← Maths syllabus

SingaporeMaths

Functions and Graphs

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What do the gradient and the area under a travel graph tell us about motion?

Interpret distance-time and speed-time graphs, using the gradient and the area under the graph to find speed, acceleration and distance
A focused answer to the O-Level E-Maths outcome on travel graphs. Reading speed from the gradient of a distance-time graph, acceleration from a speed-time graph, and distance from the area under a speed-time graph.
8 min answer →

How do we use graphs to solve equations, and how do we read solutions off a curve?

Solve equations graphically by finding intersection points, and estimate solutions and gradients from a drawn curve
A focused answer to the O-Level E-Maths outcome on solving equations from graphs. Reading roots from where a curve crosses the axis, solving by intersection of two graphs, and estimating the gradient of a curve from a tangent.
8 min answer →

How do we recognise and sketch the standard non-linear graphs in the syllabus?

Recognise and sketch graphs of cubic, reciprocal and exponential functions, and describe their main features
A focused answer to the O-Level E-Maths outcome on standard graph shapes. Cubic, reciprocal and exponential curves, their asymptotes and symmetry, and recognising a function from its graph.
8 min answer →

What does the equation of a straight line tell us, and how do we find it?

Interpret and use the equation y = mx + c, find the gradient and intercept, and determine the equation of a straight line
A focused answer to the O-Level E-Maths outcome on straight-line graphs. The form y = mx + c, finding gradient and intercept, determining a line's equation from points or a graph, and parallel lines.
8 min answer →

What does the graph of a quadratic function look like, and how do we find its key features?

Sketch the graph of a quadratic function, find the intercepts and the turning point, and use the line of symmetry
A focused answer to the O-Level E-Maths outcome on quadratic graphs. The parabola shape, finding x- and y-intercepts, the turning point and line of symmetry, and the effect of the sign of the leading coefficient.
9 min answer →