Equations and Inequalities practice questions

Secondary 3 topics from the Additional Mathematics 4049 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 equations and inequalities free

What this topic covers

Worked examples

Example 1

Solve x2−x−3=0x^2 - x - 3 = 0 using the quadratic formula. Give your answers correct to 2 decimal places.
Show the worked solution
  • Identify coefficients: $a = 1$, $b = -1$, $c = -3$
  • Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
  • Substitute: $x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-3)}}{2(1)}$
  • Simplify discriminant: $x = \frac{1 \pm \sqrt{13}}{2}$
  • Calculate: $x = \frac{1 \pm 3.6056}{2}$
  • $x = -1.30$
  • or $x = 2.30$

Answer: "x1":"−1.30","x2":"2.30"{"x1":"-1.30","x2":"2.30"}

Example 2

For the equation 5x2−10x+5=05x^2 - 10x + 5 = 0, find the discriminant and state the nature of the roots.
Show the worked solution
  • Given equation: $5x^2 - 10x + 5 = 0$
  • Coefficients: $a = 5$, $b = -10$, $c = 5$
  • Discriminant $\Delta = b^2 - 4ac$
  • $\Delta = (-10)^2 - 4(5)(5)$
  • $\Delta = 100 - 100$
  • $\Delta = 0$
  • Since $\Delta = 0$, the equation has two equal real roots.

Answer: "discriminant":"0","nature":"twoequalrealroots"{"discriminant":"0","nature":"two equal real roots"}

Example 3

Find the discriminant of 3x2=−x+13x^2 = -x + 1.
Show the worked solution
  • $3x^2 = -x + 1 \quad \scriptsize\textit{rearrange}$
  • $3x^2 + x - 1 = 0$
  • Identify: $a = 3$, $b = 1$, $c = -1$
  • $\Delta = b^2 - 4ac$
  • $\Delta = (1)^2 - 4(3)(-1)$
  • $\Delta = 1 + 12$
  • $\Delta = 13$
  • Since $\Delta > 0$, the equation has two real and distinct roots.

Answer: 1313

Questions parents ask

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Which syllabus does this follow?

Additional Mathematics (4049), 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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