EDEXCEL MATHS A LEVEL PURE MATHS 1
CERTIFICATION TEST PAPER 2026 COMPLETE
SOLUTIONS GRADED A PLUS
◉ 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.
◉ 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).
CERTIFICATION TEST PAPER 2026 COMPLETE
SOLUTIONS GRADED A PLUS
◉ 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.
◉ 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).
