Core 3 - Modulus + Iterations

Question 1

When solving a modulus equation, what is the first thing you should do? Why is this helpful?

Answer 1

Draw a sketch of the two lines with intercepts. This helps to visualise where the graphs cross.

Question 2

When you find the modulus of a quadratic, what must you consider about the gradient?

Answer 2

Gradient must be increasing, because it is reflected, and goes off towards infinity.

Question 3

Which two equations must you solve for |2x-3| ,|2x+5|?

Answer 3

-2x+3=2x+5

2x-3=2x+5

Question 4

What are the two methods of solving iterations visually? What is the rule?

Answer 4

Cobweb or staircase

UP to the curve,
ACROSS to the line.

Question 5

When finding an equations suitable for iterations, what must you ensure?

Answer 5

x appears on both sides, so x=kx.

Question 6

When solving modulus equations, for example |6x^2 + 2x + 1| = 6, what are the two equations to solve?

Answer 6

|6x^2 + 2x + 1| = 6

|6x^2 + 2x + 1| = -6

Question 7

What happens when sketching |f(x)|

Answer 7

All negative values of f(x) reflected in x axis into positive quadrants

Question 8

What happens when sketching f(|x|)

Answer 8

All negative x values are replaced by the reflection of the positive x values. There is a line of symmetry in x=0

Question 9

What happens when sketching |f(|x|)|

Answer 9

The values of f(|x|) are first plotted, where only negative x values are replaced by +ve ones, then all negative y values reflected in x axis

Question 10

When writing the inequality for the modulus equation you have solved, which mistake should you DEFINITELY AVOID???

Answer 10

writing -1