[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-274409-105":59,"doc-detail-274409-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","grade-9-mathematics-sample-questions-and-explanations","Grade 9 Mathematics Sample Questions - and Explanations","","Grade 9 Mathematics sample questions with answer explanations covering key algebra and data skills. Problems include scientific notation with exponents, interpreting two-way tables to determine a percentage, identifying conditions for linear functions, computing distances using the Pythagorean theorem, solving linear equations, and classifying rational numbers and equivalent expressions. Additional tasks address comparing scales with powers of ten and drawing conclusions from scatter-related soccer data, with supporting worked solutions for correct choices.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/grade-9-mathematics-sample-questions-and-explanations/274409/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/grade-9-mathematics-sample-questions-and-explanations/274409.png","ImageObject",300,407,{"name":92,"@type":93},"Aditya","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",25,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you find the exponent in a scientific-notation area problem for a square microchip?","Question",{"text":113,"@type":114},"Square the given side length to get the area in scientific notation, then match the result to b × 10^a to read off the exponent a.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the percentage x determined from a Soap L and Soap M two-way table?",{"text":118,"@type":114},"First add the “Do Not Use Soap L” row entries to get the total not using Soap L. Then divide the “Use Soap M” entry in that row by the row total and convert to a whole-number percentage.",{"name":120,"@type":111,"acceptedAnswer":121},"What method finds the distance between two points such as (3, 20) and (11, 5)?",{"text":122,"@type":114},"Use the Pythagorean theorem: compute the absolute differences in x and y to get the legs, then set the hypotenuse squared equal to leg1^2 + leg2^2 and take the square root.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},274409,1789476939,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144},962085564549,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Grade 9 Mathematics Sample Questions  \n1. The side length of a certain square microchip, expressed in scientific notation, is 1.2 × 10 − 3 meter. If the area of this microchip is expressed in scientific notation as b × 10a square meter, what is the value of a?  \n2. A company surveyed 800 people about their use of Soap L and Soap M. The table shows the results.  \nSOAP SURVEY  \n\n|  | Use\u003Cbr>Soap M | Do Not\u003Cbr>Use\u003Cbr>Soap M |\n| --- | --- | --- |\n| Use Soap L | 148 | 252 |\n| Do Not Use\u003Cbr>Soap L | 264 | 136 |\n\nBased on the results, of those who do not use Soap L, x% use Soap M. What is the value of x, expressed as a whole number?  \n3. The values in the table represent a function. What value of R makes the function linear?  \n\n| x | y |\n| --- | --- |\n| − 4 | 2 |\n| − 1 | − 1 |\n| 3 | R |\n\n4. What is the distance, in units, between the points (3, 20) and (11, 5)?  \nE. 8 F. 15 G. 17 H. 23  \n3  \n5. 3 (x − 4) + 4x = 4 − x + 8 (6 + x)  \nWhat is the solution to the equation shown above?  \nA. x = 8  \nB. x = 65  \n[C.](C. no)[ no](C. no) solution  \nD. infinite number of solutions  \n6. Which expression represents a rational number?  \nE  3 8  \nF. π  \n_  \nG. √3  \n_  \nH. √83  \n2  \n7. Which expression is equivalent to −102?  \nA. − 68  \nB  1  612  \nC. 6 − 5  \nD. 612  \n3  \n8. Which table best represents alinear function?  \nE.  \nF.  \n\n| x | y |\n| --- | --- |\n| − 3 | 5 |\n| − 1 | 3 |\n| 0 | 1 |\n\n\n| x | y |\n| --- | --- |\n| − 2 | 7 |\n| − 1 | 4 |\n| 0 | 3 |\n\nG.  \nH.  \n\n| x | y |\n| --- | --- |\n| − 4 | − 17 |\n| − 3 | − 12 |\n| 1 | 8 |\n\n\n| x | y |\n| --- | --- |\n| − 1 | 3 |\n| 0 | 3 |\n| 2 | 5 |\n\n3  \n9. The diameter of Biological Cell A is  \n6 × 10 − 7 meter. The diameter of Biological Cell B is 3 × 10 − 8 meter. Which statement correctly compares the diameters of these two cells?  \nA. The diameter of Cell A is 2 times the diameter of Cell B.  \nB. The diameter of Cell B is 2 times the diameter of Cell A.  \nC. The diameter of Cell A is 20 times the diameter of Cell B.  \nD. The diameter of Cell B is 20 times the diameter of Cell A.  \n2  \n10.  \nSOCCER DATA  \n\n| Player | Seasons\u003Cbr>Played | Goals\u003Cbr>Scored |\n| --- | --- | --- |\n| Isabella | 3 | 5 |\n| Porter | 6 | 10 |\n| Jazmine | 4 | 6 |\n| Colin | 1 | 3 |\n\nThe data in the table show the number of seasons some players on a soccer team played versus the number of goals they scored. Which conclusion is supported by the data?  \nE. There are multiple outliers in the data set.  \nF. There is a positive association between seasons played and goals scored.  \nG. There is a negative association between seasons played and goals scored.  \nH. There is no association between seasons played and goals scored.  \n4  \n11. What is the value of y when  \n0.25 (y + 8) = 15?  \nA. 1.75  \nB. 3.25  \nC. 28  \nD. 52  \n12. What is the volume, in cubic inches, of a beach ball with a diameter of 24 inches?  \nE. 48π  \nF. 256π  \nG. 576π  \nH. 2,304π  \n13. How many integers, n, satisfy the condition 5 \u003C √_n \u003C 6?  \nA. 0  \nB. 5.5  \nC. 10  \nD. 11  \nGrade 9  \nMathematics Explanations of Correct Answers  \n1. (− 6) Since the microchip is a square, the  \narea of the microchip is (1.2 × 10 − 3 )2 square meter.  \n(1.2 × 10 − 3 )2 =( 1.2)2 × (10 − 3 )2 =  \n1.44 × 10 − 6  \nSo the value of a, the exponent, is − 6 .  \n2. (66) First, determine the number of people who do not use Soap L.  \n264 + 136 = 400  \nThen determine what percentage of those people use Soap M.  \n264 = 0.66 = 66%  \n400  \nSince 66% of the people who do not use Soap L use Soap M, the value of x is 66.  \n3. (− 5) A linear function consists of ordered pairs that make a linear equation true, with a consistent slope, m , and a  \ny-intercept, b. Use the slope formula and the two given ordered pairs to determine the slope.  \nm =  2 − ( − 1)  =  3  = − 1 − 4 − ( − 1) − 3  \nThen use the slope and one of the given ordered pairs to determine the  \ny-intercept. The equation is in slopeintercept form.  \ny = ( − 1)x + b  \n2 = ( − 1)( − 4) + b  \n2 = 4 + b − 2 = b  \nUse the slope and the y-intercept to determine the ","cbCaibEx9nA1g4ig","https://ap.wps.com/l/cbCaibEx9nA1g4ig","pdf",626734,"English","# Sample Questions\n## Algebra, Equations, and Expressions\n## Functions, Tables, and Associations\n## Geometry and Measurement\n# Mathematics Explanations of Correct Answers","[{\"question\":\"How do you find the exponent in a scientific-notation area problem for a square microchip?\",\"answer\":\"Square the given side length to get the area in scientific notation, then match the result to b × 10^a to read off the exponent a.\"},{\"question\":\"How is the percentage x determined from a Soap L and Soap M two-way table?\",\"answer\":\"First add the “Do Not Use Soap L” row entries to get the total not using Soap L. Then divide the “Use Soap M” entry in that row by the row total and convert to a whole-number percentage.\"},{\"question\":\"What method finds the distance between two points such as (3, 20) and (11, 5)?\",\"answer\":\"Use the Pythagorean theorem: compute the absolute differences in x and y to get the legs, then set the hypotenuse squared equal to leg1^2 + leg2^2 and take the square root.\"}]","Grade 9 Mathematics Sample Questions - and Explanations | PDF",23]