air?","back":"A solution written as $(x, y)$, where the $x$-value is listed first.","points":1},{"id":"af0fcb03-1a36-4c25-b9ac-745b5060c056","cardType":"cloze","front":"A linear equation contains variables only to the [ ] power, while a quadratic equation contains a squared term.","back":"A linear equation contains variables only to the first power, while a quadratic equation contains a squared term.","points":null},{"id":"f968e148-4b9f-4e6e-9b99-b3dc23bdb156","cardType":"cloze","front":"A linear equation contains variables only to the first power, while a quadratic equation contains a [ ] term.","back":"A linear equation contains variables only to the first power, while a quadratic equation contains a squared term.","points":null},{"id":"2f88ae3c-7288-4f39-8d92-7f5cd9901bbc","cardType":"basic","front":"What is the primary algebraic method for solving a linear and quadratic pair?","back":"Substitution.","points":1},{"id":"204ae636-8ae0-4911-8b09-8914dd6b762c","cardType":"cloze","front":"The variable isolated on one side of an equation is known as the [ ].","back":"The variable isolated on one side of an equation is known as the subject.","points":null},{"id":"1a0b5ca8-9281-4370-b8a9-dba25a726a6e","cardType":"basic","front":"Why is substitution used to solve simultaneous equations?","back":"It creates one quadratic equation in one variable.","points":2},{"id":"a7df4998-c5ca-4e76-a3f4-cb6536b6df66","cardType":"basic","front":"What is the standard form of a quadratic equation in one variable?","back":"$$ax^2 + bx + c = 0$, where $a \\neq 0$.","points":1},{"id":"50d7307d-65ce-4d3f-a6af-fe6281a19d8f","cardType":"cloze","front":"When substituting an expression like $y = 5 - 3x$ into a quadratic, you must use [ ] to ensure the whole expression is squared.","back":"When substituting an expression like $y = 5 - 3x$ into a quadratic, you must use brackets to ensure the whole expression is squared.","points":null},{"id":"5cae1241-0aef-4aeb-ad2e-18a59f787761","cardType":"basic","front":"State the quadratic formula for $ax^2 + bx + c = 0$.","back":"$$x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$","points":1},{"id":"5f44a2dd-2bf3-47c7-a552-b23c340a0f99","cardType":"cloze","front":"The expression $b^2 - 4ac$ is called the [ ].","back":"The expression $b^2 - 4ac$ is called the discriminant.","points":null},{"id":"6f5a1ed4-7050-48eb-b04d-9eb1e767b54a","cardType":"basic","front":"How does the discriminant ($b^2 - 4ac$) relate to the number of solution pairs?","back":"

Positive: Two real solutions.
Zero: One repeated solution.
Negative: No real solutions.

","points":3},{"id":"e754cc0a-cafa-4a7e-89e6-1a164c110e29","cardType":"basic","front":"What does a negative discriminant indicate about the relationship between a line and a curve?","back":"The line misses the curve (they do not intersect).","points":2},{"id":"d24a78b9-afc6-4fca-801e-7b77e12c9745","cardType":"basic","front":"How should solution pairs be presented to avoid marks for \"unpaired answers\"?","back":"As distinct coordinate pairs, e.g., $(3, 4)$ and $(-4, -3)$.","points":1},{"id":"86034bf1-e5d6-476b-aeab-8bbd9a674da8","cardType":"basic","front":"When a question requires answers to 3 significant figures, when should you round?","back":"Only at the final step

Quadratic Simultaneous Equations Flashcards

Quadratic Simultaneous Equations Flashcards

Quadratic Simultaneous Equations Flashcards

Quadratic Simultaneous Equations Flashcards