MathAmigo

Quadratic Equations and Graphs

Secondary 2 practice

Start free

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 9x2−36=09x^2 - 36 = 0. Find the positive value of xx.
Show the worked solution
  • 9x2−36=09x^2 - 36 = 0
  • 9(x2−4)=0take out the common factor 99(x^2 - 4) = 0 \quad \scriptsize\textit{take out the common factor 9}
  • 9(x−2)(x+2)=0difference of two squares9(x - 2)(x + 2) = 0 \quad \scriptsize\textit{difference of two squares}
  • x=2 or x=−2x = 2 \text{ or } x = -2
  • The positive value of x is 2.\text{The positive value of } x \text{ is } 2.

Answer: 22

Example 2

The graph of y=x2−7x−8y = x^2 - 7x - 8 crosses the xx-axis at two points. Find the larger xx-intercept.
Show the worked solution
  • Set y=0y = 0: x2−7x−8=0x^2 - 7x - 8 = 0
  • (x−(−1))(x−(8))=0(x - (-1))(x - (8)) = 0
  • (x+1)(x−8)=0(x + 1)(x - 8) = 0
  • x=−1x = -1 or x=8x = 8
  • The larger xx-intercept is x=8x = 8.

Answer: 88

Example 3

A triangle has base (x+4)(x + 4) cm and height (2x−2)(2x - 2) cm. The area is 1414 cm². Find the value of xx.
Show the worked solution
  • 12×(x+4)×(2x−2)=14area formula\frac{1}{2} \times (x + 4) \times (2x - 2) = 14 \quad \scriptsize\textit{area formula}
  • (x+4)(2x−2)=28multiply both sides by 2(x + 4)(2x - 2) = 28 \quad \scriptsize\textit{multiply both sides by 2}
  • 2x2+6x−8=28expand2x^2 + 6x - 8 = 28 \quad \scriptsize\textit{expand}
  • 2x2+6x−36=0rearrange2x^2 + 6x - 36 = 0 \quad \scriptsize\textit{rearrange}
  • (x−3)(2x+12)=0factorise(x - 3)(2x + 12) = 0 \quad \scriptsize\textit{factorise}
  • x=3x = 3 or x=−6x = -6 (rejected since base must be positive)
  • Therefore x=3x = 3.

Answer: 33

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.

Other Secondary 2 topics