Looking back at the 2015 exam through the score distribution

To evaluate the quality of an exam in general and a particular exam in particular, the score distribution is the most authentic basis. Through the score distribution, we can see the classification of the exam, as well as have plans and methods to improve and enhance the quality of the exam next year.

This year's Math score distribution is saddle-shaped. From this score distribution we can see some of the following issues:

+ In Math, scores from 6.5 to 7 are common. Nationwide, only 86 candidates scored 10, the total number of candidates scoring 9 is 8,152. In Math, nearly 12,000 candidates scored zero.

+ 2015 is the first year of organizing a national exam (combining two exams: High School Graduation and University Entrance into one), so the exam must meet two requirements: used for graduation and as a basis for university and college admission. The exam basically meets the graduation requirements (the number of easy questions accounts for about 60%) and this is clearly shown in the score distribution (the number of candidates achieving the highest score of 6.5) and then gradually decreases at levels of 7.8 and 8.5.

+ The number of candidates with low scores and absolute scores is small. The peak of the score spectrum tends to shift to the right (previous years tended to shift more to the left). This shows that the innovation has brought better results than previous years.

+ However, the score distribution is not yet beautiful and not symmetrical, there are many "sawtooth effects" and it does not have the standard shape of an upside-down bell tower (that is, for each subject, there will be a few students who are very poor, a few students who are poor, a few students who are good, a few students who are very good, the rest are concentrated in the middle, which is average-good. The level of weak-poor-good-good for each subject is different, the level of difficulty of the test is also different, so the top of the bell will fluctuate more or less to the right or left and the slope of the bell body will change). This reflects that the test is not highly classified (especially for students at the average-good level), shown in the fact that the number of candidates who scored 9 is higher than the number of candidates who scored 8.5 or the score of 3 is slightly higher than the 3.5. The reason is that question 9 has not really differentiated the difficulty in the second idea (0.5 points).

The organization of the 2015 national high school exam received much public consensus because it reduced the pressure on candidates. Although the exam still had some limitations as analyzed above, in general, it followed the direction of innovation and improved in quality.

Mr. Nguyen Ba Tuan

Review orientation for candidates taking the 2016 national high school exam

We all know that before announcing the organization of a common national exam, public opinion was struggling to debate and analyze which exam should be eliminated between the two options of high school graduation exam and university entrance exam. The final option chosen for the 2015 exam seems to be an “intermediate” solution with 60% of the questions for each exam being for the purpose of high school graduation exam, the remaining 40% of the questions being for the purpose of university entrance exam. Through the results of the exam, it can be seen that this is a solution that is in line with the innovation orientation of the Ministry of Education and Training.

One thing that can be seen in the general high school graduation exam questions and Math exam questions in particular in 2015 is the proposal to have easy and medium questions (used for graduation about 60%) and difficult and extremely difficult questions (about 40%) as a basis for university admission. In 2016, basically the Math exam questions will still follow that direction.

To complete the Math exam well in the 2016 National High School Exam, the first requirement for candidates is to have a firm grasp of the exam structure as well as the difficulty level for each question in the exam so that students will have a reasonable review direction. Refer to the following:

Questions are on a scale of 0 – 6:

Question 1 - Knowledge of function survey (Grade 12) (1 point). For this question, students only need to grasp basic knowledge in the textbook and pay attention when presenting to be able to achieve maximum score.

Question 2 – Find the largest and smallest values (Grade 12) (1 point). In this question, students only need to master the rules for finding the largest and smallest values presented in the textbook to be able to get points in this question.

Question 3 – Complex numbers (grade 12) (0.5 points) and exponential and logarithmic equations (0.5 points) (grade 12). This question is still at an easy level, only requiring candidates to have a firm grasp of basic knowledge in textbooks such as the concept of complex numbers, formulas for exponential and logarithmic equations, and understanding how to simply apply the knowledge to be able to do it.

Question 4 - Integration (grade 12) (1 point) requires students to grasp basic knowledge in textbooks about the method of changing variables and the method of integrating by parts.

Question 5 - Analytical geometry in space (grade 12) (1 point) is an average level question, only requiring students to grasp basic knowledge in the textbook to write equations of planes, lines, and spheres when knowing the most basic elements about it, grasping the relationship between that basic knowledge. Students who practice well the exercises in the textbook can do this question and get full points.

Question 6 - Trigonometry (grade 11) (0.5 points) and probability, Newton's binomial, combinations, permutations, permutations (0.5 points) (grade 11). This is a question related to grade 11 knowledge, students with average academic ability are often afraid of these questions, but in fact, the new way of making questions only requires students to diligently review the basic knowledge in textbooks to be able to do it. Starting from question 6, there is a requirement to apply existing knowledge and handle real-life situations in the exam at a higher level. For trigonometry questions, students learn and grasp formulas in grade 10, remember basic equations in grade 11 to be able to do it. Probability questions are often questions related to reality with simple application.

Questions used for university admission (6.5 – 10 points)

Question 7 – Composite spatial geometry (grades 11-12) (1 point). This is a “bridge” question between the difficult and easy parts. Students with average academic ability can do this question if they try hard. The questions are often about volume and distance. Students only need to grasp the knowledge in the textbook, practice regularly to grasp the methods to be able to conquer this question (because the amount of knowledge required is not much and there are specific instructions to apply to problems about composite spatial geometry).

Question 8 – Oxy plane analytic geometry (grade 10 - combining knowledge of geometry at grade 2) (1 point). This is a difficult question, for good and excellent students. However, good students can also get some points. The key to these types of questions is that students must see the properties of perpendicularity or equality. Students only need to learn and understand the types of properties commonly encountered in this section to be able to complete this question. The 2015 exam also followed that tradition, the key to the problem was to find the perpendicularity, this question ensured classification but did not promote much creativity of students because it was quite familiar in recent years.

Question 9 - Equations, systems of equations, inequalities, systems of inequalities (grade 10 - combined with knowledge of grade 12) (1 point). This is a question that gets 9 points in the exam, which is difficult. However, there are currently many tools to help students solve and earn points. The most important thing is that students must know how to apply the method, see the key points of the knowledge problem, regularly practice to scan the types of exercises, read and learn more solving methods outside of the textbook. This question is quite good in presenting the problem at two levels, but it is also a fairly familiar type of exercise that uses the monotony of functions.

Question 10 – Inequalities or finding min, max (grade 10 - combining general knowledge, especially grade 12) (1 point). This is the most difficult question in the exam, requiring students to have a broad understanding and be highly creative in applying the knowledge and methods they have learned.

Mr. Nguyen Ba Tuan

Lecturer at Hanoi University of Industry