Edexcel AS Pure Maths, AS-Level Pure Maths, pure
maths As level Answers 2023
Quadratic Formula
Domain - answer-The set of possible inputs for a function.
Range - answer-The set of possible outputs of a function.
Discriminant - answer-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.
Types of Lines for Regions - answer-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 ≤ f(x) or y ≥ f(x) then the curve y = f(x) is included in the region,
and is represented by a solid line.
Graph Translations - answer-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.
Graph Stretches - answer-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.
Graph Reflections - answer-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.
, Edexcel AS Pure Maths, AS-Level Pure Maths, pure
maths As level Answers 2023
Gradient of Equation - answer-m = (y₂ - y₁) ÷ (x₂ - x₁)
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)
maths As level Answers 2023
Quadratic Formula
Domain - answer-The set of possible inputs for a function.
Range - answer-The set of possible outputs of a function.
Discriminant - answer-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.
Types of Lines for Regions - answer-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 ≤ f(x) or y ≥ f(x) then the curve y = f(x) is included in the region,
and is represented by a solid line.
Graph Translations - answer-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.
Graph Stretches - answer-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.
Graph Reflections - answer-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.
, Edexcel AS Pure Maths, AS-Level Pure Maths, pure
maths As level Answers 2023
Gradient of Equation - answer-m = (y₂ - y₁) ÷ (x₂ - x₁)
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)
