Core Chapter 1

Question 1

How to get surd out of denominator

Answer 1

Times by inverted surd (eg +/2 would go to -/2)

Question 2

a^m x a^n

Answer 2

a^m+n

Question 3

a^m / a^n

Answer 3

a^m-n

Question 4

a^-b

Answer 4

1/a^b

Question 5

a^b/c

Answer 5

b/a^c

Question 6

a^0

Answer 6

=1

Question 7

~/ab

Answer 7

~/a x b

Question 8

~/a/b

Answer 8

~/a / ~/b

Question 9

Completing the square

Answer 9

X^2 + 4x -12

= (x+4/2)^2 -(4/2)^2 -12

Question 10

Completing the square with an x^2 multiple

Answer 10

Don’t fret!

2x^2 + 12x + 13

2(x^2 + 12/2x + (0.5 x 12/2)^2 ) +13
2(x^2 + 6x + 9) + 13
2(x^2 + 6x + 9) + 13 -2(9)
2(x+6/2)^2 +13-18
2(x+3)^2 -5

Question 11

Discriminant >0

Answer 11

2 real roots

Question 12

Discriminant =0

Answer 12

1 root

Question 13

Discriminant <0

Answer 13

No real roots

Question 14

Discriminant equation

Answer 14

b^2-4(a x c)

Question 15

y= f(x)
y= f(x+2)

Answer 15

Moves along +2 (along x axis)

Question 16

y= f(x)
y= 2f(x)

Answer 16

Points on axis remain the same- the graph is stretched by the factor

Question 17

y=f(x)

y=-f(x)

Answer 17

Graph is inverted

Question 18

y=f(x)

y= f(2x)

Answer 18

Points on axis are extended outwards or inwards by such a factor