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ZIMSEC O-Level Exponents and surds — practice questions

Explore 9 free Exponents and surds questions in ZIMSEC O-Level Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Exponents and surds questions and exercises with answers

Showing questions 1–9 of 9.

What is a radical called when it works out to an irrational number?Read the answer and worked solution →Which name is also used for an exponent?Read the answer and worked solution →An even root is being taken. What must be true of the radicand for the root to be real?Read the answer and worked solution →What happens to a fraction when its denominator is rationalised?Read the answer and worked solution →Written in simplest surd form, the square root of 50 becomes which expression?Read the answer and worked solution →Which strategy is used first when an exponential expression is manipulated?Read the answer and worked solution →Solve for x if 3 raised to the power x equals 81.Read the answer and worked solution →Rationalising the denominator of 6 divided by the square root of 3 gives which expression?Read the answer and worked solution →Catch every real number typeRead the answer and worked solution →

Worked practice questions

What is a radical called when it works out to an irrational number?

  1. A surd
  2. A ratio
  3. A power
  4. A digit
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Correct answer: A. A surd

1. A radical is a number written under a root sign. 2. A surd is a radical which results in an irrational number. 3. The square root of 9 is not a surd, because it works out to the whole number 3. 4. The square root of 7 is a surd, because no fraction of two integers is equal to it. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 1: Exponents and surds_

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Which name is also used for an exponent?

  1. The radicand
  2. The index
  3. The fraction
  4. The bracket
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Correct answer: B. The index

1. An exponent is the small raised number written after a base. 2. The exponent, also called the index or power, indicates how many times the multiplication is repeated. 3. The radicand is a different part of the notation, since it is the number under a root sign. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 1: Exponents and surds_

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An even root is being taken. What must be true of the radicand for the root to be real?

  1. It must be negative
  2. It must be positive
  3. It must be a fraction
  4. It must be a decimal
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Correct answer: B. It must be positive

1. The radicand is the number sitting under the root sign. 2. For an even root, the radicand must be positive, otherwise the roots are not real. 3. Squaring any real number gives a positive answer, so nothing squares to give a negative number. 4. An odd root is the other case, where the radicand may be positive or negative. _Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 1: Exponents and surds_

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