過去的研究指出影響數學科試題難易度的主要因素有三：所評量的數學內容、解題時的思考策略及解題所需的步驟數；過去的研究也認為綜合此三因素可預估試題的難易度。我們發現這些研究對難易度的預估的確有所助益。但也發現約有百分之十的試題預估成效有所不足。本研究主要目的為指出考生是否熟悉試題的內涵是影響試題難易度的另外一個重要的因素。考慮加進新的因素並擴充過去用三因素做難易度的預估，本研究綜合建議一因素指標模式，以增加預估難易度的準確性。再者，多選題步驟數的計算方法，一直是難易度預估的一大困擾；本研究對此也做了說明。 本研究將 91~96 年，大考中心所用數學試題，命題者所做難易度預估與考生答題反應差異較大者，利用因素指標模式與多選題步驟數的計算方式進行初步檢驗，發現本研究所提方法可能可以增加試題難易度預估的準確性。 雖然如此，仍然有少數試題偏離我們預估的難易度，希望往後的研究能修正或補充本研究之不足，讓我們對數學試題難易度的預估能更準確。

Based upon previous researches, the testing topics evaluated, problem solving tactics and steps involved are three major factors that influence the difficulty of the math tests. Combining these three factors, previous researches also indicated how to predict the difficulty of a test. We found that these predictions are quite helpful, but still there were about 10% of the test items, the predictions were less accurate. The main purpose of this research is to point out that the examinee’sfamiliarity to the content of the test items is another important factor. Adding this factor to the original three, we suggested a Factor-Indexed Model to increase the prediction accuracy. Furthermore, the calculation of solving steps for a multiple-choice test item was always a major obstacle to the prediction of difficulty. We also address this issue in this research. We picked the math exam items of the previous years (2002~2007), for which the examiner’s difficulty prediction and examinee’s response had large variance, and tested by our Factor-Indexed model and the calculation of solving steps, we found that our research would increase the accuracy of the prediction. Nevertheless, there is still prediction bias to some test items by our methods, and we hope that future researches will improve further so that one can have better control of the difficulty prediction.