Correct Option: A. 1 in 134 Explanation of the Correct Answer To determine which gradient is the steepest, we need to understand what the gradient ratios mean. A gradient expressed as "1 in X" indicates that for every 1 unit of vertical rise, there is a horizontal run of X units. Therefore, a smaller value of X indicates a steeper gradient.

1. Understanding the Ratios:
2. 1 in 134 means for every 1 unit of vertical rise, there are 134 units of horizontal distance.
3. 1 in 351 means for every 1 unit of vertical rise, there are 351 units of horizontal distance.
4. 1 in 531 means for every 1 unit of vertical rise, there are 531 units of horizontal distance.
5. 1 in 315 means for every 1 unit of vertical rise, there are 315 units of horizontal distance.
6. Comparing the Gradients:
7. To find out which gradient is the steepest, we can compare the values of X in each case:
   • 1 in 134: X = 134
   • 1 in 351: X = 351
   • 1 in 531: X = 531
   • 1 in 315: X = 315
8. The smaller the value of X, the steeper the gradient. Therefore, we can rank the gradients from steepest to least steep:
   • 1 in 134 (steepest)
   • 1 in 315
   • 1 in 351
   • 1 in 531 (least steep)
9. Conclusion:
10. Since 1 in 134 has the smallest denominator, it represents the steepest gradient. Thus, the correct answer is A. 1 in 134.

Explanation of Why Other Options Are Incorrect

• B. 1 in 351: This gradient is less steep than 1 in 134 because it has a larger denominator (351). It means that for every 1 unit of vertical rise, there is a longer horizontal distance compared to 1 in 134.
• C. 1 in 531: This is the least steep gradient of all the options provided. The denominator (531) is the largest, indicating that it has the longest horizontal run for the same vertical rise.
• D. 1 in 315: While this gradient is steeper than 1 in 351 and 1 in 531, it is still less steep than 1 in 134. The denominator (315) is larger than 134, making it less steep.

Common Pitfalls

• Misunderstanding the Ratio: Students often confuse the meaning of the gradient ratios. Remember, a smaller denominator indicates a steeper slope.
• Overlooking Comparisons: When comparing multiple gradients, it’s essential to rank them based on their denominators systematically.
• Assuming All Gradients Are Similar: Each gradient represents a different slope, and it’s crucial to analyze each one carefully.

Revision Summary

• A gradient of "1 in X" indicates the vertical rise over horizontal run; smaller X means steeper slope.
• The steepest gradient among the options is 1 in 134, as it has the smallest denominator.
• Always compare the denominators directly to determine steepness.
• Be cautious of misinterpretations of gradient ratios in exam questions.