Welcome to our FREE Pre-Algebra Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help you succeed on the Pre-Algebra Math test. Not only does the test closely match what you will see on the real Pre-Algebra, but it also comes with detailed answer explanations.
For this practice test, we’ve selected 20 real questions from past exams for your Pre-Algebra Practice test. You will have the chance to try out the most common Pre-Algebra Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.
Use our free Pre-Algebra Math practice tests and study resources (updated for 2022) to ace the Pre-Algebra Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.
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10 Sample Pre-Algebra Math Practice Questions
1- Mr. Jones saves $2,500 out of his monthly family income of $55,000. What fractional part of his income does he save?
A. \(\frac{1}{22} \)
B. \(\frac{1}{11} \)
C. \(\frac{3}{25} \)
D. \(\frac{2}{15} \)
2- Four one-foot rulers can be split among how many users to leave each with \(\frac{1}{6} \) of a ruler?
A. 4
B. 6
C. 12
D. 24
3- Simplify the expression.
\((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 )\)
A. \(4x^3-12x^2\)
B. \(4x^4+4x^3-12x^2\)
C. \(8x^3-12x^2\)
D. \(x^4+4x^3-12x^2\)
4- In two successive years, the population of a town is increased by \(15\%\) and \(20\%\). What percent of the population is increased after two years?
A. \(32\%\)
B. \(35\%\)
C. \(38\%\)
D. \(68\%\)
5- What is the surface area of the cylinder below?
\(\img{https://appmanager.effortlessmath.com/public/images/questions/82.png}\)
A. \(48 {\pi} \space in^2\)
B. \(57 {\pi} \space in^2\)
C. \(66 {\pi} \space in^2\)
D. \(288 {\pi} \space in^2\)
6- A cruise line ship left Port A and traveled 80 miles due west and then 150 miles due north. At this point, what is the shortest distance from the cruise to port A in miles? ____________
7- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?
A. \((200) (0.70)\)
B. \((200) – 200 (0.30)\)
C. \((200) (0.15) – (200) (0.15)\)
D. \((200) (0.85) (0.85)\)
8- Solve: \(5 + 8 \times (- 2) – [4 + 22 \times 5] \div 6 = ? \)
A. \(-30\)
B. \(-20\)
C. \(-10\)
D. 0
9- Which of the following points lies on the line \(x+2y=4\)?
A. \((-2, 3)\)
B. \((1, 2)\)
C. \((-1, 3)\)
D. \((-3, 4)\)
10- 5 less than twice a positive integer is 83. What is the integer?
A. 39
B. 41
C. 42
D. 44
11- 11 yards 6 feet and 4 inches equal to how many inches?
A. 388
B. 468
C. 472
D. 476
12- Mr. Carlos’s family is choosing a menu for their reception. They have 3 choices of appetizers, 5 choices of entrees, 4 choices of cake. How many different menu combinations are possible for them to choose from?
A. 12
B. 32
C. 60
D. 120
13- The average of five consecutive numbers is 38. What is the smallest number?
A. 38
B. 36
C. 34
D. 12
14- What is the difference between the smallest 4–digit number and the biggest 4–digit number?
A. 6666
B. 6789
C. 8888
D. 8999
15- How many tiles of 8 cm\(^2 \) are needed to cover a floor of dimension 6 cm by 24 cm?
A. 6
B. 12
C. 18
D. 24
16- A ladder leans against a wall forming a \(60^ \circ \) angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?
A. 30 feet
B. 40 feet
C. 50 feet
D. 60 feet
17- The average weight of 18 girls in a class is 60 kg and the average weight of 32 boys in the same class is 62 kg. What is the average weight of all the 50 students in that class?
A. 60
B. 61.28
C. 61.68
D. 62.90
18- An angle is equal to one-fifth of its supplement. What is the measure of that angle?
A. 20
B. 30
C. 45
D. 60
19- In a stadium, the ratio of home fans to visiting fans in a crowd is 5:7. Which of the following could be the total number of fans in the stadium?
A. 12,324
B. 42,326
C. 44,566
D. 66,812
20- If \(40\%\) of a class are girls, and \(25\%\) of girls play tennis, what percent of the class play tennis?
A. \(10\%\)
B. \(15\%\)
C. \(20\%\)
D. \(40\%\)
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Answers:
1- A
2,500 out of 55,000 equals to \(\frac{2500}{55000}= \frac{25}{550}= \frac{1}{22} \)
2- D
\(4 \div \frac{1}{6} = 24 \)
3- B
Simplify and combine like terms.
\((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 ) {\Rightarrow} (6x^3-8x^2+2x^4 )-4x^2+2x^4-2x^3 {\Rightarrow}
4x^4+4x^3-12x^2\)
4- C
the population is increased by \(15\%\) and \(20\%\).
\(15\%\) increase changes the population to \(115\%\) of original population.
For the second increase, multiply the result by \(120\%\).
\((1.15) \times (1.20) = 1.38 = 138\%\)
38 percent of the population is increased after two years.
5- C
Surface Area of a cylinder \(= 2\pi\) r (r + h),
The radius of the cylinder is \(3(6 \div 2)\) inches and its height is 8 inches. Therefore,
Surface Area of a cylinder \(= 2\pi (3) (3 + 8) = 66\pi\)
6- 170
Use the information provided in the question to draw the shape.
\( \img {https://appmanager.effortlessmath.com/public/images/questions/22222222222222222222222222222.JPG
} \)
Use Pythagorean Theorem: \(a^2 + b^2 = c^2 \)
\(80^2 + 150^2 = c^2 {\Rightarrow} 6400 + 22500 = c^2 {\Rightarrow} 28900 = c^2 {\Rightarrow} c = 170\).
7- D
To find the discount, multiply the number by (\(100{\%} – \)rate of discount).
Therefore, for the first discount we get: \((200) (100{\%} – 15{\%}) = (200) (0.85) = 170\)
For the next \(15{\%}\) discount: \((200) (0.85) (0.85)\)
8- A
Use PEMDAS (order of operation):
\(5 + 8 \times (-2) – [4 + 22 \times 5] \div 6 = 5 + 8 \times (-2) – [4 + 110] \div 6 = 5 + 8 \times (-2) – [114] \div 6 = 5 + (-16) – 19
5 + (-16) – 19 = -11 – 19 = -30\)
9- A
\(x+2y=4\). Plugin the values of \(x\) and \(y\) from the choices provided. Then:
A. \((-2,3) x+2y=4(\rightarrow )-2+2(3)=4(\rightarrow )-2+6=4\) This is true!
B. \((1,2) x+2y=4(\rightarrow )1+2(2)=4(\rightarrow )1+4=4\) (This is NOT true!)
C. \((-1,3) x+2y=4(\rightarrow )-1+2(3)=4(\rightarrow )-1+6=4\) (This is NOT true!)
D. \((-3,4) x+2y=4(\rightarrow )-3+2(4)=4(\rightarrow )-3+8=4\) (This is NOT true!)
10- D
Let \(x\) be the integer. Then:
\(2x – 5 = 83\)
Add 5 both sides: \(2x = 88\)
Divide both sides by \(2: x = 44\)
11- C
\(11 \times 36 + 6 \times 12 + 4 = 472\)
12- C
To find the number of possible outfit combinations, multiply the number of options for each factor:
\(3 \times 5 \times 4 = 60\)
13- B
Let \(x\) be the smallest number. Then, these are the numbers:
\(x, x+1, x+2, x+3, x+4 \)
average \(= \frac{sum of terms}{number of terms} \Rightarrow 38 = \frac{x+(x+1)+(x+2)+(x+3)+(x+4)}{5} \Rightarrow 38= \frac{5x+10}{5} \Rightarrow 190 = 5x+10 \Rightarrow 180 = 5x \Rightarrow x=36 \)
14- D
The smallest 4–digit number is 1000, and the biggest 4–digit number is 9999. The difference is: 8999
15- C
The area of the floor is: 6 cm \(\times\) 24 cm = 144 cm\(^2 \)
The number of tiles needed \(= 144 \div 8 = 18\)
16- D
The relationship among all sides of the special right triangle
\(30^ \circ -60^ \circ – 90^ \circ \) is provided in this triangle:
\( \img {https://appmanager.effortlessmath.com/public/images/questions/10-explain-1.png} \)
In this triangle, the opposite side of the \(30^ \circ \) angle is half of the hypotenuse.
Draw the shape for this question:
The latter is the hypotenuse. Therefore, the latter is 60 ft.
\( \img {https://appmanager.effortlessmath.com/public/images/questions/10-explain-2.png} \)
17- B
average \(= \frac{sum of terms}{number of terms}\)
The sum of the weight of all girls is: \(18 \times 60 = 1080\) kg
The sum of the weight of all boys is:\( 32 \times 62 = 1984\) kg
The sum of the weight of all students is: \(1080 + 1984 = 3064\) kg
average \(= \frac{3064}{50}=61.28 \)
18- B
The sum of supplement angles is 180. Let \(x\) be that angle. Therefore,
\(x + 5x = 180\)
\(6x = 180\), divide both sides by 6: \(x = 30\)
19- A
In the stadium the ratio of home fans to visiting fans in a crowd is \(5:7\). Therefore, total number of fans must be divisible by \(12: 5 + 7 = 12.\)
Let’s review the choices:
A. \(12,324: 12,324 \div 12 = 1027\)
B. \(42,326: 42,326 \div 12 = 3,527.166\)
C. \(44,566: 44,566 \div 12 = 3,713.833\)
D. \(66,812: 66,812 \div 12 = 5,567.666\)
Only choice A when divided by 12 results in a whole number.
20- A
The percent of girls playing tennis is:
\(40 \% \times 25\% = 0.40 \times 0.25 = 0.10 = 10\%\)
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FAQs
Focus on learning the basics well, and you'll be able to pass a challenging pre-algebra class with ease.
- Pre-algebra Terminology. Memorizing vocabulary words might not seem like much fun, but pre-algebra is built upon basic terminology. ...
- Understand Equations. ...
- Track Your Work. ...
- Get Help.
Take Practice Tests for the TSIA2
One of the best ways to prepare for the TSIA2 is by taking practice exams. These practice exams can help students become familiar with the format of the test and the types of questions that will be asked in each section.
What should I study for the TSIA2 math test? ›
Need to prepare for the math section of the TSIA2 test? We offer a complete course for the new 2021 version of the test.
- Exponents.
- Factors and multiples.
- Greatest Common Factor.
- Integers and evaluating expressions.
- Order of Operations.
- Expressions, equations, and formulas.
- Inequalities.
- Decimals and percents.
Pre-algebra is a common name for a course in middle school mathematics in the United States, usually taught in the 7th grade or 8th grade. The objective of it is to prepare students for the study of algebra.
Can you skip Pre-Algebra? ›
Some math programs will tell you that you can skip Pre-Algebra and still have success in Algebra 1.
Is Pre-Algebra easy? ›
That depends on how good you are at math altogether. If you are good at math then it will be easy. It also depends on your tutor, grad level, and what you are doing.
What happens if you fail TSIA2? ›
You cannot pass or fail the TSI assessment. Based on how you perform, you may either enroll in: College-level courses that match your skill level, or. College readiness courses or interventions to improve your skills and prepare you for success in college-level courses.
Is a 990 a good TSI score? ›
College-ready Mathematics scores: If you score between 950 to 990 on the Math Multiple Choice, you are determined to be college-ready. If you score below 950 on the MC, you are routed to the Diagnostic test. If you score above 6 on the Diagnostic test, you are considered college-ready.
Is 950 a good TSI math score? ›
For TSI Assessment, v2 (TSIA2), administered AFTER 1/11/21: The minimum passing standards for the TSIA2 are as follows: Mathematics: a College Readiness Classification (CRC) score of at least 950; or a CRC score below 950 and a Diagnostic level of 6.
What kind of Math is on the TSIA2 Math test? ›
The TSIA2 Mathematics test covers four main categories: Quantitative Reasoning, which includes calculating ratios, proportions, and percents, as well as identifying, manipulating, and interpreting linear equations and expressions. problems in context.
The TSIA includes the subject areas of math, reading, and writing. The TSIA2 will include math and one section encompassing English, Language Arts, and Reading, which we'll call ELAR. The math content area will have a more balanced focus on a variety of math reasoning skills with less heavy reliance on algebra.
How many questions are on TSIA2 Math? ›
The Mathematics TSIA2 components consist of a multiple-choice college readiness classification (CRC) test (20 questions) to assess if a student is college ready or not and a multiple-choice diagnostic test (48 questions) designed to identify strengths and weaknesses.
Is Pre-Algebra harder than algebra? ›
Algebra has much more advanced concepts than pre-algebra. You learn about laws of exponents, logarithms, fundamental theorems, and complex numbers, conic sections, etc. Pre-algebra helps students to have the basic command of algebra topics.
Is grade 8 Pre-Algebra? ›
Pre-Algebra is a math class typically taken before Algebra I to prepare your student for success in Algebra I. It is normally taken in 8th grade. Pre Algebra is a math class typically taken before Algebra I to prepare your student for success in higher level math classes.
Is Pre-Algebra honors? ›
The Pre-Algebra Honors course moves at a rigorous pace as it prepares students with the foundation of skills needed for entry into the eighth-grade Algebra I Honors course. Mastery of many basic skills (such as decimal and fraction operations) is assumed as these topics will be extended to higher levels.
What age is Pre-Algebra? ›
PRE-ALGEBRA for VISUAL LEARNERS (Ages 10 to Adult; 1 to 4 Students) This hands-on tool is designed to teach the concepts behind the rules of integers and basic algebra.
How important is Pre-Algebra? ›
Pre-algebra provides students with the opportunity to obtain a higher level of mastery and application of skills such as fractions, decimals, integers and percentages. This is when students really start learning and applying basic knowledge of simple variables, equations and exponents.
Can you graduate if you fail algebra 1? ›
Students who fail Algebra I are required to recover the credit during high school to earn a diploma, and online credit recovery courses have become a popular strategy in schools and districts around the country.
How long does it take to learn Pre-Algebra? ›
Note: This course was originally designed as a course in a Teacher Education program. Therefore, it might take more than 36 weeks, or 180 days, to complete. Depending on the level of your students, some units may go faster or slower than others.
What is 9th grade math called? ›
9th grade math usually focuses on Algebra I, but can include other advanced mathematics such as Geometry, Algebra II, Pre-Calculus or Trigonometry.
Eighth-grade math is typically a course in pre-algebra to help prepare students for high school algebra.
Is a 930 a good TSI score? ›
This student will be considered college ready. A student earned a 930 on the ELAR CRC portion of the TSIA2, a 6 on the diagnostic portion of the TSIA2, and a 6 on the TSIA1 Essay portion. This student will be considered college ready.
What is a bad TSI math score? ›
You are considered college ready if your score falls within the range of 350–390. If your score is 349 or lower, you may be placed in a developmental course or intervention.
What if I can't pass the TSI? ›
If you do not pass one or all parts (reading, writing and math) of the TSI Assessment, you may be required to enroll in developmental education coursework or accelerated intervention before you can enroll in a college credit course for the subject in which you did not pass.
Can you use a calculator on the TSIA2? ›
Note: Handheld calculators of any type are not permitted for use with the online TSIA2 Mathematics Test. Some, but not all, of the math questions contain one or more pop-up calculators for use in solving problems asked.
What is the highest grade you can get on the TSI? ›
Once you enter your essay into an on-screen textbox and submit it for scoring, the system automatically evaluates the essay and returns a score from 1 to 8, as well as a holistic score description that summarizes the quality of your essay.
How many questions can you get wrong on the TSI math? ›
In TSI math you will need a minimum score of 350, which means you can miss between 1 and 3 questions.
What is a passing TSIA2 math score? ›
What Is The Passing Score For The TSIA2 Test? Mathematics: A College Readiness Classification (CRC) score of at least 950; or a CRC score below 950 and a Diagnostic level of 6. English Language Arts Reading: A College Readiness Classification (CRC) score equal to or greater than 945 and an essay score of at least 4.
Is TSI required for college? ›
If you are an incoming college student in Texas, you are required to take the TSI Assessment — unless you are already exempt (read below) — to determine your readiness for college-level work.
How do I become exempt from TSI test? ›
A student must achieve a combined score of 40 on the English and Reading (E+R) tests to be exempt for both reading and writing or ELAR sections of the TSI Assessment. A student must achieve a minimum score of 22 on the mathematics for an exemption in math. There is no composite score.
How many times can I take the TSI Assessment? There is no limit to the number of times the TSI Assessment may be taken. However, the TSI Assessment fee of $50 must be paid each time the TSI Assessment is taken at Texas Tech University.
Is the TSI timed? ›
How long does the TSI Assessment take? The TSI Assessment is not a timed test. The average time to complete all 3 sections of the test is 3–5 hours.
Is tsia and TSIA2 the same? ›
The TSIA2 will differ from the TSIA by having reading and writing combined into one section which will be called the English Language Arts Reading (ELAR) section. There will still be a Mathematics section for the exam.
How many do you have to get right to pass the math TSI? ›
Mathematics: a minimum score of 950 or less than 950 and a diagnostic level 6. ELAR (English language arts, writing and reading): a minimum score of 945 on the multiple-choice section with an essay score of 5-8, or less than 945 on the multiple-choice section, a diagnostic level of 5 or 6, and an essay score of 5-8.
Is TSIA2 harder than TSI? ›
Here are the basic facts: The content tested on the TSIA2 is largely the same as that tested on the old TSI Assessment. The skills have just been slightly reorganized and only a few new ones have been added. The test administration process is where things have been altered, and that is likely a very good thing for you.
Do you need a calculator for the math TSI? ›
The mathematics portion of the TSI test contains 20 questions. The test covers data analysis, geometry, and algebra on both intermediate and basic levels. Students are not allowed to use a calculator when taking a TSI assessment. A pop-up calculator is embedded in the test for some questions.
How do I pass my math TSI? ›
How do I study for the TSI Math?
- Pre-Tests. Start each section with a short pre-test to determine if you already know the material.
- Instruction and Guided Practice. Use video and audio explanations as a core component of your TSI math test prep.
- Practice Tests. Make sure you're ready for the real thing.
For decades, a math puzzle has stumped the smartest mathematicians in the world. x3+y3+z3=k, with k being all the numbers from one to 100, is a Diophantine equation that's sometimes known as "summing of three cubes."
What is the hardest math? ›
5 of the world's toughest unsolved maths problems
- Separatrix Separation. A pendulum in motion can either swing from side to side or turn in a continuous circle. ...
- Navier–Stokes. ...
- Exponents and dimensions. ...
- Impossibility theorems. ...
- Spin glass.
It's called a Diophantine Equation, and it's sometimes known as the “summing of three cubes”: Find x, y, and z such that x³+y³+z³=k, for each k from one to 100.
Pre-Algebra tees up Algebra for 5th to 8th graders.
Can you fail algebra 1 in 8th grade? ›
Most likely you will pass to the 9th grade BUT you will still have to take credit recovery class to pass algebra. You have to have algebra to graduate.
What happens if I fail Pre-Algebra in 8th grade? ›
You probably will still move to the 10th grade but be required to repeat it until you pass it with at least a D grade. Perhaps you can re-take the class in a summer session. If you fail algebra a second time the school may offer a different math class as a substitute. Ask your counselor.
Is Pre-Algebra accelerated? ›
“Accelerated”—the course is taken EARLIER than it would normally–6th grade Pre-algebra, 7th grade Algebra I, and 8th grade Algebra I are all accelerated a year or two. For example: In APS, the base case is Algebra I in 9th grade. Any student taking Algebra I earlier than 9th grade is considered 'accelerated'.
Is Pre-Algebra advanced? ›
Since Pre AP Algebra I is an advanced high school math course, your child's grade is used to calculate their high school GPA and it will transfer to the high school.
What grade is calculus? ›
Calculus is usually taken by high-school seniors or university freshmen, but can occasionally be taken as early as tenth grade.
How can I help my child with Pre-Algebra? ›
Making Pre-Algebra Simple
- Learn a Topic One Step at a Time. Students will often struggle with math when the class moves on to the second step of a topic before they are competent with the first one. ...
- Draw the Process. ...
- Repetition. ...
- Show Every Step of the Solution. ...
- Practice with Games.
Pre Algebra is the first math course in high school and will guide you through among other things integers, one-step equations, inequalities and equations, graphs and functions, percent, probabilities. We also present an introduction to geometry and right triangles.
Is algebra 1 hard for a 7th grader? ›
In math, concepts begin to jump from concrete to more abstract, making 7th grade algebra a challenging course for many students. It's important that you set your child up for success when they move up to 8th grade.
Why do kids struggle with algebra? ›
Algebra is overwhelming for many students because it's the first math class they take where they must wrestle with variables, abstract concepts, and creative problem solving. And there's often not enough done in the classroom to connect Algebra to their everyday lives and explain why it's worth understanding.
A = B, A + C = B + C, and A - C = B - C have the same solutions (where A, B, and C are algebraic expressions). solutions (where Aand B are algebraic expressions and C is any nonzero constant, C ≠ 0).
What is the best age to start algebra? ›
Typically, algebra is taught to strong math students in 8th grade and to mainstream math students in 9th grade. In fact, some students are ready for algebra earlier.
Should 8th graders take Pre-Algebra? ›
Eighth-grade math is typically a course in pre-algebra to help prepare students for high school algebra.
How do I know if my child is ready for algebra? ›
Here are some of the math concepts and skills students need to master in preparation for Algebra 1:
- Fluency with basic math operations (addition, subtraction, multiplication, and division)
- A solid understanding of fractions, percents, and decimals--and how they're all related.
- Ratio and proportion.
- Probability.
A pre-algebra course gives students the fundamental knowledge they'll need to do well when it comes time to take Algebra 1. Pre-algebra introduces topics like percentages, decimals and linear equations – all of which will be useful for students in Algebra 1.
What class comes after Pre-Algebra? ›
The typical order of math classes in high school is:
Geometry. Algebra 2/Trigonometry. Pre-Calculus. Calculus.
