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Equations and Inequalities

Secondary 3 Additional Math practice

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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.

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What this topic covers

Worked examples

Example 1

Solve 2x2−5x+1=02x^2 - 5x + 1 = 0 using the quadratic formula. Give your answers correct to 2 decimal places.
Show the worked solution
  • Identify coefficients: a=2a = 2, b=−5b = -5, c=1c = 1
  • Quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
  • Substitute: x=−(−5)±(−5)2−4(2)(1)2(2)x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(2)(1)}}{2(2)}
  • Simplify discriminant: x=5±174x = \frac{5 \pm \sqrt{17}}{4}
  • Calculate: 17=4.1231\sqrt{17} = 4.1231 (to 4 d.p.)
  • x≈5±4.12314x \approx \frac{5 \pm 4.1231}{4}
  • x=0.22x = 0.22 or x=2.28x = 2.28 (to 2 d.p.)

Answer: "x1":"0.22","x2":"2.28"{"x1":"0.22","x2":"2.28"}

Example 2

For the equation −2x2−x−4=0-2x^2 - x - 4 = 0, find the discriminant and state the nature of the roots.
Show the worked solution
  • Given equation: −2x2−x−4=0-2x^2 - x - 4 = 0
  • Coefficients: a=−2a = -2, b=−1b = -1, c=−4c = -4
  • Discriminant Δ=b2−4ac\Delta = b^2 - 4ac
  • Δ=(−1)2−4(−2)(−4)\Delta = (-1)^2 - 4(-2)(-4)
  • Δ=1−32\Delta = 1 - 32
  • Δ=−31\Delta = -31
  • Since Δ<0\Delta < 0, the equation has no real roots.

Answer: "discriminant":"−31","nature":"norealroots"{"discriminant":"-31","nature":"no real roots"}

Example 3

Find the discriminant of (x−4)(x+3)=−1(x - 4)(x + 3) = -1.
Show the worked solution
  • (x−4)(x+3)=−1(x - 4)(x + 3) = -1
  • x2−x−12=−1expandx^2 - x - 12 = -1 \quad \scriptsize\textit{expand}
  • x2−x−11=0rearrangex^2 - x - 11 = 0 \quad \scriptsize\textit{rearrange}
  • Identify: a=1a = 1, b=−1b = -1, c=−11c = -11
  • Δ=b2−4ac\Delta = b^2 - 4ac
  • Δ=(−1)2−4(1)(−11)\Delta = (-1)^2 - 4(1)(-11)
  • Δ=1+44\Delta = 1 + 44
  • Δ=45\Delta = 45

Answer: 4545

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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