Equations, Inequalities and Graphs: worked exam questions
7 solved equations, inequalities and graphs questions, each worked line by line the way the 0606 mark scheme rewards. Learn the method in the Equations, Inequalities and Graphs topic notes, then see it applied here.
A Modulus Equation That Needs Checking
Solve |x − 3| = 2x, where the variable on the right means each answer must be checked, a 0606 question on why one case gets rejected.
Number of Solutions from a Modulus Graph
Use the graph of y = |x² − 4| against a horizontal line to count how many solutions an equation has, a 0606 reasoning question on modulus graphs.
Sketching the Graph of a Modulus Function
Sketch y = |2x − 4|, find its vertex and intercepts, and state its range, the standard 0606 modulus-graph skill that underpins modulus equations.
Solving |2x − 4| = x + 1 Graphically and Algebraically
Solve |2x − 4| = x + 1, interpreting the two solutions as where a V-shaped graph meets a straight line, a 0606 modulus-graph question.
Solving |x + 1| = |2x − 4|
Solve an equation with a modulus on each side by considering both sign cases, a 0606 question where both solutions turn out valid.
Solving a Cubic Inequality Graphically
Solve a factorised cubic inequality by reading the sign of the curve between its roots, a 0606 question using a quick sketch to get the regions right.
Solving a Modulus Inequality
Solve |2x − 1| < 5 by unfolding it into a double inequality, a 0606 question on the 'less than' modulus case that gives a single bounded region.
Worked examples show the routine. A tutor builds it into your child.
Weekly 1-to-1 classes with a founder-vetted 0606 specialist, your child's own working marked line by line against real mark schemes. A 1-hour trial class first, always.