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ILEIID 2025 | International Journal of Research and Innovation in Social Science (IJRISS)
ISSN: 2454-6186 | DOI: 10.47772/IJRISS
Special Issue | Volume IX Issue XXIV October 2025
Analysis of Summative Pre-Calculus Assessment for Computer
Science Students
*1
Azimah Suparlan,
2
Fairuz Shohaimay,
3
Aszila Asmat
1,2,3
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Pahang
Branch, Raub Campus, Malaysia
DOI: https://dx.doi.org/10.47772/IJRISS.2025.924ILEIID0036
Received: 23 September 2025; Accepted: 30 September 2025; Published: 30 October 2025
ABSTRACT
In foundational courses like Pre-Calculus, summative assessment is a common method to evaluate student
learning in mathematics. Many students were seen struggling to pass the Pre-Calculus course, especially
students with an inadequate SPM-level mathematics. Although educators are aware of the challenges faced by
these students, few studies have investigated their performance patterns in the summative assessment. This
study aims to analyse students’ performance in the Pre-Calculus summative assessment by examining the
distribution of marks and the questions students choose to attempt. The summative assessment is an individual
written final examination comprising 25 questions on various topics in this course. Data from the answer
scripts of 32 repeat students were collected and analysed using descriptive analysis. Results show that all
students attempted questions on inequalities, complex numbers, and systems of linear equations, with the
median scores being higher than the average scores. Conversely, students performed poorly on questions on
trigonometry, suggesting that the topic is challenging. Despite the limited sample size and scope, this study
lays the groundwork for curriculum assessment in the Pre-calculus course. More broadly, this move helps to
strengthen mathematical learning and contribute to the ove 335-343. rall improvement of STEM education.
Keywords: Mathematics education, Pre-calculus course, Summative assessment, STEM education
INTRODUCTION
Summative assessment is one of the main tools in higher education used to evaluate students' learning and
achievement at the end of the semester. In mathematics education, the closed-book final examination remains
the traditional way to measure students' ability to recall and apply mathematical procedures to solve problems
(Iannone & Simpson, 2022). For Computer Science students, the Pre-Calculus course is the algebraic and
analytical prerequisite for later courses such as Calculus, Discrete Mathematics, and Linear Algebra. However,
many students faced difficulties in the Pre-Calculus course, which can hinder their progress in other courses
within the Computer Science programme. Therefore, analysis of students’ performance in summative
assessment is vital, especially for students who repeat the course.
Previous research on mathematics assessment in higher education has reported varied findings on students
performance in acquiring mathematical skills (Nortvedt & Buchholtz, 2018). Some studies have also explored
teaching strategies towards improving students' performance and learning experience in mathematics. Despite
these insights, few studies have been conducted on how repeat students perform in Pre-Calculus summative
assessment within Computer Science programmes. It is essential to analyse the summative assessment, for
example, the final examination data, because it can reveal students’ cumulative understanding at the end of the
semester. Furthermore, summative assessments are usually the only standardised evaluation method across all
cohorts over time (Iannone & Simpson, 2022). By analysing the distribution of marks based on topics,
educators can better understand students’ strengths and weaknesses in learning mathematical skills.
Based on the mixed evidence in previous studies, this study focuses explicitly on the summative assessment
component to identify student performance at the topic level. Although formative assessments are needed to
monitor ongoing students’ learning progress, this research is a preliminary investigation to develop a baseline
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ILEIID 2025 | International Journal of Research and Innovation in Social Science (IJRISS)
ISSN: 2454-6186 | DOI: 10.47772/IJRISS
Special Issue | Volume IX Issue XXIV October 2025
understanding of how students attempt and perform based on different mathematical topics. By concentrating
on the final examination data, the findings are expected to form subsequent future works to understand the
factors of mathematical anxiety among students. Moreover, the analysis will also give valuable insights into
developing assessment designs and teaching strategies. This detailed understanding is essential in Malaysian
tertiary education, where many students enrolling for science-based programs frequently exhibit varying levels
of preparedness stemming from their SPM-level mathematics education.
This article is organised as follows. Section 2 provides the literature review on the trend of mathematics
performance in secondary schools, the contributing factors and methods proposed to analyse students’
performance. Next, Section 3 explains the methodology and data used in this study. The results are discussed
in Section 4. Finally, Section 5 presents the conclusion and future research direction.
LITERATURE REVIEW
Trend in Mathematics Performance in Secondary Level Education
Several studies have reported a worrying decline in students’ mathematics performance in secondary school.
According to the international assessments, Trends in International Mathematics and Science Study (TIMSS),
Malaysia’s ranking decreased from 1999 to 2007 (Ismail & Awang, 2012). Results from the 2022 Programme
for International Student Assessment (PISA) also reported poor performance among Malaysian students, with
a lower ranking than other ASEAN counterparts (Ling & Krishnasamy, 2023). The findings by Wei et al.
(2025) revealed that over 50% of Malaysian students have poor basic mathematics proficiency. These findings
showed the challenging role of educators in teaching mathematics to ensure that students can gain basic
mathematical knowledge. Poor mathematics performance among secondary school students will negatively
affect university intake, especially in STEM-related fields (Idris, 2006).
Factors Influencing Mathematics Performance
Many studies reported several key factors contributing to poor mathematics performance among undergraduate
students. Math anxiety is one of the psychological factors affecting students’ confidence and problem-solving
efficiency (Omar et al., 2022; Khoo et al., 2024). High levels of math anxiety are consistently associated with
poor mathematics performance at the secondary school level (Zakaria et al., 2012; Buratta et al., 2019). Other
studies also found that cognitive factors such as a weak mathematical background (Lishchynska et al., 2023)
and students’ inadequate learning initiative (Sergejeva & Zeidmane, 2023) significantly contribute to
undergraduates’ mathematics performance. While in Malaysia, findings revealed challenges in teaching
quality, the type of pre-university education background and language usage influence students’ performance
in mathematical courses (Abdullah et al., 2025; Kamal et al., 2015).
Methods in the Analysis of Students’ Performance in Mathematics
Several statistical methods are commonly employed to analyse mathematics assessments for undergraduate
students. These methods help understand various factors influencing student performance and improve
assessment techniques. Descriptive statistics summarise students' performance based on average scores,
distribution of marks and pass rate, which can help educators identify areas that are challenging for students.
Additionally, descriptive techniques are used to analyse teachers’ perceptions of assessment approaches in
teaching mathematics (Dogan, 2011). Regression, cluster and factor analysis have also been used to identify
the relationship between students’ satisfaction and teaching quality that influences their performance
(Kuznetsova, 2019). In a study conducted by Adnan et al. (2011), multiple linear regression was used to
predict students’ performance in mathematics and statistics courses.
METHODOLOGY
This study uses an exploratory research approach to comprehend and investigate the question-answering
patterns for the Pre-Calculus course among university students. All 32 students who had registered for this
course were involved as participants in this study. These students were in the second year of the Diploma in
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ILEIID 2025 | International Journal of Research and Innovation in Social Science (IJRISS)
ISSN: 2454-6186 | DOI: 10.47772/IJRISS
Special Issue | Volume IX Issue XXIV October 2025
Computer Science program and were taking this course for the second time. Students enrolling in the Pre-
Calculus course should have a solid foundation in mathematics. Based on the Malaysian Certificate of
Education (SPM) results, all these students passed the mathematics subjects, with 10 receiving grades A and
A-. In addition, out of all the students, only six took Additional Mathematics during the SPM examination,
with only three passing.
The Pre-Calculus course consists of four chapters, namely Coordinates, Graphs and Lines (Chapter 1),
Functions (Chapter 2), Systems of Equations and Inequalities (Chapter 3) and Trigonometry (Chapter 4).
Chapter 1 introduces fundamental mathematical concepts for pre-calculus, including the real number system,
inequalities, absolute value, complex numbers, the Cartesian coordinate plane, graphing, and analytic
geometry. Chapter 2 explores functions in mathematics, introducing definitions, properties, and operations.
Students learn to solve complex equations and transform graphs for visualisation. On the other hand, Chapter 3
focuses on trigonometry, introducing circular measure, fundamental ratios, graphing functions, identities, and
solving equations. It equips students with analytical tools for advanced mathematics, physics, and engineering.
Finally, Chapter 4 teaches students how to solve systems of equations and inequalities, enabling them to
analyse complex problems involving multiple relationships or constraints.
The summative assessment for the Pre-Calculus course used in this study is taken from the final examination
conducted at the end of the semester. The assessment consists of 25 short-answer questions drawn from the
four chapters altogether. Table 1 provides information on the chapter and topic for each question.
Table 1. Chapters and topics for each question in the Pre-Calculus final examination paper
Question
Chapter
Topic
1
1 (Coordinates, Lines and
Graphs)
Solving inequalities: Quadratic
2
Solving inequalities: Linear
3
Solving inequalities: Absolute Value
4
Complex Number
5
Plane Analytic Geometry: Lines
6
Plane Analytic Geometry: Parabola
7
Plane Analytic Geometry: Circle
8
2 (Functions)
Domain and Range of Function
9
Inverse Function
10
Composite Function
11
Long Division
12
Solving Exponential Equation
13
Transformation of Graph
14
3 (Systems of Equations and
Inequalities)
System of Linear Equations
15
System of Nonlinear Equations
16
Solving Systems of Inequalities by
Graphing Techniques
17
4 (Trigonometry)
Solution of Trigonometric Equation
18
Circular Measure: Angle
19
Circular Measure: Arc Length
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ILEIID 2025 | International Journal of Research and Innovation in Social Science (IJRISS)
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20
Circular Measure: Sector Area
21
Graph of Trigonometric Function
22
Six trigonometric ratios and
trigonometric identities
23
Six trigonometric ratios and
trigonometric identities
24
Solution of Triangle: Heron's
Formula
25
Solution of Triangle: Area
According to Table 1, 28% of the 25 questions were drawn from Chapter 1, 24% from Chapter 2, 12% from
Chapter 3 and the rest from Chapter 4. The marks for each question ranged from 2 to 5 marks, with a total of
100 marks. The assessment score is calculated and then classified into four different achievement levels as
stated in Table 2.
Table 2. Level of Achievement
Marks
Above 70
50-69
30-49
Below 30
Students were given three hours to answer all questions in the final examination. Data were collected based on
the students’ answer scripts, which were then analysed by the examiner. The marks scored for each question
were recorded for every student. Questions that were left blank, without any written answer, are considered
“not attempted” by students. Descriptive analysis is then used to analyse the data, which includes tabulation,
graphical representation, and the average and median marks scored by the students.
RESULTS AND DISCUSSION
The study includes 32 students, 56.25% male and the rest female. Students were given a set of assessments
consisting of 25 short-answer questions with a total mark of 100 covering various topics from four chapters in
the Pre-calculus course. Figure 1 depicts the distribution of total summative assessment scores among students.
Figure 1. Distribution of total summative assessment scores among students
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ILEIID 2025 | International Journal of Research and Innovation in Social Science (IJRISS)
ISSN: 2454-6186 | DOI: 10.47772/IJRISS
Special Issue | Volume IX Issue XXIV October 2025
Based on Figure 1, the majority of students scored between 30 and 49 marks, with no students scoring 70 or
above. This finding shows that most students were at an average level of achievement on the assessment
given. The details for each question in the summative assessment and its distribution of attempts are shown in
Table 3.
Based on Table 3, the results indicate that all students attempted to answer Questions 1 (solving inequalities
(quadratic)), Question 2 (solving inequalities (linear)), and Question 4 (complex numbers).
Table 3. Percentage frequency distribution of the attempts for each question based on the topics
Question
Topic
No. of Students
Attempted (n=32)
Percentage of
Attempt (%)
1
Solving inequalities: Quadratic
32
100
2
Solving inequalities: Linear
32
100
3
Solving inequalities: Absolute
Value
30
93.75
4
Complex Number
32
100
5
Plane Analytic Geometry: Lines
30
93.75
6
Plane Analytic Geometry: Parabola
26
81.25
7
Plane Analytic Geometry: Circle
29
90.63
8
Domain and Range of Function
24
75
9
Inverse Function
19
59.38
10
Composite Function
18
56.25
11
Long Division
26
81.25
12
Solving Exponential Equation
16
50
13
Transformation of Graph
17
53.13
14
System of Linear Equations
32
100
15
System of Nonlinear Equations
28
87.5
16
Solving Systems of Inequalities by
Graphing Techniques
25
78.13
17
Solution of Trigonometric Equation
10
31.25
18
Circular Measure: Angle
27
84.38
19
Circular Measure: Arc Length
27
84.38
20
Circular Measure: Sector Area
24
75
21
Graph of Trigonometric Function
25
78.13
22
Six trigonometric ratios and
trigonometric identities: Sum of
two angles
23
71.88
23
Six trigonometric ratios and
trigonometric identities:
Pythagorean identity
16
50
24
Solution of Triangle: Heron's
Formula
22
68.75
25
Solution of Triangle: Area
20
62.5
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In contrast, other questions received a high number of attempts, reaching 90% of students. Only Question 6
had the lowest attempt percentage (81.25%), but it still registered an acceptable rate. Overall, all students try to
answer every question in Chapter 1. Similar results can be seen for questions drawn from Chapter 3, with all
students attempting to answer Question 14, which is related to a system of linear equations. For Question 15 (a
system of nonlinear equations) and Question 16 (solving systems of inequalities by graphing techniques), the
percentage of students trying to answer these questions is considered quite high, with 87.5% and 78.13%
respectively. Thus, it is fair to state that the majority of students attempt to answer all questions related to
Chapter 1 and Chapter 3.
On the other hand, for Chapter 2, which pertains to functions, the number of students who attempted to answer
the questions was relatively less compared to Chapter 1 and Chapter 3, except for Question 8 (domain and
range function) and Question 11 (long division). Both questions show relatively high responses among
students, with percentages of 75% and 81.25% respectively. Meanwhile, out of nine questions drawn from
Chapter 4, only three have a considerable number of students attempting to answer them: Questions 18, 19,
and 21, with percentages of responses exceeding 75%. Nevertheless, there are no questions which all students
do not attempt to answer.
The analysis of the most and the least attempted questions, along with the full marks and average and median
marks scored by students, is displayed in Tables 4 and 5.
Table 4. The Average and Median Marks for the Top Five Most Attempted Questions
Question No.
Topic
No. of Students
Attempted (n=32)
Full mark
Average mark
Median Mark
1
Solving
inequalities:
Quadratic
32
5
3.38
4
2
Solving
inequalities:
Linear
32
4
2.5
3
3
Solving
inequalities:
Absolute Value
30
4
2.13
2
4
Complex Number
32
5
3.66
4
5
Plane Analytic
Geometry: Lines
30
5
2.93
4
Based on Table 4, Questions 1 to 5 are listed as the most attempted questions. The highest mark was recorded
for Question 4 (Complex Number), with an average mark of 3.66 out of 5. The median mark is 4, which
suggests that many students have a good understanding of the topic. Results were similar to Question 1
(Solving Inequalities: Quadratic), where the students scored on average 3.38 out of 5 and a median of 4. Most
students could apply principles in quadratic and complex number problems successfully.
However, the performance is poor for Question 2 (Solving Inequalities: Linear), where students only achieved
an average of 2.5 with a median of 3, indicating moderate understanding. The lowest result is in Question 3
(Solving Inequalities: Absolute Value), where the average was 2.13 with a median of 2, indicating significant
difficulty with absolute value concepts. For Question 5 (Plane Analytic Geometry: Parabola). The median
score of 4 implies many students performed well; however, the mean of 2.93 suggests some students scored
very low, which lowers the mean, indicating a wide variation in performance on this topic.
Moving on to the least attempted questions in Table 5, five questions are listed, with three questions from
Chapter 2 (Questions 10, 12, and 13) and the rest from Chapter 4. The average score for all questions ranges
from 0.5 to 1.22, indicating weak performance, lack of confidence and understanding of these topics. The same
result can be observed by analysing the median value for four of the five questions, which was zero, suggesting
that half of the students received no marks for these topics. All questions had 23 or fewer attempts, except for
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ILEIID 2025 | International Journal of Research and Innovation in Social Science (IJRISS)
ISSN: 2454-6186 | DOI: 10.47772/IJRISS
Special Issue | Volume IX Issue XXIV October 2025
Question 17, which received only 10 attempts and yielded a mean and median of 0.6 and 0.0, respectively. It is
fair to conclude that most students refuse to answer Question 17 related to the solution of trigonometric
equations. Students struggle with solving equations due to the need to identify identity and quadrants and solve
equations in quadratic form.
Table 5. The Average and Median Marks for the Top Five Least Attempted Questions
Question No.
Topic
No. of Students
Attempted
(n=32)
Full
mark
Average
mark
Median
Mark
10
Composite Function
18
4
1.22
0
12
Solving Exponential
Equation
16
6
0.63
0
13
Transformation of Graph
17
5
1.12
1
17
Solution of
Trigonometric Equation
10
5
0.6
0
23
Six Trigonometric Ratios
and Trigonometric
Identities
23
3
0.5
0
Consistent with the findings reported by Rohimah and Prabawanto (2020), this study reveals that students
faced difficulties in solving trigonometric identity problems, including general formulas, comparison
relationships, and algebraic calculations. According to Mukuka and Taura (2025), the issues encountered
included algebraic manipulation, reference angles, angle relations between quadrants, and degree-radian
conversion. Another study conducted by Usman and Hussaini (2017) also revealed that students often find
trigonometry more difficult and complex than other areas in mathematics.
Overall, the results show students’ performance patterns across different mathematics topics, indicating a
learning challenge. The students showed satisfactory algebra and number manipulation mastery in topics; the
same students avoided questions on transcendental equations and functions. These findings may be linked to
poor basic mathematics at primary and secondary school levels, mathematics anxiety, lack of motivation and
self-efficacy among students. This study purposely focused on the summative assessment as a stepping stone,
since the data gives a baseline performance of mathematics knowledge before proceeding to other indicators.
The findings are valuable to guide future work in designing practical formative assessment and teaching
strategies to increase students’ motivation in learning mathematics. Longitudinal tracking can give valuable
trends of how the students’ performance in Pre-Calculus can affect their learning process in other mathematics
courses like Calculus, Discrete Mathematics and Linear Algebra. Ultimately, these insights aim to support
efforts in improving mathematics curriculum and teaching methods to strengthen the STEM-related fields.
CONCLUSION
This study analysed the performance of repeat students in a Pre-Calculus summative assessment, showing that
questions on inequalities, complex numbers, and plane analytic geometry were most frequently attempted,
while trigonometric concepts, exponential equations, and composite functions were least attempted. These
results highlight challenges in specific mathematical areas and focus on the need for assessment refinement
and instructional emphasis on the least attempted questions. Though the assessment only includes summative
assessment in terms of the written test, the findings contribute possibilities for enhancing both curriculum and
assessment design. Future research should use longitudinal studies to investigate how students' achievement in
the Pre-Calculus course affects their performance in subsequent courses. In addition, studies with different
teaching methods and larger and more diverse groups of students, including first-time students, are necessary
to confirm these findings and support improvements in STEM achievement.
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ACKNOWLEDGEMENTS
The authors thank the reviewers for constructive comments and valuable suggestions.
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