IGCSE Maths Edexcel A 4MA1

interpret information presented in a range of linear and non-linear graphs

To include speed/time and distance/time graphs

understand and use conventions for rectangular Cartesian coordinates

plot points $(x, y)$ in any of the four quadrants or locate points with given coordinates

determine the coordinates of points identified by geometrical information

determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points

draw and interpret straight line conversion graphs

To include currency conversion graphs

find the gradient of a straight line

gradient = (increase in y) ÷ (increase in x)

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 $(0, 2)$*

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 $ax + by = c$*

**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)**

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

interpret and analyse transformations of functions and write the functions algebraically

find the gradients of non-linear graphs

By drawing a tangent

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: $~x^3 - 3x^2 + 2 = 0$*

calculate the gradient of a straight line given the coordinates of two points

Find the equation of the straight line through $(1, 7)$ and $(2, 9)$

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 $(3, 7)$