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5 of 5 objectives have lessons · 0 studied · 0 secure
What Cambridge says you should be able to do, in our words. Codes are the topic number plus the objective’s position.
Carry out the process of completing the square for a quadratic polynomial ax² + bx + c, and use a completed-square form.
For example, to locate the vertex of the graph of y = ax² + bx + c or to sketch that graph.
Taught in: Completing the square and the vertex · 6 questions
Find the discriminant of a quadratic polynomial ax² + bx + c and use the discriminant.
For example, to decide how many real roots the equation ax² + bx + c = 0 has. Knowledge of the term 'repeated root' is included.
Taught in: The discriminant and the nature of roots, Finding the set of values of k · 13 questions
Solve quadratic equations, and quadratic inequalities, in one unknown.
By factorising, by completing the square and by using the formula.
Taught in: Quadratic inequalities, Solving quadratic equations: three methods, Finding the set of values of k · 12 questions
Solve by substitution a pair of simultaneous equations in which one equation is linear and the other is quadratic.
Examples: x + y + 1 = 0 with x² + y² = 25; 2x + 3y = 7 with 3x² = 4 + 4xy.
Taught in: Simultaneous equations: one linear, one quadratic · 5 questions
Recognise and solve equations in x that are quadratic in some function of x.
Examples: x⁴ − 5x² + 4 = 0, 6x + √x − 1 = 0, tan²x = 1 + tan x.
Taught in: Equations that are quadratic in a function of x · 5 questions