EDEXCEL MATHS A LEVEL PURE MATHS 1 FINAL
PAPER 2026 STUDY GUIDE DETAILED ANSWERS
READY
◉ Equation of a Line.
Answer: y - y₁ = m(x - x₁)
with coords (x₁, y₁)
◉ Distance Formula.
Answer: √((x₂ - x₁)² + (y₂ - y₁)²)
from (x₁, y₁) to (x₂, y₂)
◉ Perpendicular Bisector.
Answer: -1/m
where m is original gradient
◉ Standard Equation of a Circle.
Answer: (x - a)² + (y - b)² = r²
,with centre (a, b) and radius r
◉ Equation of a Circle (fg).
Answer: x² + y² + 2fx + 2gy + c = 0
with centre (-f, -g) and radius √(f² + g² - c)
◉ Circle Theorems.
Answer: • Tangent to a circle is perpendicular to the radius of the
circle at the point of intersection.
• Perpendicular bisector of a chord will go through the circle centre.
• If triangle forms across the circle, its diameter is the hypotenuse of
the right-angled triangle.
• Equations of the perpendicular bisectors of two different chords
will intersect at the circle centre.
◉ Factor Theorem.
Answer: If f(p) = 0, (x - p) is a factor of f(x)
◉ Mathematical Proofs.
Answer: • State any info/assumptions
, • Show every step clearly
• Make sure every step follows logically from the previous step
• Cover all possible cases
• Write a statement of proof at the end of your working
◉ Truth by Exhaustion.
Answer: Break the statement into smaller cases and prove each case
separately.
◉ Truth by Counter-Example.
Answer: Find one example that does not work for the statement.
◉ Pascal's Triangle.
Answer: The (n + 1)th row of Pascal's triangle gives the coefficients
in the expansion of (a + b)ⁿ
◉ Factorial Formula.
Answer: n! = n x (n - 1) x (n - 2) x ... x 2 x 1
◉ Factorials in Pascal's Triangle.
Answer: The number of ways of choosing r from a group of n items
is:
PAPER 2026 STUDY GUIDE DETAILED ANSWERS
READY
◉ Equation of a Line.
Answer: y - y₁ = m(x - x₁)
with coords (x₁, y₁)
◉ Distance Formula.
Answer: √((x₂ - x₁)² + (y₂ - y₁)²)
from (x₁, y₁) to (x₂, y₂)
◉ Perpendicular Bisector.
Answer: -1/m
where m is original gradient
◉ Standard Equation of a Circle.
Answer: (x - a)² + (y - b)² = r²
,with centre (a, b) and radius r
◉ Equation of a Circle (fg).
Answer: x² + y² + 2fx + 2gy + c = 0
with centre (-f, -g) and radius √(f² + g² - c)
◉ Circle Theorems.
Answer: • Tangent to a circle is perpendicular to the radius of the
circle at the point of intersection.
• Perpendicular bisector of a chord will go through the circle centre.
• If triangle forms across the circle, its diameter is the hypotenuse of
the right-angled triangle.
• Equations of the perpendicular bisectors of two different chords
will intersect at the circle centre.
◉ Factor Theorem.
Answer: If f(p) = 0, (x - p) is a factor of f(x)
◉ Mathematical Proofs.
Answer: • State any info/assumptions
, • Show every step clearly
• Make sure every step follows logically from the previous step
• Cover all possible cases
• Write a statement of proof at the end of your working
◉ Truth by Exhaustion.
Answer: Break the statement into smaller cases and prove each case
separately.
◉ Truth by Counter-Example.
Answer: Find one example that does not work for the statement.
◉ Pascal's Triangle.
Answer: The (n + 1)th row of Pascal's triangle gives the coefficients
in the expansion of (a + b)ⁿ
◉ Factorial Formula.
Answer: n! = n x (n - 1) x (n - 2) x ... x 2 x 1
◉ Factorials in Pascal's Triangle.
Answer: The number of ways of choosing r from a group of n items
is:
