A-level Maths Test With Solutions (A+)
if two lines are perpendicular, what must their gradients equal to when multiplied
together? - correct answer--1
What is the equation to calculate the gradient of a line? - correct answer-y₂-y₁/x₂-x₁
What is the equation to calculate the length of a line? - correct answer-√(y₂−y₁)^2 + (x₂-
x₁)^2
What is the equation to calculate the midpoint of a line? - correct answer-(x₂+x₁) over 2 ,
(y₂+y₁) over 2
What is the equation of a circle? - correct answer-x²+y²=r²
How do you find the midpoint of a circle from the equation? - correct 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. - correct 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? - correct 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? - correct 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? - correct 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? - correct
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? - correct answer-Try small integers using substitution
How do you quickly find a remainder of an equation given a factor? - correct answer-
Substitute in the factor, and this will equal the remainder
What change does the a in f(x) + a cause to a graph? - correct answer-It causes the
graph to move in the direction of the y axis
if two lines are perpendicular, what must their gradients equal to when multiplied
together? - correct answer--1
What is the equation to calculate the gradient of a line? - correct answer-y₂-y₁/x₂-x₁
What is the equation to calculate the length of a line? - correct answer-√(y₂−y₁)^2 + (x₂-
x₁)^2
What is the equation to calculate the midpoint of a line? - correct answer-(x₂+x₁) over 2 ,
(y₂+y₁) over 2
What is the equation of a circle? - correct answer-x²+y²=r²
How do you find the midpoint of a circle from the equation? - correct 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. - correct 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? - correct 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? - correct 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? - correct 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? - correct
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? - correct answer-Try small integers using substitution
How do you quickly find a remainder of an equation given a factor? - correct answer-
Substitute in the factor, and this will equal the remainder
What change does the a in f(x) + a cause to a graph? - correct answer-It causes the
graph to move in the direction of the y axis
