Edexcel AS Pure Maths, AS-Level Pure Maths EXAM Questions & Answer
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1. Quadratic Formula
2. Domain The set of possible inputs for a function.
3. Range The set of possible outputs of a function.
4. Discriminant b² - 4ac > 0 then two distinct real roots.
b² - 4ac = 0 then one repeated real root.
b² - 4ac < 0 then a quadratic function has no
real roots.
5. Types of Lines for Regions If y < f(x) or y > f(x) then the curve y = f(x) is
not included in the region, and is represented
by a dotted line.
If y df(x) or y ef(x) then the curve y = f(x) is
included in the region, and is represented by
a solid line.
6. Graph Translations y = f(x) + a is a translation of the graph y = f(x)
by a upwards.
y = f(x + a) is a translation of the graph y = f(x)
by a to the left.
, Edexcel AS Pure Maths, AS-Level Pure Maths EXAM Questions & Answer
| 100% Verified solutions |Questions with Correct Answers 2025 latest u
date!!
7. Graph Stretches y = af(x) is a stretch of the graph y = f(x) by a
scale factor of a in the vertical direction.
y = f(ax) is a stretch of the graph y = f(x) by a
scale factor of 1/a in the horizontal direction.
8. Graph Reflections y = -f(x) is a reflection of the graph of y = f(x)
in the x-axis.
y = f(-x) is a reflection of the graph of y = f(x)
in the y-axis.
9. Gradient of Equation m = (y₂ - y₁) ÷ (x₂ - x₁)
10. Equation of a Line y - y₁ = m(x - x₁)
with coords (x₁, y₁)
11. Distance Formula ((x₂ - x₁)² + (y₂ - y₁)²)
from (x₁, y₁) to (x₂, y₂)
12. Perpendicular Bisector -1/m
where m is original gradient
13. Standard Equation of a Circle (x - a)² + (y - b)² = r²
with centre (a, b) and radius r
14. Equation of a Circle (fg) x² + y² + 2fx + 2gy + c = 0
with centre (-f, -g) and radius (f² + g² - c)
, Edexcel AS Pure Maths, AS-Level Pure Maths EXAM Questions & Answer
| 100% Verified solutions |Questions with Correct Answers 2025 latest u
date!!
15. Circle Theorems • 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 di-
ameter is the hypotenuse of the right-angled
triangle.
• Equations of the perpendicular bisectors of
two different chords will intersect at the circle
centre.
16. Factor Theorem If f(p) = 0, (x - p) is a factor of f(x)
17. Mathematical Proofs • 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
18. Truth by Exhaustion Break the statement into smaller cases and
prove each case separately.
19. Truth by Counter-Example Find one example that does not work for the
statement.
20. Pascal's Triangle The (n + 1)th row of Pascal's triangle gives the
coefficients in the expansion of (a + b)ⁿ
| 100% Verified solutions |Questions with Correct Answers 2025 latest u
date!!
1. Quadratic Formula
2. Domain The set of possible inputs for a function.
3. Range The set of possible outputs of a function.
4. Discriminant b² - 4ac > 0 then two distinct real roots.
b² - 4ac = 0 then one repeated real root.
b² - 4ac < 0 then a quadratic function has no
real roots.
5. Types of Lines for Regions If y < f(x) or y > f(x) then the curve y = f(x) is
not included in the region, and is represented
by a dotted line.
If y df(x) or y ef(x) then the curve y = f(x) is
included in the region, and is represented by
a solid line.
6. Graph Translations y = f(x) + a is a translation of the graph y = f(x)
by a upwards.
y = f(x + a) is a translation of the graph y = f(x)
by a to the left.
, Edexcel AS Pure Maths, AS-Level Pure Maths EXAM Questions & Answer
| 100% Verified solutions |Questions with Correct Answers 2025 latest u
date!!
7. Graph Stretches y = af(x) is a stretch of the graph y = f(x) by a
scale factor of a in the vertical direction.
y = f(ax) is a stretch of the graph y = f(x) by a
scale factor of 1/a in the horizontal direction.
8. Graph Reflections y = -f(x) is a reflection of the graph of y = f(x)
in the x-axis.
y = f(-x) is a reflection of the graph of y = f(x)
in the y-axis.
9. Gradient of Equation m = (y₂ - y₁) ÷ (x₂ - x₁)
10. Equation of a Line y - y₁ = m(x - x₁)
with coords (x₁, y₁)
11. Distance Formula ((x₂ - x₁)² + (y₂ - y₁)²)
from (x₁, y₁) to (x₂, y₂)
12. Perpendicular Bisector -1/m
where m is original gradient
13. Standard Equation of a Circle (x - a)² + (y - b)² = r²
with centre (a, b) and radius r
14. Equation of a Circle (fg) x² + y² + 2fx + 2gy + c = 0
with centre (-f, -g) and radius (f² + g² - c)
, Edexcel AS Pure Maths, AS-Level Pure Maths EXAM Questions & Answer
| 100% Verified solutions |Questions with Correct Answers 2025 latest u
date!!
15. Circle Theorems • 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 di-
ameter is the hypotenuse of the right-angled
triangle.
• Equations of the perpendicular bisectors of
two different chords will intersect at the circle
centre.
16. Factor Theorem If f(p) = 0, (x - p) is a factor of f(x)
17. Mathematical Proofs • 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
18. Truth by Exhaustion Break the statement into smaller cases and
prove each case separately.
19. Truth by Counter-Example Find one example that does not work for the
statement.
20. Pascal's Triangle The (n + 1)th row of Pascal's triangle gives the
coefficients in the expansion of (a + b)ⁿ
