Mathematics Indices Questions and Answers for WAEC, NECO, JAMB, GCE, Post-UTME and NABTEB (PART 1)

Mathematics Indices Questions and Answers for WAEC, NECO, JAMB, GCE, Post-UTME and NABTEB

Are you preparing for the 2027 WAEC, NECO, JAMB, GCE, Post-UTME or NABTEB Mathematics examination?

If YES, you must know about indices well.

One of the topics that students meet in Mathematics but in various forms is indices. You can be asked to simplify an expression, solve an equation that contains powers, use negative or fractional index numbers, or use the index laws to a more complex expression.

This Page includes 90+ original Mathematics indices questions from basic to more challenging.

The following questions are appropriate for revision for:

• WAEC
• NECO
• JAMB
• GCE
• Post-UTME
• NABTEB

Indices, Logarithms and surds, including laws of indices and equations involving indices have been incorporated into the current JAMB Mathematics Syllabus. The laws of indices, zero indices, negative indices and fractional indices are also part of the WAEC General Mathematics syllabus materials.

Note: These are genuine practice questions from past exams questions paper made for revision purposes. They are not leaky WAEC, NECO, JAMB, GCE, Post-UTME or NABTEB questions nor are they guaranteed questions that will come out in any 2027 exam.

Understanding the Laws of Indices

•          Multiply, same base, add the powers:

•          Divide, same base, subtract the powers:

•          Power of a power, multiply the powers:

•        Power zero:

•              Negative power, flip the number:

•        Fractional power:  and

•          Same base on both sides: if , then

•        Difference of two squares:

•          Standard form: , where  is at least 1 but less than 10

•          Significant figures (s.f.): start counting from the first non-zero digit. Look at the next digit: if it is 5 or more, round up; if it is 4 or less, leave the last digit as it is.

•        Sum of odd numbers:  (the first  odd numbers)

MATHEMATICS INDICES OBJECTIVE QUESTIONS AND ANSWERS

Question 1

If , find . [2009 Q31]

Options: A. 2 B. 1 C.  D.

Step 1: Change everything to base 3. ,  and .

Step 2: Same base, so equate the powers.

Answer: C.

Question 2

Simplify

Options: A. 16 B. 8 C. 4 D. 1 [2014 Q35]

Step 1: Change everything to base 2. ,  and .

Step 2: Top and bottom.

Step 3: Divide (subtract the powers).

Step 4: Take the square root.

Answer: C.

Question 3

If , find the value of .

Options: A. 1 B.  C.  D.  [2015 Q4]

Step 1: Change to base 3.  and .

Step 2: Write 1 as a power of 3. , so

Answer: B.

Question 4

If , find

Options: A.  B.  C.  D.  [2015 Q7]

Step 1: Split the power (adding powers means multiplying).

Step 2: Rewrite  using .

Step 3: Put it together.

Answer: A.

Question 5

Given that , find .

Options: A.  B.  C.  D.  [2010 Q18]

Step 1: Change 25 to base 5. , so .

Step 2: Divide (subtract the powers).

Step 3: Equate the powers. The right side is .

Answer: C.

Question 6

Simplify

Options: A.  B.  C.  D.  [2008 Q10]

Step 1: Take the cube root of each part separately.

Step 2: Multiply them together.

Answer: C.

Question 7

Simplify

Options: A.  B. 9 C.  D.  [2016 Q7]

Step 1: Change to base 3.  and .

Step 2: Top.

Step 3: Divide.

Answer: B.

Question 8

If , find the value of

Options: A.  B.  C.  D.  [2008 Q30]

Step 1: Find . , so .

Step 2: Put  into the expression.

Step 3: Split  as , so we can pair the 2s with the 5s.

Answer: B. . Option D reads the same in the scan, so one of them is probably a misprint.

Question 9

Simplify

Options: A. 1 B.  C.  D.   [2007 Q7]

Step 1: Expand the bottom. Everything inside the bracket gets the power 3.

Step 2: Divide. The  cancels.

Answer: C.

Question 10

If , find .

Options: A.  B.  C.  D.  [2007 Q13]

Step 1: Change to base 2.  and .

Step 2: Equate the powers and solve.

Answer: D.

Question 11

If , find the value of .

Options: A.  B.  C.  D. 3 [2011 Q46]

Step 1: Change to base 3.

Step 2: Equate the powers.

Step 3: Divide both sides by  to get .

Answer: B.

Question 12

If , find the value of .

Options: A. 1 B. 2 C. 3 D. 4 [2009 Q13]

Step 1: Take the cube root of both sides. .

Step 2: Solve.

Answer: A.

Question 13

If , find .

Options: A. 1 B.  C. 2 D.   [2013 Q2]

Step 1: Change to base 3.

Step 2: Equate the powers and solve.

Answer: B.

Question 14

Given that , find  in terms of .

Options: A.  B.  C.  D.  [2017 Q43]

Step 1: Find  in terms of . A negative power means “flip”.

Step 2: Split .

Answer: A.

Question 15

Solve:

Options: A.  B.  C.  D.   [2012 Q39]

Step 1: First part. Flip the fraction to remove the negative sign, then take the cube root.

Step 2: Second part. The power  means square root.

Step 3: Multiply.

Answer: A.

Question 16

If  and , calculate

Options: A.  B. 1 C.  D.   [2013 Q11]

Step 1: Work out each power.

Step 2: Top and bottom.

Answer: C.

Question 17

Simplify  and express your answer in standard form.

Options: A.  B.  C.  D.   [2010 Q1]

Step 1: Write each number in standard form.

Step 2: Multiply the numbers, then the powers of 10.

Answer: D.

Question 18

Evaluate

Options: A.  B.  C.  D.  [2008 Q2]

Step 1: Use the difference of two squares on the top.

Step 2: Cancel the common bracket .

Answer: B.

Question 19

Find the product of 0.0403 and 0.0021, leaving your answer in standard form.

Options: A.  B.  C.  D.   [2008 Q3]

Step 1: Write each number in standard form.

Step 2: Multiply the numbers, then the powers of 10.

Step 3: Combine. , which is  to 3 s.f.

Answer: B.

Question 20

Simplify , leaving your answer in standard form.

Options: A.  B.  C.  D.  [2007 Q3]

Step 1: Divide the numbers and the powers of 10 separately.

Step 2: Combine.

Step 3: Put it in standard form. , so

Answer: B.

Question 21

Express the square root of 0.000144 in standard form.

Options: A.  B.  C.  D.  [2009 Q6]

Step 1: Write the number as a whole number times a power of 10.

Step 2: Take the square root of each part.

Step 3: Standard form.

Answer: C.

Question 22

Multiply  by  and leave your answer in standard form.

Options: A.  B.  C.  D.  [2013 Q1]

Step 1: Multiply the numbers, then the powers of 10.

Step 2: Combine.

Step 3: Standard form. The first number must be between 1 and 10, so .

Answer: C.

Question 23

Evaluate

Options: A. 1 B. 2.02 C. 20.02 D. 202 [1988 Q1]

Step 1: Use the difference of two squares.

Step 2: Work out each bracket.

Answer: D.

Question 24

Simplify

Options: A. 0 B.  C.  D.  [1988 Q3]

Step 1: Work out each part.

Step 2: Multiply.

Answer: D.

Question 25

Which of the following is equal to ?

Options: A.  B.  C.  D.  [1994 Q2]

Step 1: Break 72 into prime factors.

Step 2: Break 125 into prime factors.

Step 3: Combine.

Answer: A.

Question 26

Evaluate

Options: A. 6 B. 5 C. 4 D. 3 [1994 Q4]

Step 1: Top.

Step 2: Bottom. The negative power means flip.

Step 3: Divide. Dividing by  is the same as multiplying by 2.

Answer: A.

Question 27

Simplify

Options: A. 0 B. 2 C. 4 D. 10 [1994 Q5]

Step 1: Work out each part.

Step 2: Multiply.

Answer: C.

Question 28

Given that , find .

Options: A.  B.  C.  D.  [1999 Q24]

Step 1: Take the square root of each part of .

Step 2: Multiply.

Answer: C.

Question 29

Solve the equation .

Options: A.  B.  C.  D.  [2005 Q12]

Step 1: Change 8 to base 2.

Step 2: Equate the powers and solve.

Answer: B.

Question 30

Simplify

Options: A.  B.  C.  D.  [1996 Q4]

Step 1: Divide the numbers.

Step 2: Divide the powers of  (subtract the powers).

Step 3: Combine.

Answer: D.

Question 31

Simplify

Options: A.  B. 3 C.  D.  [1995 Q4]

Step 1: Write 0.027 as a fraction.

Step 2: Flip the fraction to remove the negative sign.

Step 3: Take the cube root of top and bottom.

Answer: D.

Question 32

Simplify

Options: A. 1 B.  C.  D.  [1989 Q32]

Step 1: Top.

Step 2: Bottom. Take the cube root first, then square.

Step 3: Divide.

Answer: D.

Question 33

Simplify

Options: A. 350 B. 35 C.  D.  [1990 Q1]

Step 1: Work out each part.

Step 2: Multiply.

Answer: C.

Question 34

If , what is ?

Options: A. 1 B. 1.5 C. 4.5 D. 18 [1990 Q2]

Step 1: Write 27 as a power of 3. .

Step 2: Equate the powers.

Answer: B.

Question 35

Simplify

Options: A. 8 B. 4 C.  D.   [1998 Q4]

Step 1: Change the mixed number. .

Step 2: Flip the fraction to remove the negative sign.

Step 3: Square root first, then cube.

Answer: A.

Question 36

It is observed that , , . If , find .

Options: A. 6 B. 7 C. 8 D. 9 [1999 Q3]

Step 1: Spot the pattern. Adding the first 2 odd numbers gives , the first 3 give , the first 4 give . So the first  odd numbers add up to .

Step 2: Count the numbers in . There are 8 of them.

Step 3: Use the pattern.

Step 4: Find . , so .

Answer: C.

Question 37

Simplify

Options: A.  B.  C.  D. 4 [1998 Q7]

Step 1: Work out each part.

Step 2: Put the numbers in.

Answer: C.

Question 38

Given that , find .

Options: A.  B.  C.  D. 2 [2000 Q29]

Step 1: Change to base 3.

Step 2: Equate the powers and solve.

Answer: B.

Question 39

Simplify

Options: A.  B.  C.  D.  [1991Q10]

Step 1: Write  as a power of 2. .

Step 2: Multiply it into each term (add the powers).

Step 3: Put it together.

Answer: A.

Question 40

Simplify

Options: A.  B.  C.  D.  [1992 Q7]

Step 1: Write the top and bottom as fourth powers.  and .

Step 2: Take the fourth root.

Answer: D.

CONTINUE READING CLICK HERE

How to Prepare for Indices Questions in 2027 Examinations

• Try not to just regurgitate the six laws.
• 
  
• Practise applying them.
• 
  
• Begin with some easy multiplication and division problems.
• 
  
• Then move to:
• 
  
• Negative indices
• 
  
• Fractional indices
• 
  
• Write expressions with multiple variables
• 
  
• Equations involving indices
• 
  
• Word problems
• 
  
• Mixed examination questions
• The more variations of questions you practice, the more you will be able to see which is the proper approach.

Common Mistakes Students Make in Indices

1. Incorrectly adding indices to the divisor during division.Error 1: Adding indices to the divisor when dividing.
2. One of the common mistakes students make is adding indices when raising a power to another power, as in the following: x^2^2^y^2^ = x^?^y^?^
3. Suppose the answer is negative, because of the negative index.
4. Not remembering the meaning of fractional exponents as roots.
5. Solving an index equation without first having to make the bases equal.

How to Use These Questions for WAEC, NECO, JAMB, GCE, Post-UTME and NABTEB

The following are tips on how to use these questions for WAEC, NECO, JAMB, GCE, Post-UTME and NABTEB exams.

Practise objective and school exam written solutions for school exams like WAEC and NECO.

In JAMB, and Post-UTME, practice a lot to solve questions quickly since you will be testing under computer based test conditions, generally.

To prepare for GCE and NABTEB, practice objectives with the understanding of the rules.

Agood revision method is:

step 1: Educate yourself on the law.

Step 2: Review 2 to 3 examples.

Step 3: Solve the problems without referring to the solution.

Step 4: Indicate your responses.

Step 5: Record all the errors.

Step 6: Make another try at the same questions.

Don't only measure yourself by the number of questions you get right.

Use the number of errors you are able to avoid.

Final Advice

The rules make indices much easier to understand, rather than trying to recall the answers individually.

Spend time mastering:

Multiplication of powers

Division of powers

Power of a power

Zero indices

Negative indices

Fractional indices

Equations involving indices

Then practise mixed questions.

In your WAEC, NECO, JAMB, GCE, Post-UTME or NABTEB study, include indices in your daily problems revision.

Keep in mind that the questions in this article are for practice purposes and not the actual questions. Not leaked exam questions and should not be regarded as guaranteed predictions of what any examination body will include in 2027.

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Disclaimer

The article is for educational & revision purposes. Although the examination syllabus, format and administrative details might change, candidates should check with the relevant body for the latest information.

AYOMITECH has designed the Mathematics questions and solutions in this article for practice. They are not examination questions, questions that are leaked, nor guarantees as to which questions will appear in the examination.