graphically and algebraically
Question 1 : A curve has equation y = 4x^{2}+ 5x + 3
and a line has equation y = x + 2. Show algebraically that they intersect at only one point ?
14.4- Properties of quadratic functions
Identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically
Recognise, sketch and interpret graphs of linear functions, quadratic
functions, simple cubic functions, the reciprocal function y=1/x with x ≠ 0
14.5- Kinematic Graphs
Plot and interpret graphs (including reciprocal graphs) and graphs of
non-standard functions in real contexts to find approximate solutions to
problems such as simple kinematic problems involving distance, speed and acceleration
14.6- Summary and Review
Question 1 : f(x) = 5 – x and g(x) = 3x + 7 .
Calculate f(2x) + g(x – 1) and Solve g^{-1} (x) = 2x ?
14.7- Assessment 14
Question 1 : Elisabeth goes on a car journey. For the first 30 minutes her average speed is 40 miles per hour. She then stops for 15 minutes. She then completes the journey at an average speed of 60 miles per hour. The total journey time is 1 hour. What is her overall average speed?
Question 2 : A is (2, 12) and B is (8, 2). What is the midpoint AB?
Question 3 : Is the point (–5, –6) above, below or on the line y = 3x + 7 ?
Question 4 : Show that the lines y = 3x + 7 and 2y – 6x = 8 are parallel ?