A Level Mathematics
Edexcel
Paper 2 – Pure Mathematics
Predicted Paper 2022
Name ………………………………………………
Date ………………………………………………
2 hours allowed
Calculator Paper
Maximum Mark: 100
YouTube Tutorials for GCSE and A-Level | Proudly partnered with Primrose Kitten 1
, Question 1
The equation 𝑥 3 − 𝑥 2 − 4𝑥 + 8 = 0 has exactly one real root 𝑎
(i) Show that the Newton-Raphson iterative formula for finding this root can
be written as:
2𝑥𝑛 3 − 𝑥𝑛 2 − 8
𝑥𝑛+1 =
3𝑥𝑛 2 − 2𝑥𝑛 − 4
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
(3)
(ii) Apply the iterative formula with initial value 𝑥1 = −2 to find 𝑥2 , 𝑥3 , 𝑥4
correct to four significant figures.
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
(1)
YouTube Tutorials for GCSE and A-Level | Proudly partnered with Primrose Kitten 2
, (iii) Use a change of sign method to show that 𝑎 = −2.284 is correct to four
significant figures.
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
(3)
(Total 7 Marks)
YouTube Tutorials for GCSE and A-Level | Proudly partnered with Primrose Kitten 3
Edexcel
Paper 2 – Pure Mathematics
Predicted Paper 2022
Name ………………………………………………
Date ………………………………………………
2 hours allowed
Calculator Paper
Maximum Mark: 100
YouTube Tutorials for GCSE and A-Level | Proudly partnered with Primrose Kitten 1
, Question 1
The equation 𝑥 3 − 𝑥 2 − 4𝑥 + 8 = 0 has exactly one real root 𝑎
(i) Show that the Newton-Raphson iterative formula for finding this root can
be written as:
2𝑥𝑛 3 − 𝑥𝑛 2 − 8
𝑥𝑛+1 =
3𝑥𝑛 2 − 2𝑥𝑛 − 4
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
(3)
(ii) Apply the iterative formula with initial value 𝑥1 = −2 to find 𝑥2 , 𝑥3 , 𝑥4
correct to four significant figures.
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
(1)
YouTube Tutorials for GCSE and A-Level | Proudly partnered with Primrose Kitten 2
, (iii) Use a change of sign method to show that 𝑎 = −2.284 is correct to four
significant figures.
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………………………
(3)
(Total 7 Marks)
YouTube Tutorials for GCSE and A-Level | Proudly partnered with Primrose Kitten 3
