A level Maths question with answers
if two lines are perpendicular, what must their gradients equal to when multiplied
together? - - -1
-What is the equation to calculate the gradient of a line? - - y₂-y₁/x₂-x₁
-What is the equation to calculate the length of a line? - - √(y₂−y₁)^2 + (x₂-x₁)^2
-What is the equation to calculate the midpoint of a line? - - (x₂+x₁) over 2 ,
(y₂+y₁) over 2
-What is the equation of a circle? - - x²+y²=r²
-How do you find the midpoint of a circle from the equation? - - (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. - - 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? - - An x⁴ looks like a W
A -x⁴ looks like an upside down W
-What does an x³ and a -x³ graph look like? - - 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? - - 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? - - 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? - - Try small integers using substitution
-How do you quickly find a remainder of an equation given a factor? - - Substitute
in the factor, and this will equal the remainder
-What change does the a in f(x) + a cause to a graph? - - 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? - - It causes the graph to
move in the direction of the x axis
if two lines are perpendicular, what must their gradients equal to when multiplied
together? - - -1
-What is the equation to calculate the gradient of a line? - - y₂-y₁/x₂-x₁
-What is the equation to calculate the length of a line? - - √(y₂−y₁)^2 + (x₂-x₁)^2
-What is the equation to calculate the midpoint of a line? - - (x₂+x₁) over 2 ,
(y₂+y₁) over 2
-What is the equation of a circle? - - x²+y²=r²
-How do you find the midpoint of a circle from the equation? - - (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. - - 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? - - An x⁴ looks like a W
A -x⁴ looks like an upside down W
-What does an x³ and a -x³ graph look like? - - 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? - - 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? - - 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? - - Try small integers using substitution
-How do you quickly find a remainder of an equation given a factor? - - Substitute
in the factor, and this will equal the remainder
-What change does the a in f(x) + a cause to a graph? - - 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? - - It causes the graph to
move in the direction of the x axis
