Graphs of Functions and Graphical Solution practice questions

Secondary 3 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise graphs of functions and graphical solution free

What this topic covers

Worked examples

Example 1

Given y=1x2−xy = \dfrac{1}{x^2} - x, find the value of yy when x=3x = 3.
Show the worked solution
  • $y = \dfrac{1}{x^2} - x$
  • Substitute $x = 3$:
  • $y = \dfrac{1}{3^2} - (3) \quad \scriptsize\textit{substitute}$
  • $y = \dfrac{1}{9} - 3$
  • $y = \frac{1}{9} - \dfrac{27}{9} \quad \scriptsize\textit{common denominator}$
  • $y = \dfrac{1 - 27}{9}$
  • $y = -\frac{26}{9}$

Answer: −26/9-26/9

Example 2

An object travels at a constant speed of 2020 m/s for 88 seconds. Find the distance travelled, in metres.
Show the worked solution
  • Distance $=$ area under the speed-time graph
  • The graph is a rectangle with width $8$ s and height $20$ m/s.
  • $\text{Distance} = 20 \times 8$
  • $= 160$ m

Answer: 160160

Example 3

A car travels 6060 km at 3030 km/h, rests, then travels 9090 km at 3030 km/h. The average speed for the whole journey is 2525 km/h and the total time is 66 hours. Find the duration of the rest.
Show the worked solution
  • $\text{Total distance} = 60 + 90 = 150$ km
  • $\text{Time travelling first leg} = \frac{60}{30} = 2$ h
  • $\text{Time travelling second leg} = \frac{90}{30} = 3$ h
  • $\text{Total travelling time} = 2 + 3 = 5$ h
  • $\text{Rest duration} = \text{total time} - \text{travelling time}$
  • $= 6 - 5$
  • $= 1$ h

Answer: 11

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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