Equations and InequalitiesAQA GCSE Maths: Flashcards

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State the quadratic formula.

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State the quadratic formula.: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
How do you solve a linear equation with the unknown on both sides?: Collect all unknown terms on one side and number terms on the other, then simplify and divide.
What are the three algebraic methods for solving a quadratic equation?: Factorising, completing the square, and the quadratic formula.
What is a simultaneous equation?: One of two or more equations solved together so that the same values of the unknowns satisfy all of them.
How do you solve linear/quadratic simultaneous equations?: Substitute the linear equation into the quadratic equation, then solve.
What is iteration used for?: Finding an approximate numerical solution to an equation that cannot easily be solved algebraically, using a recursive formula $x_{n+1}=f(x_n)$ .
When solving an inequality, when must you flip the inequality sign?: When you multiply or divide both sides by a negative number.
What does an open circle mean on a number line inequality diagram?: The boundary value is not included (a strict inequality, $<$ or $>$ ).
What does a closed circle mean on a number line inequality diagram?: The boundary value is included ( $\leq$ or $\geq$ ).
On a graph, what does a dashed line represent?: A strict inequality boundary ( $<$ or $>$ ), not included in the solution.
On a graph, what does a solid line represent?: An included inequality boundary ( $\leq$ or $\geq$ ).
How can approximate solutions to an equation be found graphically?: By plotting the relevant graph(s) and reading off the $x$ -value(s) where they cross or intersect.
Solve $x^2 = 9$ .: $x = 3$ or $x = -3$