math p 3 revision

7/31/2019 Math p 3 Revision

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Rawafed Private School

P3 Exam

Mathematics

Grade 10

(2011 - 2012)

Students Name: ................................

Section: .................


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Math - P3 Revision Page 1

- Simplify each logarithm.

1.5

1log

25

2.6

log 6 6

3.4log 2

4. 37log 49

5. 321

log4

6. 12

log 8


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- Solve for x.

1. 6log 3x

2.4

3log

2x

3. log 64 6x

4.1

log 72

x

5. ln 3x

6. ln( 4) 1x

7. 2ln 9x


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8. 2xe

9.2

25x

e

10. 2 2xe

11. 3xe

12. ln(ln ) 0x

13. ln 1x

14. ln ln( 3) ln10x x

15. 2 7 12 0x ee e


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16. 23 7 3 10 0x x

- Express 2 36log M N in terms of 6log M and 6log N .

- Express 2 5logM

Nin terms of 2log M and 2log N .

- Express as a single logarithm.

a. 10 10log 3logp q

b. 10 104 log 2 log 2p q


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- If 10log 2 0.30 and 10log 3 0.48 , find the following.

a. 10log 18

b.10

20log

3

c. 10log 5

d.10 3

1log

2

- Solve each equation.

1. log ( 3) log 8 log 2b b bx


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2. log log ( 5) log 6a a ax x

3. 22log ( 9) 4x

Questions 4 - 5: a. Give the solution in calculation ready form.

b. Give the solution to three significant digits.

4. 3 30x

5. 212 1000x


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- Write each equation in exponential form.

1. ln100 4.61

2.2

1ln 2

e

- Write each equation in logarithmic form.

1. 3 20.1e

2. 3 1.40e

- Simplify. If the expression is undefined, say so.

1. 10ln e

2.1

lne

3.ln5e


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- Write as single logarithm.

1. ln8 ln2

2.1

ln 8 ln 5 33

- Problem Solving:

1. How long will it take an investment of $1000 to triple in value if it is invested at an annual

rate of 12% compounded quarterly?

2. A certain bacteria population, doubles in size every 12 hours. By how much will it grow in

2 days?

3. The half-life of carbon-14 (C-14) is 5730 years. How much of a 10.0 mg sample will

remain after 4500 years?


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4. The value of a new $12,500 automobile decrease 20% per year. Find its value after 3 years.

5. A culture of yeast doubles in size every 20 min. The size of the culture is now N0. Find its

size in 12 hours.

6. The radioactive gas radon has a half-life of approximately1

32

days. About how much of a

l00 g sample will remain after 1 week?

7. How long will it take you to double your money if you invest it at a rate of 8%

compounded annually?


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- Tell whether each sequence is arithmetic, geometric, or neither. Then supply the

missing terms of the sequence.

1. 20, 17, 14, 11, ______, ______

2. 1,1

4,

1

9,

1

16, ______, ______

- Find the first four terms of the sequence with the given formula. Then tell whether the

sequence is arithmetic, geometric, or neither.

1. 4 3nt n

2.13n

nt

3. 2 3n

nt


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- Find a formula for the nth term of each arithmetic sequence.

1. 24, 32, 40, 48 . . .

2. -3, -10, -17. -24 . . .

- Find the specified term of each arithmetic sequence.

1. 4, 9, 14, 19 . . . ; 21t

2. -2, -11, -20 . . . ; 25t

3. 1 5t , 3 20t ; 12t

4. 5 24t , 9 40t ; 1t


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- Find the arithmetic mean of each pair of numbers.

1.4 11

,5 5

2. 2 , 3 2

- Insert four arithmetic means between each pair.

11, _______, _______, _______, _______, 35

- Find a formula for the nth term of each geometric sequence.

1. 2, 6, 18, 54 . . .

2. 1, 2 , 2, 2 2

3. -1, 0.1, -0.01, 0.001


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- Find the specified term of each geometric sequence.

1. 2, 6, 18, 54 . . . ; t10

2. 40, -20, 10, -5 . . . ; t11

3. t2 = 18, t3 = 12; t5

4. t1 = 5, t3 = 80; t6

5. t3 = -12, t6 = 96; t9

- Find the geometric mean of the following pair of numbers.

1.1

12,

1

18


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- Write each series in expanded form.

1.

6

1

( 10)

n

n

2.

6

1

2n

n

3.

10

4

(3 2)n

n

- Write each series using sigma notation.

1. 2 + 4 + 6 + --- + 1000

2. 13 + 23 + 33 + --- + 203

3.1

2+

2

3+

3

4+ --- +

99

100


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math p 3 revision

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