Unit 1 test revision

Question 1

midpoint

Answer 1

((x1+x2)/2,(y1+y2)/2))

Question 2

perpendicular gradient

Answer 2

-(1/m)

gradient=m

Question 3

finding the equation of a straight line

Answer 3

y-y1=m(x-x1)

where m is the gradient and (x1,y1) is a point on a line.

Question 4

equations of circles

Answer 4

The equation of a circle is (x-a)^2+(y-b)^2=r^2

where r^2 is the radius and (a,b) is the centre of the circles.

Question 5

SURDS

Answer 5

root 320

root 16*20

root 16 * root 20

4root20

4root4*5

4*2 root5

8root5

Question 6

Multiplying surds

Answer 6

5root3 * 3root2

5*3=15

root3*root2=root6

15root6

Question 7

Dividing surds

Answer 7

root8/9

root8/root9

root8/3

2root2/3

Question 8

Rationalising

Answer 8

2/5root3

times by the surd on the bottom

2root3/15

Question 9

negative and fractional indices

Answer 9

3^-2

3^2=9

reciprocal of 9

1/9

so x^-n = 1/x^n

Question 10

fractional indices

Answer 10

x^1/n =^nrootx

25^1/2 =root25=5

27^1/3=^3root27=3

Question 11

Exact trig values

Answer 11

sin0=0
cos0=1

sin180=0
cos180=-1

sin360=0
cos360=1

Question 12

Exact trig values 2

Answer 12

sin30=1/2
cos30=root3/2
tan30=root3/3

sin45=root2/2
cos45=root2/2
tan45=1

sin60=root3/2
cos60=1/2
tan60=root3

sin90=1
cos90=0

Question 13

What do the different numbers do to the sine rule?

Answer 13

The number in front of the trig ratio determinds how high tue curve is.

ie: y=2cos(x), its peak is at 2

The number in front of the x determinds how long the distance between the peaks are.

ie: y=cos(4x)

Question 14

Gradient

Answer 14

(y2-y1)/(x2-x1)