[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143213-105":59,"doc-detail-143213-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","algebraic-proof-questions-exam-style-practice","Algebraic Proof Questions - Exam Style Practice","","Exam-style algebra proof questions focused on divisibility, parity (even/odd), and identities involving consecutive integers. The set requires showing full working, checking answers, and completing every problem, with multiple prompts asking students to prove sums and products are always divisible by specific numbers or always even/odd. It also includes algebraic manipulations of expressions with variables and sequence-based reasoning.",{"@graph":69,"@context":122},[70,84,105],{"@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/algebraic-proof-questions-exam-style-practice/143213/",{"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/algebraic-proof-questions-exam-style-practice/143213.png","ImageObject",300,407,{"name":92,"@type":93},"Olivia Brown","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-20","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main skill emphasized in these questions?","Question",{"text":112,"@type":113},"Proving algebraic statements about divisibility and whether expressions are always even or odd, typically using identities and manipulation of consecutive integers.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Do students need to show workings for each problem?",{"text":117,"@type":113},"Yes. The guidance explicitly requires always showing workings for the answers.",{"name":119,"@type":110,"acceptedAnswer":120},"Is there a question that uses a sequence rather than only variable identities?",{"text":121,"@type":113},"Yes. One question defines a linear sequence and asks for the nth term, then creates a new sequence by squaring terms and adding 5, requiring proof that all new terms are divisible by 6.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},143213,1787693699,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":52,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":143},16904993612988,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Exam Style Questions  \nEnsure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed  \nGuidance  \n1. Read each question carefully before you begin answering it.  \n2. Don’t spend too long on one question.  \n3. Attempt every question.  \n4. Check your answers seem right.  \n5. Always show your workings  \nwestminstermath  \n99 7944423  \n1. Prove that the sum of three consecutive integers is divisible by 3.  \n(3)  \n2. Prove (n + 6)² − (n + 2)² is always a multiple of 8  \n3. Prove (n + 10)² − (n + 5)² is always a multiple of 5  \n(4)  \n4. Prove the sum of two consecutive odd numbers is even.  \n5. Prove (2n + 1)(3n − 2) − (6n − 1)(n − 2) is always even  \n(3)  \n6. Prove that the sum of three consecutive even numbers is always a multiple of 6  \nwestminstermath  \n99 7944423  \n7. Prove the sum of four consecutive odd numbers is always a multiple of 8  \n(4)  \n8. Prove (2n + 9)² − (2n + 5)² is always a multiple of 4  \nwestminstermath 99 7944423  \n(4)  \n9. Prove (n + 1)² + (n + 3)² − (n + 5)² = (n + 3)(n − 5)  \n(4)  \n10. Prove the product of two even numbers is always even  \nwestminstermath  \n99 7944423  \n11. Prove the product of three consecutive odd numbers is odd  \n(3)  \n12. Prove algebraically that the sum of the squares of two odd integers is always even.  \nwestminstermath  \n99 7944423  \n13. Prove that when two consecutive integers are squared, that the difference is equal to the sum of the two consecutive integers.  \n(4)  \n14. Prove algebraically that  \n(4n + 1)² − (2n − 1) is an even number  \nfor all positive integer values of n.  \nwestminstermath  \n99 7944423  \n15. Prove that 3n(3n + 4) + (n − 6)² is positive for all values of n  \n(4)  \n16. The first five terms of a linear sequence are 5, 1, 17, 23, 29 …  \n(a) Find the nth term of the sequence  \n(2)  \nA new sequence is generated by squaring each term of the linear sequence and then adding 5.  \n(b) Prove that all terms in the new sequence are divisible by 6.  \nwestminstermath 99 7944423  \n(4)  \n17. Prove that the product of two consecutive even numbers is a multiple of 4.  \n(3)  \n18. Prove that when any odd integer is squared, the result is always one more than a multiple of 8.  \n(4)  \n19. Prove that the product of two odd numbers is always odd.  \nwestminstermath 99 7944423  \n(3)","cbCaip8BaGuYCq5Y","https://ap.wps.com/l/cbCaip8BaGuYCq5Y","pdf",89761,"English","# Exam Style Questions\n## Divisibility and parity proofs\n## Algebraic identities with consecutive integers\n## Sequences and general divisibility results","[{\"question\":\"What is the main skill emphasized in these questions?\",\"answer\":\"Proving algebraic statements about divisibility and whether expressions are always even or odd, typically using identities and manipulation of consecutive integers.\"},{\"question\":\"Do students need to show workings for each problem?\",\"answer\":\"Yes. The guidance explicitly requires always showing workings for the answers.\"},{\"question\":\"Is there a question that uses a sequence rather than only variable identities?\",\"answer\":\"Yes. One question defines a linear sequence and asks for the nth term, then creates a new sequence by squaring terms and adding 5, requiring proof that all new terms are divisible by 6.\"}]","Algebraic Proof Questions - Exam Style Practice | PDF",25]