C1: indices and quadratics

Question 1

a^m * a^n

Answer 1

a^(m+n)

Question 2

a^m / a^n

Answer 2

a^(m-n)

Question 3

(a^m)^n

Answer 3

a^mn

Question 4

a^(m/n)

Answer 4

n√a^m

Question 5

(a/b)^-n

Answer 5

(b^n)/(a^n)

Question 6

√(a^2 * b)

Answer 6

a√b

Question 7

Rationalise the denominator of a/√b

Answer 7

a/√b * √b/√b = (a√b)/b

Question 8

Rationalise the denominator of 1/(a + √b)

Answer 8

1/(a + √b) * (a - √b)/(a - √b) = (a - √b)/(a^2 - b)

Question 9

How do you complete the square?

Answer 9

factorise the coefficient of x^2 out of the first two terms
a(x^2 + bx/a) + c = 0
a(x - b/2a)^2 - (b/2a)^2 + c = 0

Question 10

Give the quadratic formula.

Answer 10

x = (-b +- √b^2 - 4ac)/2a

Question 11

Give the discriminant.

Answer 11

b^2 - 4ac

Question 12

What information does the discriminant give?

Answer 12

if < 0, no solutions
if = 0, one solution
if > 0, two solutions

Question 13

How do you solve quadratics in completed square form?

(x + a)^2 - b = 0

Answer 13

(x + a)^2 = b
x + a = +-√b
x = a + √b or x = a - √b

Question 14

How do you solve quadratic inequalities?

Answer 14

find the points where x = 0
draw a graph
shade above/below as applicable

Question 15

How do you solve simultaneous equations wherein one is linear and one quadratic?

Answer 15

rearrange the linear to make one unknown the subject

substitute into quadratic