Although the item response theory, the IRT, have widely been used to test systems such as the TOEFL, it is not so well known to teachers of mathematics in universities and colleges. The superiority of the IRT over the classical test method is also valid in mathematics in universities and high schools. However, the number of problems in mathematics to be tested in short time period is strictly limited, in particular in univserisies. An accurate and efficient method to evaluate the abilities of students is strongly required. In this paper, we propose to use the up-and-down method to estimate the students' abilities. The stress-strength model is also incorporated. We have found that this newly proposed method works well. Assuming that the ability of an examinee follows a normal distribution $N(￥mu, ￥sigma^2)$ and the problems follow normal distributions $N(kd, ￥tau^2)$, the optimal strategy for obtaining the estimates $￥mu$ and $￥sigma$ accurately is to set the up-and-down distance $d$ to be $￥sqrt{￥sigma^2 + ￥tau^2}/2 ￥le d ￥le 3￥sqrt{￥sigma^2 + ￥tau^2}/2$.