A LEVEL MATHS QUESTIONS AND
ANSWERS WITH SOLUTIONS 2024
if two lines are perpendicular, what must their gradients equal to when multiplied together? - ANSWER -
1
What is the equation to calculate the gradient of a line? - ANSWER y₂-y₁/x₂-x₁
What is the equation to calculate the length of a line? - ANSWER √(y₂−y₁)^2 + (x₂-x₁)^2
What is the equation to calculate the midpoint of a line? - ANSWER (x₂+x₁) over 2 , (y₂+y₁) over 2
What is the equation of a circle? - ANSWER x²+y²=r²
How do you find the midpoint of a circle from the equation? - ANSWER (x-a)²+(y-b)²=r²
If a factor of a line equation is (x-2)², or the line equation is just y=(x-2)², how many solutions does (x-2)²
give and what does this look like on a graph. - ANSWER This gives just one solution, that x=2. This means
that the line just touches the x axis at (2,0).
What does a x⁴ and a -x⁴ graph look like? - ANSWER An x⁴ looks like a W
A -x⁴ looks like an upside down W
What does an x³ and a -x³ graph look like? - ANSWER An x³ graph appears to travel from bottom left to
top right with two curves
A -x³ graph appears to travel from bottom right to top left with also two curves
How do you find the min/max point of a quadratic? - ANSWER Complete the square; the x in the bracket
will be the x coordinate and the number out the bracket will be the y coordinate
How do you establish that (x-3) for example, is a factor of an equation? - ANSWER Sub in 3 for example.
If it is a factor, there will be no remainder and it will equal 0.
, If no factors of an equation are given and you are asked to factorise, what should you do? - ANSWER Try
small integers using substitution
How do you quickly find a remainder of an equation given a factor? - ANSWER Substitute in the factor,
and this will equal the remainder
What change does the a in f(x) + a cause to a graph? - ANSWER It causes the graph to move in the
direction of the y axis
What change does the a in f(x+a) cause to a graph? - ANSWER It causes the graph to move in the
direction of the x axis
How do you change the factors of a graph that has been translated by f(x+a)? - ANSWER If it was
translated by moving to the right by 3, you would add 3 to each factor bracket. e.g (x+3) would change to
(x+6)
What can pascals triangle be used for during binomial expansion? - ANSWER Pascals triangle shows the
coefficients of the expansion.
It also shows a pattern of the a²,a³ b²,b³ etc.
What is the pattern of the a² etc and b² etc? - ANSWER The a's decrease as you go across the triangle.
The b's increase as you go across the triangle
How else can you find a coefficient of an expansion? - ANSWER Using ⁿCr
What does the n and r stand for in nCr? - ANSWER n is the number it is to the power of. r is the number
of term which you want to find
What does r start at? - ANSWER It starts from 0 and then progresses
What is nC0 always equal to no matter what n is? - ANSWER 1
ANSWERS WITH SOLUTIONS 2024
if two lines are perpendicular, what must their gradients equal to when multiplied together? - ANSWER -
1
What is the equation to calculate the gradient of a line? - ANSWER y₂-y₁/x₂-x₁
What is the equation to calculate the length of a line? - ANSWER √(y₂−y₁)^2 + (x₂-x₁)^2
What is the equation to calculate the midpoint of a line? - ANSWER (x₂+x₁) over 2 , (y₂+y₁) over 2
What is the equation of a circle? - ANSWER x²+y²=r²
How do you find the midpoint of a circle from the equation? - ANSWER (x-a)²+(y-b)²=r²
If a factor of a line equation is (x-2)², or the line equation is just y=(x-2)², how many solutions does (x-2)²
give and what does this look like on a graph. - ANSWER This gives just one solution, that x=2. This means
that the line just touches the x axis at (2,0).
What does a x⁴ and a -x⁴ graph look like? - ANSWER An x⁴ looks like a W
A -x⁴ looks like an upside down W
What does an x³ and a -x³ graph look like? - ANSWER An x³ graph appears to travel from bottom left to
top right with two curves
A -x³ graph appears to travel from bottom right to top left with also two curves
How do you find the min/max point of a quadratic? - ANSWER Complete the square; the x in the bracket
will be the x coordinate and the number out the bracket will be the y coordinate
How do you establish that (x-3) for example, is a factor of an equation? - ANSWER Sub in 3 for example.
If it is a factor, there will be no remainder and it will equal 0.
, If no factors of an equation are given and you are asked to factorise, what should you do? - ANSWER Try
small integers using substitution
How do you quickly find a remainder of an equation given a factor? - ANSWER Substitute in the factor,
and this will equal the remainder
What change does the a in f(x) + a cause to a graph? - ANSWER It causes the graph to move in the
direction of the y axis
What change does the a in f(x+a) cause to a graph? - ANSWER It causes the graph to move in the
direction of the x axis
How do you change the factors of a graph that has been translated by f(x+a)? - ANSWER If it was
translated by moving to the right by 3, you would add 3 to each factor bracket. e.g (x+3) would change to
(x+6)
What can pascals triangle be used for during binomial expansion? - ANSWER Pascals triangle shows the
coefficients of the expansion.
It also shows a pattern of the a²,a³ b²,b³ etc.
What is the pattern of the a² etc and b² etc? - ANSWER The a's decrease as you go across the triangle.
The b's increase as you go across the triangle
How else can you find a coefficient of an expansion? - ANSWER Using ⁿCr
What does the n and r stand for in nCr? - ANSWER n is the number it is to the power of. r is the number
of term which you want to find
What does r start at? - ANSWER It starts from 0 and then progresses
What is nC0 always equal to no matter what n is? - ANSWER 1
