Chap 10 - Straight line, quadratic equations

Question 1

Formula for straight lines

Answer 1

• y = mx + c
  -m = gradient
  -c = y-intercept
  -y & x = not fixed values

Question 2

formula for gradient of straight line

Answer 2

-rise/ run
-without graph: need 2 points
y2 - y1/ x2 - x1
-always make fraction

Question 3

formula for y-intercept of straight line

Answer 3

-need 1 point & gradient
y - y1 = m (x - x1)

Question 4

how to find gradient of perpendicular straight line (has to intersect at 90)

Answer 4

-m for perpendicular is inverse
- flip fraction & make ( - )

Question 5

How to find equation of parallel straight line

Answer 5

-m is same
-change c only

Question 6

How to find intercept knowing the other of straight line

Answer 6

-if don’t know y = auto - (0, __)
-if don’t know x = auto - (__, 0)
-use the equation and make the known intercept = 0

Question 7

formula for midpoint of straight line

Answer 7

• x1 + x2/ 2 (for x)
• y1 + y2/ 2 (for y)
• (x, y)

Question 8

formula for length of straight line

Answer 8

-use Pythagoras
-√ (x2 - x1)^2 + (y2 - y1)^2

Question 9

what does gradient measure

Answer 9

steepness

Question 10

which direction is ( - ) straight line graph

Answer 10

south east from origin

Question 11

which direction is ( + ) straight line graph

Answer 11

North east from origin

Question 12

what is undefined gradient of straight line

Answer 12

-straight line up
-x = ___
-x/0

Question 13

What is 0 gradient of straight line

Answer 13

-straight line horizontal
-y = ___
-0/x

Question 14

highest power for linear, quadratic, cubes

Answer 14

-1
-2
-3

Question 15

note: (x - 3 )^2 ≠ x^2 - 9

Question 16

note: be careful of signs when solving equations

Question 17

What is DOPS

Answer 17

-diff of perfect squares
- a^2 - b^2 = (a + b)(a - b)
-eg. x^2 - 9 = (x + 3)(x - 3)

Question 18

note: use HCF for factorizing

Question 19

Cheats method for quadratic equations

Answer 19

-only use if no no. before letter
- x^2 _ (no.s [ + ] [letter]) _ (no.s [x])
-eg. (x - 2)^2 = (x - 2)(x - 2)
= x^2 - 4x + 4

Question 20

note: Factorising:
-2( - ) = ( - )( + )
-1( - ) = 2( - )

Question 21

How to solve quadratic equations

Answer 21

-identify by checking highest power is 2
-has 0, 1, 2 ans
-factories
-solve each bracket
-2 ans = 2 x-intercept
-1 ans = 1 x-intercept
-0 ans = 0 x-intercept