Common AEIS Math Questions Solved Step-by-Step | Free Worksheet

Are you or your child preparing for the AEIS (Admissions Exercise for International Students) examination to enter Singapore’s education system? The Math component can be particularly challenging for many international students who are adapting to Singapore’s curriculum standards.

At EduFirst Learning Centre, we’ve helped hundreds of international students successfully prepare for and pass the AEIS examination. From our experience, we’ve identified the most common types of Math questions that appear in the test and developed effective strategies to solve them.

In this comprehensive guide, we’ll walk you through typical AEIS Math questions with detailed step-by-step solutions. We’ll also provide a free downloadable worksheet so you can practice these concepts at home. Whether you’re aiming for primary or secondary school admission, mastering these fundamental mathematical concepts will significantly boost your chances of success in the AEIS examination.

Understanding the AEIS Math Examination

The AEIS Math examination is designed to assess whether international students have the mathematical knowledge and problem-solving skills necessary to integrate into Singapore’s education system. The test is aligned with Singapore’s renowned math curriculum, which emphasizes conceptual understanding, procedural fluency, and mathematical reasoning.

For primary school admission (typically for students aged 7-12), the examination covers topics such as whole numbers, fractions, decimals, measurement, and basic geometry. For secondary school admission (typically for students aged 13-16), the test includes more advanced concepts like algebra, statistics, and complex geometric problems.

What makes the AEIS Math test particularly challenging is its focus on problem-solving rather than mere computational skills. Students are expected to apply mathematical concepts to solve real-world problems, often presented in unfamiliar contexts.

Key Math Concepts Tested in AEIS

Before diving into specific questions, let’s understand the core mathematical concepts typically assessed in the AEIS examination:

Primary Level (P2-P6):

1. Whole Numbers: Place values, the four operations (addition, subtraction, multiplication, division), and number patterns.

2. Fractions: Equivalent fractions, comparing fractions, operations with fractions.

3. Decimals: Converting between fractions and decimals, operations with decimals.

4. Percentage: Converting between fractions, decimals, and percentages; finding percentages of quantities.

5. Ratio: Expressing ratios in simplest form, dividing quantities in given ratios.

6. Measurement: Length, mass, volume, time, and area.

7. Geometry: Properties of basic shapes, angles, and perimeter/area calculations.

Secondary Level (S1-S4):

In addition to reinforcing primary-level concepts, the secondary AEIS examination includes:

1. Algebra: Linear equations, algebraic expressions, and factorization.

2. Statistics: Mean, median, mode, and data interpretation.

3. Geometry: Congruence, similarity, and properties of triangles and circles.

4. Trigonometry: Basic trigonometric ratios and applications.

Common AEIS Math Questions with Step-by-Step Solutions

Let’s now examine some typical AEIS Math questions and walk through their solutions in detail. These examples represent the most common question types our students encounter during preparation for the AEIS examination.

Whole Numbers and Operations

Question 1: Jane has 384 stickers. She gives 5/8 of them to her friends and keeps the rest. How many stickers does Jane keep?

Step-by-Step Solution:

1. Find the fraction of stickers Jane keeps:
If Jane gives away 5/8 of her stickers, she keeps 1 – 5/8 = 3/8 of her stickers.

2. Calculate the number of stickers Jane keeps:
Number of stickers Jane keeps = 3/8 × 384
= 3 × (384 ÷ 8)
= 3 × 48
= 144

Therefore, Jane keeps 144 stickers.

Fractions and Decimals

Question 2: John spent 2/5 of his money on a book and 1/4 of the remainder on stationery. If he had $45 left, how much money did he have at first?

Step-by-Step Solution:

1. Let’s denote the initial amount of money as $x.

2. After buying the book, John spent 2/5 of $x, so he had $x – 2/5 × $x = 3/5 × $x remaining.

3. Then John spent 1/4 of the remainder on stationery.
Amount spent on stationery = 1/4 × (3/5 × $x) = 3/20 × $x

4. After buying stationery, John had:
3/5 × $x – 3/20 × $x = (12/20 – 3/20) × $x = 9/20 × $x

5. We’re told that John had $45 left, so:
9/20 × $x = $45
$x = $45 × 20/9
$x = $100

Therefore, John initially had $100.

Ratio and Proportion

Question 3: The ratio of boys to girls in a class is 5:4. If there are 45 students in the class, how many more boys than girls are there?

Step-by-Step Solution:

1. Find the total parts in the ratio:
Total parts = 5 + 4 = 9 parts

2. Calculate the value of each part:
Value of each part = Total students ÷ Total parts
= 45 ÷ 9
= 5

3. Calculate the number of boys and girls:
Number of boys = 5 × 5 = 25
Number of girls = 4 × 5 = 20

4. Find the difference:
Difference = 25 – 20 = 5

Therefore, there are 5 more boys than girls in the class.

Percentage

Question 4: The price of a laptop was $1,200. During a sale, its price was reduced by 15%. After the sale, the price increased by 10% of the sale price. What was the final price of the laptop?

Step-by-Step Solution:

1. Calculate the sale price:
Discount amount = 15% of $1,200 = 0.15 × $1,200 = $180
Sale price = $1,200 – $180 = $1,020

2. Calculate the price increase after the sale:
Increase amount = 10% of $1,020 = 0.1 × $1,020 = $102

3. Calculate the final price:
Final price = $1,020 + $102 = $1,122

Therefore, the final price of the laptop is $1,122.

Geometry and Measurement

Question 5: The area of a rectangular field is 420 square meters. If the length of the field is 28 meters, what is the perimeter of the field?

Step-by-Step Solution:

1. Find the width of the rectangular field using the area formula:
Area = Length × Width
420 = 28 × Width
Width = 420 ÷ 28 = 15 meters

2. Calculate the perimeter using the perimeter formula:
Perimeter = 2 × (Length + Width)
= 2 × (28 + 15)
= 2 × 43
= 86 meters

Therefore, the perimeter of the rectangular field is 86 meters.

AEIS Math Problem-Solving Strategies

Success in the AEIS Math examination requires more than just knowledge of mathematical concepts. Here are some effective problem-solving strategies that we teach at EduFirst Learning Centre:

1. Understand the problem: Read the question carefully, identify the given information, and determine what you need to find. Underlining key information can be helpful.

2. Visualize: Draw diagrams or models to represent the problem visually. Singapore’s bar model method is particularly useful for solving word problems.

3. Plan your approach: Decide on the mathematical concepts and operations needed to solve the problem. Break complex problems into simpler steps.

4. Execute systematically: Work through your solution step by step, showing all working clearly. This helps you avoid calculation errors and ensures you get partial credit even if your final answer is incorrect.

5. Check your answer: Verify that your answer makes sense in the context of the problem and that it addresses what was asked.

At EduFirst, our experienced teachers guide students through these strategies using a variety of practice problems, gradually building their confidence and proficiency in tackling AEIS Math questions.

Free AEIS Math Worksheet

To help you practice the concepts covered in this article, we’ve created a comprehensive AEIS Math worksheet with 20 practice questions covering all the key topics tested in the examination. Each question comes with a detailed solution to guide your learning.

The worksheet includes:

– 4 questions on whole numbers and operations

– 4 questions on fractions and decimals

– 4 questions on ratio and proportion

– 4 questions on percentage

– 4 questions on geometry and measurement

To download your free AEIS Math worksheet, simply click the button below:

How EduFirst Helps Students Excel in AEIS

At EduFirst Learning Centre, we’ve developed a specialized AEIS preparation program that has helped numerous international students successfully gain admission to Singapore’s primary and secondary schools. Our approach to AEIS Math preparation includes:

Small Class Sizes: With only 4-8 students per class, our teachers can provide personalized attention and address each student’s specific learning needs.

Experienced Teachers: Our teachers are well-versed in the Singapore math curriculum and have extensive experience preparing international students for the AEIS examination.

Comprehensive Curriculum: Our AEIS Math preparation covers all the key topics and question types that appear in the examination, ensuring students are thoroughly prepared.

Regular Practice Tests: We conduct regular practice tests that simulate the actual AEIS examination, helping students become familiar with the format and time constraints.

Customized Learning Materials: We provide carefully crafted worksheets, practice questions, and study notes tailored to each student’s learning level and progress.

Problem-Solving Techniques: We teach students effective problem-solving strategies specific to the Singapore math curriculum, such as the model method and heuristics.

With 25 locations across Singapore, EduFirst Learning Centre is well-positioned to support international students in their journey to join Singapore’s education system. Our track record of success speaks for itself, with a high percentage of our students successfully passing the AEIS examination each year.

Conclusion

The AEIS Math examination is a significant challenge for many international students seeking admission to Singapore schools. However, with proper preparation, understanding of key concepts, and regular practice, success is within reach.

In this article, we’ve covered the most common types of AEIS Math questions and provided detailed step-by-step solutions to help you understand the problem-solving process. The free worksheet we’ve offered will give you additional practice opportunities to strengthen your skills.

Remember that consistent practice and a strong grasp of fundamental mathematical concepts are key to excelling in the AEIS examination. If you need further guidance or personalized support in your AEIS preparation journey, EduFirst Learning Centre is here to help.

Our small class sizes, experienced teachers, and comprehensive curriculum make us the ideal partner for your AEIS preparation. We understand the challenges international students face when adapting to Singapore’s education system and have developed effective strategies to help them succeed.