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ZIMSEC O-Level Equations and inequalities — practice questions

Explore 6 free Equations and inequalities questions in ZIMSEC O-Level Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Equations and inequalities questions and exercises with answers

Showing questions 1–6 of 6.

How many solutions can a quadratic equation have at most?Read the answer and worked solution →Before a quadratic equation is solved by factorisation, what must one side equal?Read the answer and worked solution →Both sides of an inequality are divided by a negative number. What happens to the sign?Read the answer and worked solution →The value under the square root sign in the quadratic formula works out negative. What are the roots?Read the answer and worked solution →A repeated expression appears twice in a quadratic equation. What is the useful move?Read the answer and worked solution →Solve the equation x squared plus 2x minus 15 equals 0.Read the answer and worked solution →

Worked practice questions

How many solutions can a quadratic equation have at most?

  1. One
  2. Four
  3. Two
  4. Five
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Correct answer: C. Two

1. A quadratic equation is an equation of the second degree. 2. A quadratic equation has at most two solutions, which are also called roots. 3. Some quadratic equations have only one solution and some have no real solution at all. 4. No quadratic equation can ever have more than two solutions. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 2: Equations and inequalities_

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Before a quadratic equation is solved by factorisation, what must one side equal?

  1. It must equal one
  2. It must equal zero
  3. It must equal two
  4. It must equal ten
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Correct answer: B. It must equal zero

1. Factorisation starts from the standard form of a quadratic equation. 2. One side of the equation must be equal to zero. 3. Only then can the rule be used that a product of two factors is zero when one factor is zero. 4. If the right hand side is any other number, that rule gives nothing at all. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 2: Equations and inequalities_

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Both sides of an inequality are divided by a negative number. What happens to the sign?

  1. It stays the same
  2. It becomes an equals
  3. It changes direction
  4. It becomes undefined
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Correct answer: C. It changes direction

1. An inequality states which of two expressions is the larger one. 2. If an inequality is multiplied or divided by a negative number, the inequality sign changes direction. 3. So a less than sign becomes a greater than sign, and the reverse also holds. 4. Leaving the sign unchanged is the most common error in this step. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 2: Equations and inequalities_

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