# 8th Grade Diagnostic Math Test

Math Tests We’ll admit it: math learning isn’t an easy journey, and it’s even worse for 8th graders. The 8th grade is a key phase in every young learner’s math journey. This is because at this stage, kids are typically preparing to enter high school. For a math tutor or parent, this is the only chance that is left to stir or boost a child’s interest in math before they venture into high school.

But how do you ensure that they’ve learned everything they need? More importantly, how do you spot any learning gaps? This is where diagnostic tests come in. With an 8th grade math test, you’ll be able to equip your kid with everything they need for their math learning journey.

In this guide, we’ll explore the foundations of eight grade math tests and throw in a sample exercise as well.

Ready? Let’s get down to brass tacks.

## What Are Diagnostic Tests?

Picture this scenario. You’ve been feeling ill all weekend. You’re not sure what’s wrong and how to fix it. By Monday morning, you can barely lift your arm. So, you pop into the doctor’s office and ask for a test to figure out what’s wrong. Once he has made his diagnosis, he then proposes a treatment plan and you get back to yourself.

Diagnostic math tests work pretty much the same way as a doctor’s diagnosis. They’re designed to evaluate and test your child’s math knowledge to determine their fluency and spot any learning gaps. An eight grade math test is a prequel to the “treatment plan” (i.e. further lessons and teaching strategies).

## The Importance of Diagnostic 8 Grade Math Tests

Diagnostic math tests are essential for every learner. If you aren’t sure why your 8th grader needs one, here are a few reasons why these assessments are important:

### To spot learning gaps

More often than not, we go through life making assumptions about our kids and students. You expect that your 8th grader should understand certain math concepts and skills because they’ve already been taught. But what if they don’t? What if there’s a learning gap lurking and you’ve missed it?

A diagnostic mathematics test grade 8 will help you evaluate your child’s knowledge and see if they’re on track with the rest of their peers. Consequently, you’ll be able to spot any cracks in the system and figure out the problem areas.

### To ensure that students are taught the right way

It’s not enough to simply spot learning gaps. What do you do with the information you’ve been provided with? A diagnostic math test doesn’t just identify weaknesses; it also offers insight about the students’ preferred learning style. In most cases, learning gaps exist because students are taught the wrong way. With math tests for 8th grade, you’ll get further insight into strategies for teaching your kid.

### To provide progress reports and feedback

For any tutor, feedback forms an integral part of communication with parents. Most parents expect a detailed report on how their kid is performing in class. With a diagnostic test, you can track your student’s progress and gaps and offer comprehensive feedback to parents.

Print out this 8th grade math test before you begin.

Answer all of the following questions:

1. John found a smartphone online for \$550. However, there was a 20% discount on the phone and a 5% sales tax. How much did he eventually have to pay for the smartphone?
2. If x=5 and y=3, find the value of y2x +3y.
3. Mary throws a coin in the air three times.

a) What are the different outcomes?

b) What is the probability of getting tails twice?

4. Mark finds a TV that costs \$600. However, after a discussion with the manager, he gets 25% off. Which of the following expressions is equivalent to the sum Mark pays after the deduction?
1. 1800 x 0.25
2. 600-600 x 0.25
3. 750 x 0.25
4. 700 x 0.20
5. x% of 200 is 30. Find the value of x.
6. If your car can transport you up to 100 miles away with only 6 gallons of gas, how many gallons of gas do you need to travel a distance of 2500 miles?
7. Solve for x in the following equation: 3x + 15= 30
8. If x=4 and y=6, the value of x2 X y-x =?
9. Solve the following problem: 33 + 52 = ? A. 33 B. 56 C. 52 D. 15
10. Solve this problem: (15-3) – (4-10)
11. If you buy a computer that costs \$700 and there’s a 4% sales tax attached, how much do you have to pay in total?
12. You earn \$15 each week plus an extra sales commission of \$0.50 for each customer. However, you want to earn a total of \$25 each week. Which equation can you use to find x, the number of customers you need to meet this target each week?
1. 2x +15 = 25
2. 0.50x +15 = 25
3. 50x + 15 = 25
4. X + 15 = 25.
13. At Mary’s school, 3 out of every 7 8th-grade girls try out for the cheerleading squad. If there are 175 8th-grade girls in the school, how many tried out for the cheerleading squad?
14. Mrs Williams has over 400 math papers to grade.

a) If she has graded 0.40 of the papers, how many does she have left?

b) If it takes her an average of 7 minutes to grade each paper, how long will it take to finish the papers left?

15. What value of x makes this equation true? 5x -10 = 15.
1. 15
2. 10
3. 5
4. 7

NOTE: A score of 12 and above on this math test is an indication that the learner has all the math skills required for 8th graders. If your child or student struggles with this assessment, there are learning gaps that need to be filled.

## What Math Skills Are Evaluated in an 8th Grade Math Test?

As we mentioned earlier, the 8th grade is a crucial phase in every young learner’s journey. At this stage, they become acquainted with a wide range of math concepts and skills designed to ease their transition into high school. To paint a clearer picture for you, here’s a breakdown of all the math skills that are taught and evaluated in an 8th grade math test:

### Identifying rational and irrational numbers

Rational numbers are numbers that can be written as a ratio of two integers. On the other hand, an irrational number is a number that cannot be written as the ratio of two integers. In the 8th grade, kids learn all about rational and irrational numbers. They’ll learn how to identify these numbers and determine whether a number is rational or irrational.

### Pythagoras Theorem

In 8th grade, kids begin to delve further into geometry, and the study of triangles in particular. They’ll learn about the Pythagoras Theorem which states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.” It is represented by the formula: a2 + b2= c2.

Kids will learn how to apply this theorem when solving for all sides of a triangle.

### The binary number system

The binary (base two) number system is an essential concept that kids need to learn in 8th grade. Kids will learn how the binary system plays out in the real world, especially when it comes to computer technology and AI. They’ll also go a step further to learn how non-base ten numbers can be expressed as equivalent numbers in base ten.

### Expressions and equations

In 8th grade math, the curriculum is mainly geared towards equations and mathematical expressions. Kids will learn all about the relationship between two variables. They’ll also work with the different types of equations: linear equations, linear functions, and even the systems of linear equations.

## Look Online for More Math Help

Ready to take your child’s learning journey to a new level? Set up a diagnostic 8th grade math transformations test for them. An 8th grade end of year math test will help you equip your kid with all the math skills they need. If you’re looking for a wide range of options, you can find help online. However, if you’re in need of a hard-hitting, efficient route, check out Brighterly’s evaluation lesson. This package includes a comprehensive tutorial session that will test their knowledge and spot any learning gaps.

We hope this guide helps. Good luck!

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