Advance Algebra Dhan Lord B. Fortela

BS Chemical Engineering

UPLB

Digit Problems

Let

h = hundred’s digit

t = ten’s digit

u = unit’s digit

FOR 3-DIGIT NUMBER:

The number is: 100h + 10t + u

The reversed number is: 100u + 10t + h

The sum of the digits is: h + t + u

Exercise!!!

The sum of the digits of a two-digit number

is 10. When 18 is subtracted from the

number, the order of the digits will be

reversed. Find the number.

a) 82 c) 64

b) 28 d) 46

Exercise!!!

If a two-digit number has x for its unit’s

digit and y for its ten’s digit, represent the

number.

a) yx c) 10x + y

b) 10y + x d) x + y

Exercise!!!

When a two-digit number is deducted

with its reverse the result is 36. The sum

of the digits is 6. Find the number.

a) 15 c) 42

b) 51 d) 24

Number Problems

Let x be the 1st number

Let y be the 2nd number

Be familiar with the common sentence structures

First number is twice the other: x = 2y

First number is five more than thrice the other: x = 3y + 5

First number is six less than one half of the other: x = y/2 – 6

The sum of their squares: x2 + y2

The cube of their difference: (x – y)3

Exercise!!!

One number is five less than the other

number. If their sum is 135, what are the

numbers?

a) 70 & 75 c) 65 & 70

b) 60 & 65 d) 75 & 80

Exercise!!!

The sum of the reciprocals of two numbers

is 11. three times the reciprocal of one of

the numbers is three more than twice the

reciprocal of the other number. Find the

numbers.

a) 5 & 6 c) 1/5 & 1/6

b) 7 & 4 d) 1/7 & 1/4

Exercise!!!

Find the largest of three consecutive

numbers whose sum is 75.

a) 23 c) 25

b) 24 d) 26

Clock Problems

If the MINUTE hand moves a distance of

x, the HOUR hand moves x/12

If the SECOND hand moves a distance of

x, the MINUTE hand moves x/60 and the

HOUR hand moves x/720

Exercise!!!

How many minutes after 2 o’clock will the

hands of the clock be perpendicular for

the first time?

a) 15 c) 25.25

b) 20.5 d) 27.27

Exercise!!!

How many minutes after 6 o’clock will the

hands of the clock be together for the

first time?

a) 30 c) 35.50

b) 32.72 d) 40

Exercise!!!

In one day (24 hours), how many times will

the hour-hand and minute-hand of a

continuously driven clock be together?

a) 21 c) 23

b) 22 d) 24

Mixture Problems

The only additive amount is the volume

and/or mass

a% of A

b% of B

c% of A

d% of B

x% of A

y% of B ± =

amount 1 amount 2 amount 1 ±

amount 2

Exercise!!!

How many grams of gold must be added

with 500 grams of an alloy containing 30%

gold and 70% silver in order to produce

another alloy analyzing 40% gold and60%

silver?

a) 100 c) 83.33

b) 90.50 d) 75.25

Exercise!!!

A 100-kilogram salt solution originally 4%

by weight salt in water is boiled to reduce

water content until the concentration is

5% by weight salt. How much water is

evaporated?

a) 10 c) 20

b) 15 d) 25

Age Problems

Make a table of the PAST, PRESENT,

FUTURE

The difference of the ages of two persons

is constant

Person PAST PRESENT FUTURE

A

B

Exercise!!!

Two times a father’s age is 8 more than six

times his son’s age. Ten years ago, the sum

of their ages was 44. The age of the son is:

a) 49 c) 20

b) 15 d) 18

Exercise!!!

Peter’s age 13 years ago was 1/3 of his age

7 years hence. How old is Peter?

a) 15 c) 23

b) 21 d) 27

“hence” means LATER THAN

NOW

Rate/Work Problems

RATE* TIME = 1

RATE*TIME = WORK

Exercise!!!

One faucet can fill a tank in 3 hours while a

second faucet can fill it in 5 hours. If both

are opened, how many hours will it take

to fill the tank?

a) 15/6 c) 15/8

b) 15/7 d) 15/9

Exercise!!!

One faucet can fill a tank in 2 hours while a

second faucet can fill it in 3 hours. If both

are opened for 1-hour, what fraction of

the tank is filled?

a) 0.70 c) 0.75

b) 0.73 d) 0.83

Exercise!!!

Mr. Brown can wash his car in 15 minutes,

while his son John takes twice as long to

do the same job. if they work together,

how many minutes can they do the

washing?

a) 6 c) 10

b) 8 d) 12

Motion Problems

Velocity = distance / time

Distance = velocity* time

Exercise!!!

Nonoy left Pikit to drive to Davao at 6:15

PM and arrive at 11:45 PM. If he averaged

30 mph and stopped 1 hour for dinner,

how far is Davao from Pikit?

a) 128 c) 160

b) 135 d) 256

Exercise!!!

Juan can walk from his home to his office at

the rate of 5 mph and back at the rate of

2 mph. What is his average speed in mph?

a) 3.4 0 c) 2.76

b) 3.50 d) 2.86

Binomial Expansion

(x + y)n

Exercise!!!

Find the fourth term of the expansion of

(2a –c)6.

a) 180a3c3 c) 160a3c3

b) -180a3c3 d) -160a3c3

Exercise!!!

The middle term in the expansion of (x2 –

3)8 is:

a) -70x8 c) -5670x8

b) 70x8 d) 5670x8

Progression Problems

Arithmetic (constant difference)

◦ an = am + (n-m)d

◦ Sum = (n/2)(an + am)

Geometric (constant ratio)

◦ an = am r(n-m)

◦ Sum = a1 [(1-rn)/(1-r)]

Harmonic (reciprocal of Arithmetic prog.)

Exercise!!!

What is the 21st term of the sequence -9, -

6, -3, … ?

a) 49 c) 51

b) 50 d) 52

Exercise!!!

Find x in the series: 1, 1/3, 0.2, x .

a) 1/6 c) 1/7

b) 1/8 d) 1/9

Exercise!!!

The sum of all even numbers from 0 to 420

is:

a) 43410 c) 44310

b) 44300 d) 44130

Exercise!!!

How many terms of the sequence -9, -6, -3,

… must be taken so that the sum is 66?

a) 13 c) 4

b) 12 d) 11

That’s all for your Advance Algebra…

Thank you for listening!