How to Ace Mathematics Tests for Selective Schools

If you're getting ready for selective school exams, don't worry about using complicated formulas. The important thing is to understand the basic concepts and when to use them. These tests, like ACER and Edutest, check your knowledge and reasoning skills. It's a good idea to review math concepts through a course before the test day.

ACER exams focus on understanding the concepts and using tools in different situations. On the other hand, Edutest exams cover many different topics in math.

To perform well on these tests, you should follow these steps:

1. Prepare for the exam: Understand the exam structure and the time limit to manage your time better.

2. Read each question carefully: Make sure you understand the question before answering.

3. Find the answer: After understanding the question, find the right method or formula to get the correct answer.

4. Review for accuracy: Review and double-check your answer before finishing.

Math problems are often more complex than a simple equation and may involve fractions or algebra. You must know how the different parts of the problem fit together to solve it.

Math questions come in different shapes and sizes, so you must be prepared to analyze and solve various problems.

Mathematics Questions for Entrance Exam

Here are some math problems and explanations on how to solve them:

1.  5 - (-3) + 7

A. 9

B. 15

C. 22

D. - 15

Step 1: Simplifying Negative Signs

In this expression, we have a negative sign followed by another negative sign: "- (-3)."

We can simplify this by remembering that two negative signs side by side make a positive sign. So, "-(-3)" becomes "+3."

Now, the expression becomes: 5 + 3 + 7.

Step 2: Performing Addition

We can now evaluate the addition from left to right.

First, we add 5 and 3, which gives 8.

Our expression becomes: 8 + 7.

Then, we add 8 and 7, which gives 15.

Therefore, the answer to the expression "5 - (-3) + 7" is B. 15.

2. -24 ÷ (-6) ÷ 2

A. 8

B. 9

C. 2

D. 7

Let me break down the steps to solve the expression -24 ÷ (-6) ÷ 2:

Step 1: Simplifying the First Division

We begin by solving the first division operation: -24 ÷ (-6).

When we divide a negative number by another negative number, the result is a positive number. Thus, -24 ÷ (-6) equals 4.

Now, the expression becomes 4 ÷ 2.

Step 2: Simplifying the Second Division

Next, we solve the second division operation: 4 ÷ 2.

The division is simple, and 4 ÷ 2 equals 2.

Therefore, the final result is 2:

-24 ÷ (-6) ÷ 2 = 2

Hence, the answer is C. 2

3. Sarah purchased a laptop priced at $800. The store was offering a 15% discount on laptops. How much did Sarah have to pay at the store counter after the discount?

A. $850 

B. $720 

C. $680 

D. $680

To calculate the price Sarah had to pay at the store counter after the discount, we can follow these steps:

Step 1: Calculate the discount amount:

Discount amount = 15% of $800

= 0.15 * $800

= $120

Step 2: Subtract the discount amount from the original price:

Amount to pay at the store counter = $800 - $120

= $680

Therefore, Sarah had to pay $680 at the store counter after the discount.

So, the correct answer is C. $680.

4. What is 12% of $450?

A. $48 B. $54 C. $60 D. $72

To find 12% of $450, we can multiply the given number by the decimal equivalent of 12%.

Step 1: Convert 12% to its decimal form:

12% = 12/100 = 0.12

Step 2: Multiply the decimal equivalent by $450:

0.12 * $450 = $54

Therefore, 12% of $450 is $54.

So, the correct answer is B. $54

Solving Word Questions

One important skill in solving word problems is translating the information you're given into mathematical equations. By understanding key words and their symbols, like plus (+), minus (-), divided by (÷), multiplied by (×), and equals (=), you can figure out what calculations you need to do.

 If there's a number you don't know, you can represent it with letters like x, y, or z.

Converting Questions into Formulas

Once you've identified the important words and numbers, the next step is turning the question into a formula. Look for words like "sum," "added together," "difference," or "product" to know what kind of math operation to use. 

Use the right symbols for addition, subtraction, multiplication, division and equality.

Strategies for Problem Solving

If a word problem seems difficult, there are strategies to help you. One way is to substitute the answer options into your formulas using simple numbers. This lets you test different scenarios and find the solution more easily.

Key Rules to Remember:

Translate from English to Formulas: Understand what the question wants and turn it into a math equation.

Highlight Important Numbers: Find the numbers or quantities that are essential in the problem.

Use Symbols Wisely: Connect plus, minus, division, multiplication, and equal signs with the words that describe them.

Mathematics Problems for Practice

1. What is the average of the numbers in the list when the second highest number is removed?

List of numbers: 12, 18, 25, 30, 42, 50

Choices:

A. 23 

B. 26.75 

C. 32 

D. 27 

To find the average of the numbers in the list after removing the second highest number, we follow these steps:

Identify the second highest number in the list: In this case, it is 42.

Remove the second highest number from the list: 12, 18, 25, 30, 50.

Add up the remaining numbers: 12 + 18 + 25 + 30 + 50 = 135.

Count the number of remaining numbers: There are 5 numbers.

Divide the sum by the count to find the average: 135 ÷ 5 = 27.

Therefore, the average of the numbers in the list after removing the second highest number is 27 ( Choice D ).

2. Tom has a bag of fruits that contains apples and oranges. The bag weighs a total of 12 kg. However, 40% of the weight consists of oranges. How many kilograms of apples are in the bag?

A) 3.2 kg

B) 4.2 kg

C) 5.2 kg

D) 7.2 kg

Let's represent the weight of apples as 'x'.

According to the problem, 40% of the weight is of oranges, which means the weight of oranges is 40% of 12 kg.

Weight of oranges = 40% x Total weight

Weight of oranges = 40% x 12 kg

Weight of oranges = 0.4 x 12 kg

Weight of oranges = 4.8 kg

Now, to find the weight of apples, we can subtract the weight of oranges from the total weight:

Weight of apples = Total weight - Weight of oranges

Weight of apples = 12 kg - 4.8 kg

Weight of apples = 7.2 kg

Therefore, the correct answer is option D) 7.2 kg.

3. Sarah is planning a road trip. She drives at an average speed of 60 miles per hour (mph). She wants to travel a total distance of 240 miles. How long will it take her to reach her destination?

A. 2 hours 

B. 3 hours 

C. 4 hours 

D. 5 hours

To calculate how long it will take Sarah to reach her destination, we can use the formula:

Time = Distance / Speed

In this case, the distance is 240 miles and the speed is 60 mph. Plugging in these values, we get:

Time = 240 miles / 60 mph = 4 hours

Therefore, it will take Sarah 4 hours to reach her destination.

The correct answer is: C. 4 hours

Final Words

Preparing for mathematics tests for selective schools involves understanding basic concepts and knowing when to apply them, as these tests assess knowledge and reasoning skills. It is essential to familiarize yourself with the exam structure and time limit, carefully read each question, and select the appropriate method or formula to find the correct answer.

By practicing problem-solving strategies and reviewing math concepts, you can enhance your performance and increase your chances of success in these tests.