Equations and inequalities Flashcards
(14 cards)
What methods can be used to solve linear simultaneous equations?
Elimination or substitution.
How many pairs of solutions can simultaneous equations with one linear and one quadratic equation have?
Up to two pairs of solutions.
What do the solutions of a pair of simultaneous equations represent?
The points of intersection of their graphs.
What does the condition b² - 4ac > 0 indicate for a quadratic equation ax² + bx + c = 0?
Two real solutions.
What does the condition b² - 4ac = 0 indicate for a quadratic equation ax² + bx + c = 0?
One real solution.
What does the condition b² - 4ac < 0 indicate for a quadratic equation ax² + bx + c = 0?
No real solutions.
What is the solution of an inequality?
The set of all real numbers x that make the inequality true.
What are the steps to solve a quadratic inequality?
- Rearrange so that the right-hand side of the inequality is 0
- Solve the corresponding quadratic equation to find the critical values
- Sketch the graph of the quadratic function
- Use your sketch to find the required set of values.
What inequality is satisfied by the values of x for which the curve y = f(x) is below the curve y = g(x)?
f(x) < g(x).
What inequality is satisfied by the values of x for which the curve y = f(x) is above the curve y = g(x)?
f(x) > g(x).
What does y < f(x) represent on the coordinate grid?
The points below the curve y = f(x).
What does y > f(x) represent on the coordinate grid?
The points above the curve y = f(x).
What line type represents the curve y = f(x) when y > f(x) or y < f(x) and the curve is not included in the region?
Dotted line.
What line type represents the curve y = f(x) when y > f(x) or y < f(x) and the curve is included in the region?
Solid line.
