1. Gradient y2-y1/x2-x1 2. Length of a line sqrt((x2-x1)^2+(y2-y1)^2) 3. Midpoint (x1+x2/2, y1+y2/2) 4. How do you know if two lines are perpendic- ular? When you multiply the gra- dients together they should equal -1. The general rule is perpendicular = -1/m. Or you could use Pythagoras t...
Edexcel A-Level Mathematics - Pure Maths
Study online at https://quizlet.com/_8i8lqx
1. Gradient y2-y1/x2-x1
2. Length of a line sqrt((x2-x1)^2+(y2-
y1)^2)
3. Midpoint (x1+x2/2, y1+y2/2)
4. How do you know if two lines are When you multiply the
perpendic- ular? gra- dients together
they should equal -1.
The general rule is
perpendicular = -1/m.
Or you could use
Pythagoras to show
there is a right angle
5. How do you know if two lines are parallel? The gradients should be
the
same
6. What should you always remember The answer could be
when finding the square roots? posi- tive or negative
7. What is the quadratic formula? x = (-b ± b^2 - 4ac)/2a
(will
get 2 answers)
8. Describe the proof for the quadratic formula 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 sec- ond
bracket to the right side
1/
, Edexcel A-Level Mathematics - Pure Maths
Study online at https://quizlet.com/_8i8lqx
7) Square root both sides
8) Subtract the b/2a on
both sides 9) Simplify
the answer
9. What's the alternative formula you can ax2+bx+c = a(x + b/2a)2
use for completing the sqauare? + (c-b2/2a) You then
simpli- fy the second
bracket and solve the
equation
10.Describe y=(x+a)
2/
, Edexcel A-Level Mathematics - Pure Maths
Study online at https://quizlet.com/_8i8lqx
Horizontal translation,
+a move left, -a move
right, use vector (-a,0)
11. Describe y=f(x)+a Vertical translation, +a
move up, -a move down,
use vector (0/a)
12. Describe y=f(ax) Horizontal stretch by
scale factor 1/a
13. Describe y=af(x) Vertical stretch by scale
fac- tor a
14. Describe y=-f(x) Reflection of the
graph in the x axis
15. Describe y=f(-x) The graph is reflected in
the y-axis
16. Equation for real roots b2-4ac>0 Quadratic
graph passes through
x axis
17. Equation for equal roots b2-4ac=0 Quadratic
graph touches the x
axis
18. Equation for no real roots b2-4ac<0 Quadratic
graph doesn't touch x
axis
19. What is a linear model? Shows the relationship
be- tween two variables,
x and y. The graph has
a straight line and the
variables are related by
y = mx + c
20. What are the qualities of direct proportion? The two quantities
increase
3/
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