AQA A-LEVEL MATHEMATICS STUDY
GUIDE 2026 COMPLETE QUESTIONS
WITH CORRECT SOLUTIONS GRADED
A+
◉ Length of a line. Answer: sqrt((x2-x1)^2+(y2-y1)^2)
◉ Midpoint. Answer: (x1+x2/2, y1+y2/2)
◉ How do you know if two lines are perpendicular?. Answer: When
you multiply the gradients together they should equal -1. The general
rule is perpendicular = -1/m. Or you could use Pythagoras to show
there is a right angle
◉ How do you know if two lines are parallel?. Answer: The gradients
should be the same
◉ What should you always remember when finding the square
roots?. Answer: The answer could be positive or negative
◉ What is the quadratic formula?. Answer: x = (-b ± √b^2 - 4ac)/2a
(will get 2 answers)
, ◉ Describe the proof for the quadratic formula. Answer: 1) Divide by
a on both sides 2) Complete the square for ax2/a + bx2/a 3) Expand
the second bracket, (b/2a)2 4) Multiply by c/a by 4 and add the
fractions 5) Factorise into brackets 6) Add the second bracket to the
right side 7) Square root both sides 8) Subtract the b/2a on both
sides 9) Simplify the answer
◉ What's the alternative formula you can use for completing the
sqauare?. Answer: ax2+bx+c = a(x + b/2a)2 + (c-b2/2a) You then
simplify the second bracket and solve the equation
◉ Describe y=(x+a). Answer: Horizontal translation, +a move left, -a
move right, use vector (-a,0)
◉ Describe y=f(x)+a. Answer: Vertical translation, +a move up, -a
move down, use vector (0/a)
◉ Describe y=f(ax). Answer: Horizontal stretch by scale factor 1/a
◉ Describe y=af(x). Answer: Vertical stretch by scale factor a
◉ Describe y=-f(x). Answer: Reflection of the graph in the x axis
◉ Describe y=f(-x). Answer: The graph is reflected in the y-axis
GUIDE 2026 COMPLETE QUESTIONS
WITH CORRECT SOLUTIONS GRADED
A+
◉ Length of a line. Answer: sqrt((x2-x1)^2+(y2-y1)^2)
◉ Midpoint. Answer: (x1+x2/2, y1+y2/2)
◉ How do you know if two lines are perpendicular?. Answer: When
you multiply the gradients together they should equal -1. The general
rule is perpendicular = -1/m. Or you could use Pythagoras to show
there is a right angle
◉ How do you know if two lines are parallel?. Answer: The gradients
should be the same
◉ What should you always remember when finding the square
roots?. Answer: The answer could be positive or negative
◉ What is the quadratic formula?. Answer: x = (-b ± √b^2 - 4ac)/2a
(will get 2 answers)
, ◉ Describe the proof for the quadratic formula. Answer: 1) Divide by
a on both sides 2) Complete the square for ax2/a + bx2/a 3) Expand
the second bracket, (b/2a)2 4) Multiply by c/a by 4 and add the
fractions 5) Factorise into brackets 6) Add the second bracket to the
right side 7) Square root both sides 8) Subtract the b/2a on both
sides 9) Simplify the answer
◉ What's the alternative formula you can use for completing the
sqauare?. Answer: ax2+bx+c = a(x + b/2a)2 + (c-b2/2a) You then
simplify the second bracket and solve the equation
◉ Describe y=(x+a). Answer: Horizontal translation, +a move left, -a
move right, use vector (-a,0)
◉ Describe y=f(x)+a. Answer: Vertical translation, +a move up, -a
move down, use vector (0/a)
◉ Describe y=f(ax). Answer: Horizontal stretch by scale factor 1/a
◉ Describe y=af(x). Answer: Vertical stretch by scale factor a
◉ Describe y=-f(x). Answer: Reflection of the graph in the x axis
◉ Describe y=f(-x). Answer: The graph is reflected in the y-axis
