MATHEMATICS A LEVEL 2025 UPDATE
COMPREHENSIVE QUESTIONS AND
ANSWERS 2025.
X^2 graph when coefficients are positive - ANSWER: U shaped graph
Area of a trapezium - ANSWER: 1/2(a+b)h
Solving Quadratics with Unknowns - ANSWER: Use the discriminant to structure another
quadratic & solve this
Solving Quadratic Inequalities - ANSWER: Get zero on one side, Solve the Inequality, Sketch &
reason
"Less than" or "Greater than" is shown by what line on a graph? (strict Inequalities) - ANSWER:
A dotted Line
A "less than or equal to" or vice versa is shown by what line on a graph? (not strict inequalities)
- ANSWER: A solid Line
A vertical Reflection in the X axis: - ANSWER: Y = -f(x)
A Horizontal reflection in the Y axis: - ANSWER: y= f(-x)
Translation up A units - ANSWER: y= f(x)+A
Translation left A units - ANSWER: y=f(x+A)
Sketching from X axis by factor A - ANSWER: y= A*f(x)
Sketching from Y-axis by factor 1/A - ANSWER: y= f(Ax)
Shape of Positive cubic graph` - ANSWER: Upwards slope, two bends
Shape of Negative Cubic Graph - ANSWER: Downwards slope, two bends
, Shape of Positive Quartic Graph - ANSWER: "W" shape
Shape of Negative Quartic Graph - ANSWER: "M" shape
graph of y=1/x - ANSWER: 2 curves, one in Positive X & Y, another in Negative X & Y.
Graph of y= -1/x - ANSWER: Opposite of y=1/x , 2 curves, one in postive y but negative x,
another in negative y but positive x
Graph of y= 3/X^2 - ANSWER: 2 reciprocal curves, both above the x axis, opposite to each
other
Graph of y= -1/x^2 - ANSWER: 2 reciprocal curve, both below x axis, opposite to each other.
Equivalent angles of Sin(x) - ANSWER: Sin(x) = Sin(180-x)
Equivalent angles of Cos(x) - ANSWER: Cos(X) = Cos(360-x)
Sin & Cos repeat every... - ANSWER: 360 degrees
Tan repeats every... - ANSWER: 180 Degrees
Tan(θ) = - ANSWER: Sin(θ)/Cos(θ)
Sin rule - ANSWER: Sin(A)/a = Sin(B)/b
Cosine rule - ANSWER: a² = b² + c² - 2bcCos(A)
Area of a triangle using Sin() - ANSWER: 1/2abSin(C)
1 is directly equivalent to... (the second trigonometric identity) - ANSWER: Sin^2(theta) +
Cos^2(theta) = 1
the nCr equation - ANSWER: n!/r!(n-r)!
A negative reciprocal of the gradient of a line gives the gradient of the... - ANSWER:
Perpendicular line
Differentiating y= ax^n - ANSWER: = nax^n-1
To find the gradient of a point on a curve - ANSWER: Differentiate the equation of the curve,
then substitute the value of the point into this, then solve.
COMPREHENSIVE QUESTIONS AND
ANSWERS 2025.
X^2 graph when coefficients are positive - ANSWER: U shaped graph
Area of a trapezium - ANSWER: 1/2(a+b)h
Solving Quadratics with Unknowns - ANSWER: Use the discriminant to structure another
quadratic & solve this
Solving Quadratic Inequalities - ANSWER: Get zero on one side, Solve the Inequality, Sketch &
reason
"Less than" or "Greater than" is shown by what line on a graph? (strict Inequalities) - ANSWER:
A dotted Line
A "less than or equal to" or vice versa is shown by what line on a graph? (not strict inequalities)
- ANSWER: A solid Line
A vertical Reflection in the X axis: - ANSWER: Y = -f(x)
A Horizontal reflection in the Y axis: - ANSWER: y= f(-x)
Translation up A units - ANSWER: y= f(x)+A
Translation left A units - ANSWER: y=f(x+A)
Sketching from X axis by factor A - ANSWER: y= A*f(x)
Sketching from Y-axis by factor 1/A - ANSWER: y= f(Ax)
Shape of Positive cubic graph` - ANSWER: Upwards slope, two bends
Shape of Negative Cubic Graph - ANSWER: Downwards slope, two bends
, Shape of Positive Quartic Graph - ANSWER: "W" shape
Shape of Negative Quartic Graph - ANSWER: "M" shape
graph of y=1/x - ANSWER: 2 curves, one in Positive X & Y, another in Negative X & Y.
Graph of y= -1/x - ANSWER: Opposite of y=1/x , 2 curves, one in postive y but negative x,
another in negative y but positive x
Graph of y= 3/X^2 - ANSWER: 2 reciprocal curves, both above the x axis, opposite to each
other
Graph of y= -1/x^2 - ANSWER: 2 reciprocal curve, both below x axis, opposite to each other.
Equivalent angles of Sin(x) - ANSWER: Sin(x) = Sin(180-x)
Equivalent angles of Cos(x) - ANSWER: Cos(X) = Cos(360-x)
Sin & Cos repeat every... - ANSWER: 360 degrees
Tan repeats every... - ANSWER: 180 Degrees
Tan(θ) = - ANSWER: Sin(θ)/Cos(θ)
Sin rule - ANSWER: Sin(A)/a = Sin(B)/b
Cosine rule - ANSWER: a² = b² + c² - 2bcCos(A)
Area of a triangle using Sin() - ANSWER: 1/2abSin(C)
1 is directly equivalent to... (the second trigonometric identity) - ANSWER: Sin^2(theta) +
Cos^2(theta) = 1
the nCr equation - ANSWER: n!/r!(n-r)!
A negative reciprocal of the gradient of a line gives the gradient of the... - ANSWER:
Perpendicular line
Differentiating y= ax^n - ANSWER: = nax^n-1
To find the gradient of a point on a curve - ANSWER: Differentiate the equation of the curve,
then substitute the value of the point into this, then solve.
