Sem 1 in Review - G10Std

Mishmash

100

the derivative of 

3x^2 -2x-2/x

6x-2+2/x^2

200

Factorize fully

x^4-16

(x^2+4)(x-2)(x+2)

300

How many real roots?

x^2+2x+4=0

None

400

Solve for x.

log_x100 = 2

 x=10 

500

Write the expression as a single logarithm.

1/4log_cx + 5log_cz - log_cy

log_c (x^1/4 z⁵ / y)

Expanding Log Expressions

100

Evaluate each expression.

Reminder: When a logarithm is written "log" without an explicit base, it refers to the common logarithm, log₁₀

a) log₈ 1/8

b) log 1000

a) -1

b) 3

200

Use the properties of logarithms to expand log x/z⁴

Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive. 

logx - 4logz

300

Use the properties of logarithms to expand the following expression. 

log rad(xy⁷ / z³)

Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive.

1/2logx + 7/2logy - 3/2logz

400

Use the properties of logarithms to expand log (z²x)

Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive. 

2logz + logx

500

Use the properties of logarithms to expand the following expression.

log((y^7)/sqrt(xz^3))

Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive.

7logy - 1/2logx - 3/2logz

7logy-1/2logx-3/2logz

More Logs/Exp

100

How can we rewrite this statement as a logarithmic equation?

b^e = n

log_b n = e

200

How can we rewrite this statement as an exponential equation?

log_a c = b

a^b = c

300

Solve for x in the equation.

log_x81 = 2

x = 9

400

Solve the equation:

2^(2x)-3(2^x)-4=0

x = 2

500

Solve the equation to find x, leaving your answer(s) as an exact value(s).

2e^(2x)-7x+6=0

x = ln(2), ln(3/2)

Brain Teasers

100

It gets wet the more it dries

A towel

200

Evereyone has it, and No one can lose it!

A shadow

300

I am where yesterday follows today, and tomorrow is in the middle!

A dictionary

400

issue.  issue.  issue.  issue.  issue.  

issue.  issue.  issue.  issue.  issue.  

Tennis shoes

(Ten-issues)

500

Your mother's brother's only brother-in-law

Your father!

BAIN TEASER II

100

I have one eye, but cannot see

A needle

200

A plane crashes on the Cambodian-Laos border and every single person died. Later a man is seen on tv claiming to have survived. How?

He is/was married

300

Mom and Dad have four daughters and every daughter has a brother. How many people in the family?

7

400

He/she who makes it has no need of it. He/she who buys it, has no use for it. He/she who uses it can neither see nor feel it. 

What is it?

A coffin

500

If you have it you do not share it. If you share it, you lose it.

A secret