GCSE Secondary Maths Age 13-17 - Algebra: Iterative Methods - Explained

The video tutorial explains how to find a solution for the equation X^3 + X = 7 between X=1 and X=2 by substitution. It then demonstrates rearranging the equation to express X in terms of the cube root. Finally, it uses an iteration formula to estimate the solution, emphasizing the importance of using a calculator for precise calculations.

What is the result when substituting X = 1 into the equation X^3 + X = 7?

• 2

• 1

• 3

• 4

What is the result when substituting X = 2 into the equation X^3 + X = 7?

• 12

• 10

• 8

• 6

How can the equation X^3 + X = 7 be rearranged?

• X = 7 + X^3

• X = cube root of (7 - X)

• X = cube root of (X - 7)

• X = 7 - X^3

What is the first estimate (X1) using the iteration formula starting with X0 = 2?

• 1.8

• 1.7

• 1.5

• 1.6

What is the final estimate (X3) after using the iteration formula three times?

• 1.738

• 1.739

• 1.740

• 1.741