NABTEB Mathematics Past Questions.

Introduction

Welcome learners, welcome to today’s tutorial. Today, we’ll be looking at NABTEB mathematics past question theories.

Let’s get started with the questions and answers.

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Example Question

Our first question says: Solve for x in the expression
8^(3x) × 8^(-1) = 32

We start by expressing all terms in powers of two. Since 8 = 2³, this becomes:

(2³)^(3x) × (2³)^(-1) = 2⁵

Simplifying:
2^(9x) × 2^(-3) = 2⁵

By the laws of indices (a^m × a^n = a^(m+n)):
2^(9x – 3) = 2⁵

Now that the bases are the same, we equate exponents:
9x – 3 = 5

Adding 3 to both sides:
9x = 8
x = 8/9

So, the value of x is 8/9.

Simplification Without Log Tables

Next, we are asked to simplify without using logarithm tables:

log 27 / log 3

We know 27 can be expressed as 3³. So:
log(3³) / log 3

Using logarithm laws (log a^m = m log a):
(3 log 3) / log 3

Cancel out log 3:
= 3

Therefore, the simplified value is 3.

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Exam Tip

Always start by simplifying problems into their basic forms—convert numbers into powers of prime bases, or express terms in simpler forms before applying laws. This saves time, reduces mistakes, and makes even tough questions easier to solve.

Watch the full tutorial here: https://www.youtube.com/watch?v=JXe7AYS8uN4

Conclusion

Practicing NAPE mathematics past questions builds speed, confidence, and clear understanding of core concepts. By applying laws of indices and logarithms, students sharpen problem-solving skills and prepare effectively for exams. Consistent practice makes success in mathematics achievable.

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