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Test your knowledge of introductory Algebra with this Algebra practice exam. Whether you are studying for a school math test or looking to test your math skills, this free practice test will challenge your knowledge of algebra.
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Free Math Worksheets — Over 100k free practice problems on Khan Academy
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That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!
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High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.
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SAT Math Practice Test
Use our SAT math practice test below to study for your exam. Our exam is full-length and 100% free.
We have updated our exam for the newest version of the SAT (digital). For help with other subjects, visit our free SAT test home.
Start with our first SAT Math practice exam.
This exam is a replica of the actual exam to help you best prepare.
More SAT Math Questions
If you want to practice for the math portion of the exam in an untimed environment, use our practice sets below.
SAT Math Practice Sets
SAT Math Overview
Beginning in the spring of 2024, the SAT is switching to a fully digital format. This new format helps streamline the exam for students.
The SAT math section includes 2 sections:
- Module 1: 22 questions, 35 minutes
- Module 2: 22 questions, 35 minutes
75% of the questions on the SAT math section will be multiple-choice. The other 25% will be student produced response questions.
There will be 4 main topics covered on the SAT math section:
- Algebra (13 -15 Questions)
- Advanced Math (13-15 Questions)
- Problem-Solving & Data Analysis (5-7 Questions)
- Geometry & Trigonometry (5-7 Questions)
Algebra questions include the following subtopics:
- Linear equations in 1 variable
- Linear equations in 2 variables
- Linear functions
- Systems of 2 linear equations in 2 variables
- Linear inequalities in 1 or 2 variables
Advanced math questions include the following subtopics:
- Equivalent expressions
- Nonlinear equations in 1 variable
- Systems of equations in 2 variables
- Nonlinear functions
Problem-solving and data analysis questions include the following subtopics:
- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of center and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and experiments
Geometry and trigonometry questions include the following subtopics:
- Area and volume formulas
- Lines, angles, and triangles
- Right triangles and trigonometry
You can learn more about SAT math by visiting the official CollegeBoard website .
Want to practice for another section of the SAT? Go to our SAT test practice page to find more exams.
SAT Math Test FAQs
Can you use a calculator on sat math section.
On the new version of the SAT (digital SAT), you will be able to use a calculator for all questions.
On the old version of the SAT (written SAT), there is 1 section in which you will be able to use a calculator and 1 section in which you will not be able to use one.
What kind of math is tested on the SAT?
The math section covers 4 main topics:
- Advanced Math
- Problem-Solving and Data Analysis
- Geometry and Trigonometry
Are all questions on SAT math multiple-choice format?
No, not all the questions are multiple-choice format. There will be questions that are student produced (student produced responses).
These questions will require you to write in your own answers. About 25% of the questions will be SPR’s.
- Authored By: Adam Groden
- Last Updated August 24, 2023
Choose Your Test
Sat / act prep online guides and tips, complete list of free sat math practice problems.
Need to study for the SAT Math section but don't know where to start? On a budget, too? Not to worry! In this article, we've put together a comprehensive list of all the best (and free!) SAT Math study materials and guides currently available online.
Note: For info on the best SAT study materials you have to pay for, check out our picks for top SAT prep books.
Feature Image: Alan O'Rourke /Flickr
The Importance of Using High-Quality SAT Math Materials
It is incredibly important to get your study materials from the right places. The SAT is a very specific kind of test, and there are many (many!) websites and programs out there that, sadly, offer only poor-quality SAT resources.
If you study using mainly inferior SAT materials, you won't get a clear sense as to how you'll do on test day. Test prep is about assessing and improving upon your current level, but you won't be able to do this if you get a false sense of your skills based on poor study materials. Ultimately, products and test questions that don't accurately reflect the SAT are a waste of time.
Therefore, it's best to prioritize official SAT materials. The SAT is designed by the College Board, and their free materials are by far the best place to start studying. From here, you can branch off into programs and materials that use (or closely resemble) official SAT material.
Now, let's look at the best resources you can use for free official SAT Math practice questions.
Top 5 Free Resources for Quality SAT Math Practice
In this section, we go over the top five free resources you can use for quality SAT Math prep.
#1: The College Board
As the creator and issuer of the SAT, the College Board is the best place to begin for collecting your free SAT Math study materials. The official website offers full-length SAT practice tests and practice questions for all sections.
The closest you can get to taking the actual SAT is the free, full-length practice exams in Bluebook , College Board’s online testing platform. The six available practice tests provide you with a sneak peek of the interface, format, and scoring of the online test, so they’re a useful tool as you prepare for the digital format.
In addition to full-length exams, Bluebook also offers previews of individual questions from the actual SAT. Even these are useful as you’re trying out the digital interface and learning what kinds of math problems to expect.
Note that if you have testing accommodations that allow you to take the test on paper, you'll want to practice on the the official, printable practice tests created for the digital SAT.
Old Official Full-Length SAT Practice Tests
While the newest practice tests will be most useful for your prep, you can also use these old (pre-digital) SAT practice tests, though keep in mind there will be differences
There are 10 official practice tests from the 2016-2023 version of the SAT. Each test comes with an answer key and in-depth answer explanations to help you understand why you got questions wrong.
Although the general format of these tests is quite different, the individual math questions will be fairly similar to what you'll see on the digital SAT. Just keep in mind that they should be used for practicing skills and concepts rather than estimating your score.
#2: Khan Academy
Khan Academy is a nonprofit and partner of the College Board that offers a free online SAT prep program and practice questions.
While most of the questions come from official SAT practice materials (such as those linked above), others have been created or adapted with approval from or in tandem with the College Board itself.
Sign up for a free Khan Academy account to get access to SAT study questions and materials, complete with guides and explanation videos to aid your studying.
#3: PrepScholar SAT Blog
Here at PrepScholar, we offer tons of free resources, including detailed guides on every SAT math topic and a complete collection of our best SAT Math articles . All our guides include definitions and explanations, examples of how you'll see the topic on the test, and real SAT practice questions with detailed answer explanations.
Browse our SAT Math guides below to get started! All guides are arranged by topic.
Integers (Basic)
Integers (Advanced)
Fractions, Ratios, and Proportions
Statistics (Mean, Median, Mode)
Probability
Single Variable Equations
Systems of Equations
- Completing the Square
Coordinate Geometry
Lines and Slopes
Reflections, Translations, and Rotations
Plane and Solid Geometry
Lines and Angles
Solid Geometry
- Trigonometry
The 28 Critical SAT Math Formulas You MUST Know
In addition, we have strategy guides that will help you solve numerous SAT Math problems across the board:
Plugging in Answers
Plugging in Numbers
If you find our guides and quizzes helpful, you can also sign up for a free five-day trial to our test prep program. Our program assesses your current strengths and weaknesses and adapts based on your progress. It gives you practice questions tailored to your areas of needed improvement and provides answer explanations for all questions.
All our questions are based off real SAT test questions and, though the full program is not free, we guarantee your money back if you do not improve by 160 points.
#4: CrackSAT.net
CrackSAT is a free, unofficial SAT website offering PDFs of official SAT practice tests and an array of both official and unofficial SAT Math questions.
Many of the questions on CrackSAT come from SAT prep books by well-known test-prep companies including The Princeton Review and Kaplan. Though generally solid, unofficial SAT questions can vary wildly in quality, so don't rely on only these to give you a sense of your math abilities. Rather, it's best to use this website after you've exhausted all the official SAT resources above.
What's especially nice about this website is its organization: math questions are available in both multiple-choice and grid-in categories to give you the full range of math practice. You can also browse problems by concept (e.g., linear functions , exponents and radicals , etc.).
You've gathered all your study material ... so now what?
How to Use SAT Math Study Materials Effectively: 6 Tips
It's just as important to know how to best utilize your SAT study materials as it is to know how to access them. These six tips will help you achieve your highest SAT Math score on test day.
#1: Take a Full Practice Test in One Sitting
You're probably most concerned about your SAT Math score, but it's still important to take a full SAT practice test so you can see how you'll fare on test day. Although answering one or two Math questions might not be too much of a challenge for you, in truth the SAT is a marathon—and if you aren't prepared, you'll likely be exhausted by the end of it. And exhaustion can lead anyone to make mistakes!
So before you dedicate your focus to the SAT Math section, take an official SAT practice test on the Bluebook app to see how your Math score fits into the larger test-taking picture. Make sure to take the whole test in one sitting; this will help you build endurance for test day.
#2: Use Proper Timing and Pace Yourself
As you take SAT practice tests and any Math-specific sections, be sure to use the same time limits you'll have on test day.
The chart below shows how much time you'll have on each SAT section as well as how much time you should (approximately) spend per question. Note that each section is split into two modules of equal lengths.
You'll have about 9 5 seconds per SAT Math question. Some questions might take you less or more time, but keep practicing so that you're not consistently spending too long on a single math question.
Remember that accuracy is only half the battle—you have to actually finish the questions within the time limits if you want to get a high Math score!
That said, don't worry if you run out of time while taking your first SAT practice test. This is completely normal and gives you a starting point from which you can later improve.
#3: Review Your Mistakes
It's one thing to take an SAT Math test, but you also need to look over your results and identify any patterns in your correct and incorrect answers. Do you tend to get the last few questions wrong on each Math section? Do function questions just seem to throw you for a loop?
First, figure out what went wrong. Then, see how you can pick up some easy points and diligently target those areas in your prep. (Remember that each Math question, no matter its difficulty, is worth the same number of points!)
#4: Target Your Biggest Weaknesses
Once you've pinpointed patterns in the errors you make, it's time to dig deeper and examine your biggest weaknesses. Your ultimate goal will be to tailor your studying so that you can focus on improving the areas you struggle with the most.
Since your overall objective is to answer as many questions as accurately as possible, you'll want to dedicate the majority of your study time to improving your weaknesses, rather than to reviewing material you already know well.
Refreshing your known material again and again might make you feel productive and confident, but it doesn't do a whole lot to improve your score. Your best bet is to focus on your problem areas by practicing and expanding your knowledge base.
#5: Set a Study Schedule
Don't be tempted to cram right before the test . You might have a busy schedule and feel as if your only option is to cram for the SAT, but improvement really happens over time. We generally advise giving yourself at least three to six months to study for the SAT.
If you don't have a lot of time left before test day, however, don't give up! No matter how much time you've got for studying, it is possible to come up with a balanced SAT study plan .
First, calculate the amount of time you have before your test date . (For example, say you've got a month before your test .)
Next, assign yourself at least three full practice tests (in addition to your normal study materials) and spread them out over the course of your study schedule. If you only have a week or so before test day, this probably won't be possible. In this case, try to fit in at least one or two practice tests wherever you can.
Nothing else replicates the SAT experience like a full practice test does, so don't underestimate its importance in your prep!
#6: Not Seeing Any Improvement? Get Additional Prep Help
Some students prefer to do all of their SAT studying by themselves, but others work better with a little guidance.
If the SAT subject matter just isn't making sense to you or you need help prioritizing your time, an SAT tutor or prep program (or both!) are excellent options to try. Both can give you that final push you need to stay focused and maximize your SAT Math score.
At PrepScholar, we offer expert SAT tutoring services in addition to a fully customizable SAT prep program . For more info, read our guides on how to find the best SAT tutor for you and how much you should spend on tutoring .
Targeted and careful practice, rest, and confidence: the perfect recipe for SAT success.
What's Next?
Don't know where to start? Take a look at our list of all math topics on the SAT Math section , and target your weaknesses with our individual SAT Math guides .
Want to know what the hardest SAT Math questions are? We've compiled a list of the 13 most challenging SAT Math questions , along with answer explanations for each.
Bitten by the procrastination bug? Time running out until test day? Check out how to beat the urge to procrastinate , and learn how to balance time for your studies.
Looking to get a perfect SAT Math score? Dig into our guide to getting a perfect 800 on SAT Math , written by a perfect scorer!
Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time.
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Have any questions about this article or other topics? Ask below and we'll reply!
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120 Math Word Problems To Challenge Students Grades 1 to 8
Written by Marcus Guido
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Use Prodigy to spark a love for math in your students – including when solving word problems!
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You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.
A jolt of creativity would help. But it doesn’t come.
Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.
This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.
There are 120 examples in total.
The list of examples is supplemented by tips to create engaging and challenging math word problems.
120 Math word problems, categorized by skill
Addition word problems.
Best for: 1st grade, 2nd grade
1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?
2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?
3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?
5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?
6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?
7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?
8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?
Subtraction word problems
Best for: 1st grade, second grade
9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?
10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?
11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?
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12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?
13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?
14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?
15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?
16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?
Multiplication word problems
Best for: 2nd grade, 3rd grade
17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?
18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?
19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?
20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?
21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?
Division word problems
Best for: 3rd grade, 4th grade, 5th grade
22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?
23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?
24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?
25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?
26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?
Mixed operations word problems
27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?
28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?
29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?
30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?
Ordering and number sense word problems
31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?
32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?
33. Composing Numbers: What number is 6 tens and 10 ones?
34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?
35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?
Fractions word problems
Best for: 3rd grade, 4th grade, 5th grade, 6th grade
36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?
37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?
38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?
39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?
40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?
41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?
42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?
43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?
44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.
45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?
46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.
Decimals word problems
Best for: 4th grade, 5th grade
47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?
48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?
49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?
50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?
51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?
52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?
Comparing and sequencing word problems
Best for: Kindergarten, 1st grade, 2nd grade
53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?
54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?
55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?
56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?
57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?
58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?
59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?
Time word problems
66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?
69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?
70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?
71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?
Money word problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade
60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?
61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?
62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?
63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?
64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?
65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?
67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.
68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?
Physical measurement word problems
Best for: 1st grade, 2nd grade, 3rd grade, 4th grade
72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?
73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?
74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?
75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?
76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?
77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?
78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?
79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?
80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?
81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?
Ratios and percentages word problems
Best for: 4th grade, 5th grade, 6th grade
82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?
83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?
84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?
85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?
86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?
87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?
88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?
Probability and data relationships word problems
Best for: 4th grade, 5th grade, 6th grade, 7th grade
89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?
90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?
91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.
92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?
93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?
94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?
95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .
Geometry word problems
Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade
96. Introducing Perimeter: The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?
97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?
98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?
99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?
100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?
101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?
102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?
103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?
104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?
105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?
106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?
107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?
108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?
109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?
110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?
111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?
112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?
113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?
114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?
Variables word problems
Best for: 6th grade, 7th grade, 8th grade
115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?
116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.
117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.
118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.
119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.
120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?
How to easily make your own math word problems & word problems worksheets
Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:
- Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.
A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.
Final thoughts about math word problems
You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.
Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.
The result?
A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.
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QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.
- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.
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Math Word Problems
Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.
There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:
- Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
- Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
- Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
- Calculate : Use your strategy to solve the problem.
- Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.
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Maths Quiz Questions
We are providing here maths quiz questions for children to help them increase their knowledge of the subject. These questions are prepared based on fundamental mathematical concepts. The problems here are provided with four multiple answers and students have to choose the right answer. The questions here could be solved by students of all the classes from 6 to 10, as they are based on basic arithmetic operations and geometrical concepts. Thus, on solving them they can also participate in quiz competitions conducted in schools.
Solving these quizzes will help students to gain more knowledge and boost their problem-solving skills. These questions are very easy to solve and will not take much time. Hence, it is recommended to all the children to solve each one of them and test their abilities.
Maths Quiz Questions with Answers (MCQs)
Let us answer here some of the quizzes which are based on simple arithmetic concepts. These problems are based on fundamental concepts, which students can easily answer without picking up a pen and paper.
Q.1. What is the sum of 130+125+191?
Q.2: If we minus 712 from 1500, how much do we get?
Q.3: 50 times of 8 is equal to:
Q.4: 110 divided by 10 is:
D. None of these
Q.5: 20+(90÷2) is equal to:
Q.6: The product of 82 and 5 is:
Q.7: Find the missing terms in multiple of 3: 3, 6, 9, __, 15
Q.8: Solve 24÷8+2.
Q.9: Solve: 300 – (150×2)
Q.10: The product of 121 x 0 x 200 x 25 is
Q.11: What is the next prime number after 5?
Also, read:
- Class 8 Maths MCQs
- Class 9 Maths MCQs
- Class 10 Maths MCQs
Maths Quizzes and Answers
Here are some quiz questions which children should be able to answer quickly.
Q.12: The circumference of the circle is also sometimes called:
Answer: Perimeter of a circle
Q.13: 90 – 35 is equal to:
Q.14: 72 divided by 8 is equal to:
Q.15: How many sides does a decagon have?
Answer: Ten
Q.16: Is -5 an integer? Yes or No.
Answer: Yes
Q.17: The value of pi is equal to:
Answer: 22/7 or 3.14
Q.18: 9 x 7 is equal to:
Q.19: Is triangle a two-dimensional or three-dimensional shape?
Answer: A two-dimensional shape
Q.20: An equilateral triangle has two of its sides equal. True or false?
Answer: False
All the sides of the equilateral triangle are equal.
Q.21: 10 is a natural number. True or false?
Answer: True
Q.22: -10 is a whole number. True or false?
Q.23: 8 raised to the power 0 is equal to:
Q.24: The largest 4 digit number is:
Answer: 9999
Q.25: The smallest 4-digit number is:
Answer: 1000
Q.26: The square of 8 is equal to:
8 2 = 8 x 8 = 64
Q.27: The square root of 5 is:
Answer: 2.23
Q.28: 3 is a perfect square. True or False?
Answer: False.
Q.29: Cube of 5 is equal to:
Answer: 125
5 3 = 5 x 5 x 5 = 125
Q.30: Cube root of 1331 is:
1331 = 11 x 11 x 11 = 11 3
Q.31: 27 is a perfect cube. True or False?
27 = 3 x 3 x 3= 3 3
Q.32: A square has all its angles equal to:
Answer: 90 degrees
Q.33: The area of rectangle is equal to:
Answer: Length x Breadth
Q.34: If a is the side of cube, then the volume of the cube is:
Answer: a 3
Q.35: A regular polygon has all its sides:
Answer: Equal
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Intermediate Algebra Problems With Answers - sample 2 :Find equation of line, domain and range from graph, midpoint and distance of line segments, slopes of perpendicular and parallel lines. Intermediate Algebra Problems With Answers - sample 3: equations and system of equations, quadratic equations, function given by a table, intersections of ...
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equation, solve. Practice Questions. Previous: Ray Method Practice Questions. Next: Equations involving Fractions Practice Questions. The Corbettmaths Practice Questions on Solving Equations.
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Good luck! Part 1: Order of Operations problems involving addition, subtraction, multiplication, and division. Problem 1:Simplify the numerical expression below. Answer. Problem 2:Simplify the numerical expression below. Answer. Problem 3:Simplify the numerical expression below. Answer.
For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8. There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:
Solution. John read the quarter of the time that Tom read. Tom read only two-fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read? Solution. Jim, Carla and Tomy are members of the same family. Carla is 5 years older than Jim.
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The numbers x , y , z and w have an average equal to 25. The average of x , y and z is equal to 27. Find w. Find x , y , z so that the numbers 41 , 46 , x , y , z have a mean of 50 and a mode of 45. A is a constant. Find A such that the equation 2x + 1 = 2A + 3 (x + A) has a solution at x = 2.
Q.32: A square has all its angles equal to: Answer: 90 degrees. Q.33: The area of rectangle is equal to: Answer: Length x Breadth. Q.34: If a is the side of cube, then the volume of the cube is: Answer: a 3. Q.35: A regular polygon has all its sides: Answer: Equal. The quiz questions based on Maths fundamentals are provided at BYJU'S for ...
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