Year 11 ADV Review

Index Laws

100

Solve for x. x= 5³ * 2² 

x= 500

200

Solve (1/4)³

1/64

300

Solve (((t²-9)/(3t-9))⁰)³

1

400

Write 64^-2/3 as a rational number

1/16

500

Find the value of (a³b²)/c² 

if a=(5/4)², b=(2/3)³, and c=(1/2)⁴

4

Trigonometry

100

1=?

cos²x + sin²x

200

Find the exact value of cosec pi/4

Square root of 2

300

How many times does the cosecant function cross the x-axis

none... it doesn't ;D

400

Find the exact value of sin120 + cos135 as a surd with a rational denominator 

(√3 - √2) /2

500

A train depot has train tracks running north for 7.8km where they meet another set of tracks going east for 5.8km into a station. What is the bearing of the depot from the station, to the nearest degree?

217 degrees

Differentiation

100

Name the four rules

Short method or Power rule, Chain rule, Product rule, Quotient rule

200

Differentiate y=x³ - 5x²

dy/dx = 3x² - 10x 

300

Differentiate and simplify 1/√ x

= 1/2 ³√ x

400

Differentiate using the Quotient rule y=(3x+1/2x-1) 

=4/(2x-1)²

500

If f(x) = √ x, what is the value f''(4)

-1/32

Logarithms

100

log(5)125

3

200

7^{log(7)^4}

4

300

Rearrange : 

log₂ ( √2/ 4)

log₂√2- log₂ 4

400

2log _x k - log_x3 + log_xp

 log _x (k^2) x p /3

500

If log_b2=0.6+ log_b3=1.1

log_b6b

2.7

Functions

100

What is the test used to determine whether a graph is a function?

Veritcal line test.

200

Describe what the function y=-x³+4x-3 looks like.

Negative, cubic function (starts high on left in Q2, and ends in Q4), y-intercept at -3.

300

What is the maximum number of x-interecepts 2x⁵+3x³-4x²+1 could have?

Max = 5 intercepts

400

Is the function f(x)=(x+2)(x³+3x-2) odd, even or neither.

f(x)=(x+2)(x³+3x-2) is neither odd or even

500

What will the zeros of 8X²+2x+6 be?

sqrt(b²-4ac) is negative, therefore there will be no zeros