#3.3A
interpret information presented in a range of linear and non-linear graphs
To include speed/time and distance/time graphs
#3.3B
understand and use conventions for rectangular Cartesian coordinates
#3.3C
plot points \((x, y)\) in any of the four quadrants or locate points with given coordinates
#3.3D
determine the coordinates of points identified by geometrical information
#3.3E
determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points
#3.3F
draw and interpret straight line conversion graphs
To include currency conversion graphs
#3.3G
find the gradient of a straight line
gradient = (increase in y) ÷ (increase in x)
#3.3H
recognise that equations of the form \(y = mx + c\) are straight line graphs with gradient \(m\) and intercept on the \(y\)-axis at the point \((0, c)\)
Write down the gradient and coordinates of the \(y\)-intercept of \(y = 3x + 5\);
Write down the equation of the straight line with gradient 6 that passes through the point \((0, 2)\)
#3.3I
recognise, generate points and plot graphs of linear and quadratic functions
To include \(x = k\), \(y = c\), \(y = x\), \(y − x = 0\)
Including completion of values in tables and equations of the form \(ax + by = c\)
#3.3J
recognise, plot and draw graphs with equation:
\(y = Ax^3 + Bx^2 + Cx + D \) in which:
(i) the constants are integers and some could be zero
(ii) the letters x and y can be replaced with any other two letters
\(y = x^3\)
\(y = 3x^3 - 2x^2 + 5x - 4\)
\(y = 2x^3 - 6x + 2\)
\(V = 60w(60-w)\)
or: \(y = Ax^3 + Bx^2 + Cx + D + \dfrac{E}{x} + \dfrac{F}{x^2} \) in which:
(i) the constants are numerical and at least three of them are zero
(ii) the letters x and y can be replaced with any other two letters
\(y = \dfrac{1}{x}, x \neq 0\)
\(y = 2x^2 + 3x + \dfrac{1}{x}, x \neq 0 \)
\(y = \dfrac{1}{x}(3x^2 - 5), x \neq 0\)
\(w = \dfrac{5}{d^2}, d \neq 0\)
or: \(y = \sin{x}\), \(y = \cos{x}\), \(y = \tan{x}\) for angles of any size (in degrees)
#3.3K
apply to the graph of \(y = f(x)\) the transformations \(y = f(x) +a\), \(y = f(ax)\), \(y = f(x + a)\), \(y = af(x)\) for linear, quadratic, sine and cosine functions
#3.3L
interpret and analyse transformations of functions and write the functions algebraically
#3.3M
find the gradients of non-linear graphs
By drawing a tangent
#3.3N
find the intersection points of two graphs, one linear (\(y_1\)) and one non-linear (\(y_2\)), and and recognise that the solutions correspond to the solutions of (\(y_2 - y_1 = 0\))
The \(x\) values of the intersection of the two graphs: \(y = 2x + 1\) and \(y = x^2 + 3x - 2\) are the solutions of: \(~x^2 + x - 3 = 0\)
Similarly, the \(x\) values of the intersection of the two graphs: \(y = 5\) and \(y = x^3 – 3x^2 + 7\) are the solutions of: \(~x^3 - 3x^2 + 2 = 0\)
#3.3O
calculate the gradient of a straight line given the coordinates of two points
Find the equation of the straight line through \((1, 7)\) and \((2, 9)\)
#3.3P
find the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given line
Find the equation of the line perpendicular to \(~y = 2x + 5\) through the point \((3, 7)\)