ALGEBRAIC PROOF: THE ARCHIVE
Edexcel 4MA1 Higher Tier • 15 Progressive Questions
0/15
Score
⚠️ CRITICAL EXAMINER TRAP ALERT
TRAP: "Prove" means use ALGEBRA (n), not test numbers.
❌ WRONG: "Testing n=1 gives 3, n=2 gives 6, so it works" → ZERO MARKS
✓ CORRECT: "n + (n+1) + (n+2) = 3n + 3 = 3(n+1), which is a multiple of 3" → FULL MARKS
Q1-5
Foundation Anchor
Grades 6-7
Q6-10
Higher Standard
Grades 7-8
Q11-15
Grade 9 Killer
Grades 8-9
1
Grades 6-7
Foundation Anchor (Grade 6-7)
Question 1
Show that 3(x+2) - 3x = 6
2
Grades 6-7
Foundation Anchor (Grade 6-7)
Question 2
Show that (x+3)² = x² + 6x + 9
3
Grades 6-7
Foundation Anchor (Grade 6-7)
Question 3
Show that the sum of 3 consecutive integers is always a multiple of 3
4
Grades 6-7
Foundation Anchor (Grade 6-7)
Question 4
Show that the sum of two odd numbers is always even
5
Grades 6-7
Foundation Anchor (Grade 6-7)
Question 5
Expand and simplify (n+2)² - n²
6
Grades 7-8
Higher Standard (Grade 7-8)
Question 6
Prove that (2n+1)² is always odd
7
Grades 7-8
Higher Standard (Grade 7-8)
Question 7
Prove that the difference between the squares of two consecutive integers is always odd
8
Grades 7-8
Higher Standard (Grade 7-8)
Question 8
Show that (n+3)² - (n-3)² is always a multiple of 12
9
Grades 7-8
Higher Standard (Grade 7-8)
Question 9
Prove that (3n+1)² - (3n-1)² is always a multiple of 6
10
Grades 7-8
Higher Standard (Grade 7-8)
Question 10
Show algebraically that 1/2 + 1/3 = 5/6
11
Grades 8-9
Grade 9 Killer (Grade 8-9)
Question 11
Prove that the sum of the squares of two consecutive odd numbers is never a multiple of 8
12
Grades 8-9
Grade 9 Killer (Grade 8-9)
Question 12
Show that 2x² + 12x + 20 is always positive for all real values of x
13
Grades 8-9
Grade 9 Killer (Grade 8-9)
Question 13
Prove that the sum of 4 consecutive integers is never divisible by 4
14
Grades 8-9
Grade 9 Killer (Grade 8-9)
Question 14
AB = 2a + b and CD = 4a + 2b. Show that AB is parallel to CD
15
Grades 8-9
Grade 9 Killer (Grade 8-9)
Question 15
Prove that the sum of any three consecutive even numbers is always a multiple of 6
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