Apply a grading curve to scores.
Grading curves come in three common forms with very different effects. Scaling the top score to one hundred multiplies everyone proportionally, so it helps high scorers most in absolute points. A flat addition helps everyone equally. The square root curve — ten times the root of the score — compresses the range from below and gives the largest boost to the weakest scores, lifting a 49 to 70 while barely moving a 90.
Top-score and flat curves
Top-score curve = raw x 100 / class high score; flat curve = raw + points added
Square root curve
Square root curve = square root of raw score x 10
The square root curve by a wide margin. A raw 36 becomes 60, whereas a top-score curve with a class high of 88 only lifts it to about 41.
These three cannot — all are monotonic increases. Curves that force a fixed distribution of grades can lower marks, because they assign grades by rank rather than by score.