Ritsumeikan Uji Junior High School
IP Course Diagnostic Exam – Year 1Introduction
Students come into the IP Course from all parts of the world, at all levels of English, as well
as at various levels of mathematics proficiency. Rather than picking any country’s standard ofmath at this grade level, the IPC Mathematics department has decided to test on the content
that is most relevant to students entering the IP Course. That content is outlined in thefollowing pages and there are example problems for each topic tested.
In addition, examinees are responsible for interpreting mathematical symbols and units
where notation and measurements may be different from standards students are used to.
Some examples of different issues students may encounter include:•Comma usage, or their absence, for large numbers, e.g.,
1 000 000 = 1000000 = 1,000,000•

Period usage and leading zeroes for decimals, e.g., 0.01 = .01•

Units and their abbreviations (“kilograms” becomes “kg”, “centimeters” becomes “cm”,etc). Understanding the units will generally not affect whether the student can answer
the problem.

Furthermore, effort is made to try and simplify the vocabulary used in word problems, butstudents are expected to understand mathematical vocabulary appropriate of this grade level.
Many of the examples below illustrate this point.
Last, the exam is 16 two-mark questions and 6 three-mark questions, totaling 50 marks.
Students have 30 minutes to finish the math portion of the IPC diagnostic exams. If a student
finds themselves spending too much time on one question, they are encouraged to skip it andcome back to it later provided there is time remaining.

Topic 1 – Fractions, Decimals, and Percentages
This is the largest section of the test, making up roughly 40% of the exam. Students should beable to convert between the three systems titled above and be able to evaluate operations withnumbers in any of the forms.
Example problems:
1) What percent of the rectangle below is shaded?

2) Simplify:9a) 8.1 ÷ 100b)

1225+3×6c) 9.99 × 5.053) Find 50% of 7. Write your answer as a fraction.
4) Order the numbers from least to greatest: 50%, 0.51,491000

Topic 2 – GeometryThe geometry section is a relatively small portion of the test, covering roughly 10% of the exam,
and will test on area, surface area, perimeter, and volume of simple shapes.
Example problems:
1) Find the perimeter and area of the rectangle below:2) If a 6-sided die has a side length of 1 cm then what is the surface area and volume ofthe die?

Topic 3 – Statistics and Probability
This section is also a relatively small portion of the test, covering roughly 15% of the exam,and focuses on reading charts, reading data sets, and simple probability.
Example problems:
1) Approximately how many students participated in the survey given below?

Favorite Sport
30
20
100Soccer

Basketball
BoysVolleyball

Badminton

Girls2) Given the spinner pictured to the right, find theprobability that the spinner lands on a space with theletter A. Note that each space of the spinner is equalin shape and size.

CABABA
B

A

Topic 4 – Number Systems and Patterns
The last topic the test covers is on number systems and patterns. This is the second largest
section of the test, making up roughly 35% of the exam. It is comprised of problems that deal
with the four basic operators, put into the form of word problems, as well as patterns problems.
Example problems:
1) Find the next number in the pattern: 1, 1, 2, 3, 5, 8, _____.
2) Given a starting number of 2 and a rule of “multiply by 2”, write the first threenumbers in the sequence.
3) If you add the same number together three times and then multiply that sum by 3, you
get 36. What is the original number?
4) A box of chocolate has 4 chocolate pieces, and Sally bought 12 boxes. If she has 8classmates she is giving the chocolate to, and she gives the chocolate out equally, howmany pieces of chocolate will each classmate receive?

Solutions
Topic 1
1. 70%
1912. A) 90 B) 18 or 1 18 or 1.05 C) 49.95
3.
4.

5

1449
1000, 50%, 0.51 or 0.049, 0.5, 0.51

Examiner’s note: credit will be given for any form of an answer (decimal, fraction,percentage, or mixed number), unless directed to answer in a specific form. Students
may be asked to simplify their answers, and if given that direction, no credit will beawarded otherwise.

Topic 2
1. P = 19 and A = 17.5
2. SA = 6 and V = 1
Examiner’s note: the answer sheets will already include the correct units for any
problems that have them, so students do not need to concern themselves with that
aspect of the problem. See the sample answer sheet on the next page.

Topic 3
1. 1302.

1
2

or 50% or 0.5

Topic 4
1. 13
2. 2, 4, 8
3. 4
4. 6
Examiner’s note: word problems do not need to be answered in the form of a sentence.
The answer sheets will already include countable or non-countable nouns. See thesample answer sheet on the next page.

IPC1 Mathematics SAMPLE Answer Sheet
Student name:Registration number:
Section A (2 marks each)

Section B (3 marks each)

113a2a2b13b

14

32mmmm315
percent

45a165b5c

17cm36a6b

7

8
km
910apples1112
dollars