REVISION

Functions

100

What is the slope of the function y=3x+7?

3

200

Find the vertex of the quadratic function:

y=x^2-6x+8

(3, -1)

300

Solve the inequality

x^2-5x-6<0

(-1,6)

400

Given the functions  f(x)=2x+3 g(x)=x^2-1 , find the explicit expressions for 

f(g(x))=?

f(g(x))= 2x^2+1

500

Find the domain of the function

f(x)=10/x-5

x=5

Sequence

100

What is the next number in the sequence?

2,4,6,8, ..... ?

10

200

A sequence starts at 50 and is reduced by 10% with each term. Find the sum of the infinite series.

S=500

300

In a sequence, 5th term is 30 and 8th term is 63. What is the rule governing this sequence, and what is the 15th term?

a_n=11n-25

140

400

A sequence begins with 12 and has a common ratio of 1/3. Find the sum of the first 8 terms.

13120/729 or 18,00 apprx

500

A sequence starts with 4 and is doubled with each term. What is the 10th term?

2048

Logarithms

100

log₃(x)=2

x=9

200

Rewrite in exponential form

log₂8=3

2³=8

300

log₂log₃81=?

2

400

solve

log₂(x-5) + log₂(x+2)=3

x=6

500

Solve

log_1/5(4-3x)>-1

-1/3<x<4/3

Exponentials

100

2^x=16

x=4

200

A population doubles every year. If it starts at 100, what is the population after 3 years?

800

300

3^(x+1) =81

3

400

9^x -4*3^x +3=0

x=0, x=1

500

27=1/3^x

x=-3