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Cambridge AS and A Level Mathematics (9709) Flashcards
50 question-and-answer cards covering Mathematics (9709) as it is examined in Cambridge AS and A Level. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Mathematics (9709) deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the geometric relationship between the graphs of y = f(x) and y = f⁻¹(x)?
They are reflections of each other in the line y = x.
What is the process to find the inverse function f⁻¹(x)?
Write y = f(x), swap x and y (or solve for x), then make y the subject; rename as f⁻¹(x).
What are ff⁻¹(x) and f⁻¹f(x) equal to?
Both equal x (over the appropriate domains).
State the equation of a straight line in gradient-intercept form.
y = mx + c, where m is the gradient and c is the y-intercept.
How do you find the gradient of a line through points (x₁, y₁) and (x₂, y₂)?
m = (y₂ − y₁) / (x₂ − x₁).
State the point-gradient form of the equation of a straight line.
y − y₁ = m(x − x₁).
What is the relationship between the gradients of two parallel lines?
Their gradients are equal (m₁ = m₂).
What is the relationship between the gradients of two perpendicular lines?
The product of their gradients is −1 (m₁ · m₂ = −1), i.e. m₂ = −1/m₁.
State the distance formula between two points (x₁, y₁) and (x₂, y₂).
d = √((x₂ − x₁)² + (y₂ − y₁)²).
State the midpoint formula for the segment joining (x₁, y₁) and (x₂, y₂).
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2).
State the equation of a circle with centre (a, b) and radius r.
(x − a)² + (y − b)² = r².
State the general expanded form of a circle's equation.
x² + y² + 2gx + 2fy + c = 0, with centre (−g, −f) and radius √(g² + f² − c).
What is the geometric property linking a tangent to a circle and the radius at the point of contact?
The tangent is perpendicular to the radius at the point of contact.
How do you find the points of intersection of a line and a curve algebraically?
Solve their equations simultaneously (usually by substitution), giving a single equation whose solutions are the intersection coordinates.
When a line meets a circle, what does the discriminant of the resulting quadratic tell you?
Δ > 0: line is a secant (two intersection points); Δ = 0: line is a tangent (one point); Δ < 0: line misses the circle.
Give the exact values of sin, cos and tan of 30°.
sin30° = 1/2, cos30° = √3/2, tan30° = 1/√3.
Give the exact values of sin, cos and tan of 45°.
sin45° = 1/√2, cos45° = 1/√2, tan45° = 1.
Give the exact values of sin, cos and tan of 60°.
sin60° = √3/2, cos60° = 1/2, tan60° = √3.
State the periods of the graphs y = sin x, y = cos x and y = tan x (in degrees).
sin and cos have period 360°; tan has period 180°.
State the Pythagorean trigonometric identity.
sin²θ + cos²θ = 1.
State the identity relating tan θ to sin θ and cos θ.
tan θ = sin θ / cos θ (for cos θ ≠ 0).
How do you convert degrees to radians?
Multiply by π/180; equivalently, 180° = π radians.
State the formula for the arc length of a sector with radius r and angle θ in radians.
Arc length s = rθ.
State the formula for the area of a sector with radius r and angle θ in radians.
Area = ½ r²θ.
What this deck covers
The Mathematics (9709) deck follows the Cambridge AS and A Level Mathematics (9709) syllabus — 11 chapters and 37 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 4.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 50 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Mathematics (9709) flashcards FAQ
How many Mathematics (9709) flashcards are in this Cambridge AS and A Level deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these Cambridge AS and A Level flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Mathematics (9709) cards cover?
They follow the Cambridge AS and A Level Mathematics (9709) syllabus — 11 chapters and 37 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.