Are you preparing for WAEC Mathematics and finding Number Bases difficult?
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This post contains number base questions fr0m past questions is designed to help WAEC, NECO, GCE and SSCE candidates master Number Bases through simple explanations, past-question practice, step-by-step solutions and an interactive CBT test.
Whether you are just learning Number Bases or you want to revise questions that have appeared in previous examinations, this page gives you a structured way to study and test yourself.
Quick Guide (read this first)
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Question 1 [2014/2]
If 23x = 325, find the value of x.
Mathematical expression
23x = 325
Solution
Step 1: Change 325 to base ten (place values 5 and 1):
325 = 3×5 + 2 = 17
Step 2: Expand 23x (place values x and 1):
23x = 2×x + 3 = 2x + 3
Step 3: Equate the two sides:
2x + 3 = 17
Step 4: Solve:
2x = 17 − 3 = 14 ⇒ x = 7
Check: 237 = 2×7 + 3 = 17 ✓
Answer: A. x = 7 |
Question 2 [2015/2]
The sum of 110112, 111112, and 100002 is 10m10n02. Find the values of m and n.
A. m=0, n=0 B. m=1, n=0 C. m=0, n=1 D. m=1, n=1
Mathematical expression
110112 + 111112 + 100002 = 10m10n02
Solution
Step 1: Change each number on the left to base ten (place values 16, 8, 4, 2, 1):
110112 = 16 + 8 + 0 + 2 + 1 = 27
111112 = 16 + 8 + 4 + 2 + 1 = 31
100002 = 16
Step 2: Add them:
27 + 31 + 16 = 74
Step 3: Expand 10m10n02 (place values 64, 32, 16, 8, 4, 2, 1):
1×64 + 0×32 + m×16 + 1×8 + 0×4 + n×2 + 0×1 = 72 + 16m + 2n
Step 4: Equate to 74:
72 + 16m + 2n = 74 ⇒ 16m + 2n = 2
Step 5: In base two, m and n can only be 0 or 1. If m = 1, then 16m = 16, which is already too big. So m = 0. Then 2n = 2, so n = 1.
Check: 10010102 = 64 + 8 + 2 = 74 ✓
Answer: C. m = 0, n = 1 |
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