c","front":"What algebraic expressions represent three consecutive integers?","back":"$$n$, $n+1$, $n+2$","points":1},{"id":"69c8f750-7a21-4fbd-ae09-4a80b1c74038","cardType":"basic","front":"What algebraic expressions represent two consecutive even integers?","back":"$$2n$ and $2n+2$","points":1},{"id":"af1ae9c4-0c10-4086-b8a1-f8f936b07e6b","cardType":"basic","front":"What algebraic expressions represent two consecutive odd integers?","back":"$$2n+1$ and $2n+3$","points":1},{"id":"d3927153-f9ff-4ad0-b2a5-b207709bb575","cardType":"basic","front":"Why is testing specific numbers (e.g., $n=1, 2, 3$) not considered a mathematical proof?","back":"

Testing only shows the statement is true for specific cases
Algebraic proof shows it is true for all allowed values

","points":2},{"id":"8d9ccbc2-7a4e-4f31-9370-6f992232bcd9","cardType":"basic","front":"What is the goal when proving an expression is a multiple of 6?","back":"Factorise the expression into the form $6(\\text{expression})$","points":1},{"id":"08065be7-be31-48eb-8aab-ee53ccfbdbd6","cardType":"basic","front":"How do you finish a proof that results in $12n$ to ensure you get the mark?","back":"State that because $n$ is an integer, $12n$ must be a multiple of 12.","points":1},{"id":"57fe4dff-3267-4366-8f17-12c4de9954c1","cardType":"basic","front":"What algebraic form should you reach to prove a result is a square number?","back":"$$m^2$ or $(\\text{expression})^2$","points":1},{"id":"244e39e0-49f9-4632-a469-5dcf2af4c516","cardType":"basic","front":"To prove a result is \"4 more than a multiple of 8\", what target form is needed?","back":"$$8k+4$ (where $k$ is an integer)","points":1},{"id":"2d355c27-2060-4176-86bd-002f38224d78","cardType":"basic","front":"When proving a sum is a square number, why is factorising often better than expanding?","back":"It leads directly to the squared bracket form $(n+a)^2$ rather than a long quadratic.","points":2},{"id":"d2da262f-6aa8-43ef-9a16-ac80c5c3a2b2","cardType":"basic","front":"Expand the identity for $(a-b)^2$.","back":"$$a^2 - 2ab + b^2$","points":1},{"id":"b73f0fd9-94d6-4a86-a595-52a3be285a6a","cardType":"basic","front":"What is the difference of two squares identity used in proofs?","back":"$$a^2 - b^2 = (a-b)(a+b)$","points":1},{"id":"34a1e847-3eab-46be-9ee9-2bccc44c82e5","cardType":"basic","front":"Prove that $2n+5$ is always odd for any integer $n$.","back":"

$2n+4$ is a multiple of 2 (even)
$2n+5$ is one more than an even number

","points":2},{"id":"92a82ebf-3753-44bf-aec9-7117b9f85b09","cardType":"cloze","front":"To prove an expression is a multiple of 12, it must be written in the form $\\text{[...]}$ where $k$ is an integer.","back":"To prove an expression is a multiple of 12, it must be written in the form $\\boxed{12k}$ where $k$ is an integer.","points":null},{"id":"e19a2730-afcf-4984-9f7e-ec9a28628ad0","cardType":"cloze","front":"The expansion of $(a+b)^2$ is $\\text{[...]}$.","back":"The expansion of $(a+b)^2$ is $\\boxed{a^2+2ab+b^2}$.","points":null},{"id":"8cd50163-4c75-4348-996d-655043cab30d","cardType":"cloze","front":"A square number is an expression that can be written in the form $\\text{[...]}$.","back":"A square number is an expression that can be written in the form $\\boxed{m^2}$.","points":null}]}],"examCountdown":null,"formulaUrl":null,"intro":"$L3c","title":"Proof Flashcards","topicSidebar":"$L3d"}]}],"topicId":"5a1179f9-3905-4fed-8ad8-ce97a08687af","walled":"$L3e"}],"$L3f"]