Quadratic Equations and Graphs practice questions

Secondary 2 topics, working towards 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 quadratic equations and graphs free

What this topic covers

Worked examples

Example 1

Solve 2x2−6x−8=02x^2 - 6x - 8 = 0. Find the larger value of xx.
Show the worked solution
  • $2x^2 - 6x - 8 = 0$
  • $(2x - 8)(x + 1) = 0 \quad \scriptsize\textit{factorise}$
  • $x = 4 \text{ or } x = -1$
  • $\text{The larger value of } x \text{ is } 4.$

Answer: 44

Example 2

Find the maximum value of y=−x2+6xy = -x^2 + 6x.
Show the worked solution
  • Line of symmetry: $x = -\dfrac{b}{2a}$
  • $x = -\dfrac{6}{2(-1)}$
  • $x = 3$
  • Substitute $x = 3$ to find the maximum value:
  • $y = -(3)^2 + 6(3) + 0$
  • $y = 9$

Answer: 99

Example 3

A rectangular garden measuring 1414 m by 77 m is surrounded by a path of uniform width. The area of the path is 100100 m². Find the width of the path.
Show the worked solution
  • Let the width of the path be $x$ m. $\quad \scriptsize\textit{define variable}$
  • The total area including the path is $(14 + 2x)(7 + 2x)$ m².
  • Area of path $=$ total area $-$ garden area:
  • $(14 + 2x)(7 + 2x) - 98 = 100$
  • $98 + 14x + 28x + 4x^2 - 98 = 100 \quad \scriptsize\textit{expand}$
  • $4x^2 + 42x = 100$
  • $4x^2 + 42x - 100 = 0 \quad \scriptsize\textit{rearrange}$
  • $(x - 2)(4x + 50) = 0 \quad \scriptsize\textit{factorise}$

Answer: 22

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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