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TRADES/APPRENTICESHIP EXAMS
MATH + READING STUDY GUIDES
NAME: ____________________
DATE: _____________________
Apprenticeship Program: ____________________
Sponsor teacher: __________________________
Date of Apprenticeship start: _________________
THE EXAMS . . .
You will be writing 2 exams at the one sitting. You will be given a Reading
Section that has a time limit of 45 minutes and a Math Section that is also
45 minutes, a total of 1.5 hours. CALCULATORS ARE NOT PERMITTED.
The exams are multiple choice and you will CIRCLE the correct answer on
the sheet provided. Do not mark the test booklets.
If you have a Learning Disability in Math or Reading, the only adjudication
service that will provide is extra time.
THE STUDY GUIDES . . .
READING
The Reading Exam measures comprehension. It is not a hard exam, but you
may be pressed for completion – keep in mind that you are asked 48
questions and you have 45 minutes to complete the test. The Directions ask
you to read a passage and then answer a question about the passage. It is
a multiple choice exam so you will choose the best answer to each question.
The passages will be in several different formats: there are the “Ad” style
and “Label” style reading passages in which you will be required to scan and
find the correct answer. There are short informational passages where you
can re-read and then find the right answers. You will be asked factual
questions as well as inferential questions where you will “read between the
lines” and make a judgmental choice. There is a poetry selection where you
will be asked what the poem is about. You do not need to know the literary
devices that you learned in school. In all of these passages you are reading
for understanding. The best advice is to place yourself and use the whole 45
minutes given for the test. In the practice guide you are given some
passages to read and then to answer. Be confident! Practice pays off!
MATH
The guide has been organized into different components. Each component
has been explained in easy to follow steps with practice questions at the end
of each component. Remember not to use a calculator. After completing all
the components, proceed to the practice exams. Practice, practice, practice.
Re-learn then memorize your times-division tables. Not using a calculator
will mean more review for you until you get in stride. Once you master
these operations you will do well! Be confident! Practice pays off!
2
READING COMPREHENSION
The following is test from a science journal.
Objects that are moving on a rotating disk or sphere tend to be deflected
from motion in a straight line by the Coriolis force. For instance, objects
which move northward or southward from the equator of the Earth tend to
be deflected eastward by the Coriolis force. The force can generate very
complex circulation patterns in atmospheres of planets which rotate very
quickly. On the other hand, the Coriolis force does not complicate the
atmospheric circulation of planets like Venus which rotate very slowly.
1.
Venus will not have
atmosphere because:
a)
b)
c)
d)
2.
complex
circulation
pattern
within
its
is a hot planet
has a ring around it
rotates very slowly
is not a complex plant
What is this text mainly about?
a)
b)
c)
d)
3.
It
It
It
It
a
Venus
Objects which move northward or southward
Coriolis force
Atmosphere
When are moving objects affected by the Coriolis force?
a)
b)
c)
d)
When they are on Venus
When they are moving on a rotating object
When they are round
They are never affected by this force.
3
The following is a text from
W.B. Yates – The Collected
Poems
The following is an editorial by
Rob Walker – Disney’s RePurpose in Life
The Empty Cup
By W.B. Yates
Everybody loves to pick on cable
companies, and the easiest target
is usually whoever your local
provider is – Time Warner, Cox,
Comcast, and so on. People tend
not to get annoyed with the
“content” firms like Disney, which
generally strike a public pose of
being at the mercy of the
distribution meanies.
In fact,
Disney has a tremendous amount
of power over what choices are
available over a given cable
system.
A crazy man that found a cup,
When all but dead of thirst.
Hardly dared to wet his mouth
Imagining, moon-accursed,
That another mouthful
And his beating heart would burst.
October last I found it too
But found it dry as bone,
And for that reason am I crazed
And my sleep is gone.
4.
In line
a)
b)
c)
d)
4, what is “accursed”
A dusty moon
A bone
Being under a curse
I don’t know
5.
In line 8 “dry as a bone”
refers to:
a) Boneless
b) Dry cup
c) Full of bones
d) I don’t know
6.
The editor is writing from the
point of view of a:
a) Consumer
b) Analyst
c) Sport fan
d) Teacher
7.
In comparison with cable
companies how is Disney
seen?
a) Like a meanie
b) Like an annoyance to
consumers
c) Like an okay company
d) Like
a
money
monolith
ANSWERS
1. c
2. c
3. b
4. c
5. b
6. a
7. c
4
QUESTIONS: Circle the correct answer
1.
What must you add before you heat the soup?
a) 1 can of milk
b) 1 can of water
c) Nothing
2.
Net wt. is the weight of;
a) Can plus food
b) Food only
3.
Tomatoes make Ethan sick. Read the list of ingredients in the soup
above. Can Ethan eat this soup?
a) Yes
b) No
4.
Marge wants to keep down the number of calories she eats. Which is
better for her?
a) ½ cup of peas, about 30 calories
b) A serving of Morgan’s Chicken Gumbo (Find the calories
under Nutrition information and compare.
5.
How many ounces of soup are in the can on the last page?
______________ ounces
5
6.
UNIT PRICE LABELS are
sometimes on shelves under
the food.
They help you
compare prices. Look at the
unit price labels at the right.
For 1 pound of soup, which
brand costs less?
a) Atlas
b) Morgan’s
7.
Which orange drink has more
orange juice in it?
a) Elmo’s
b) Sunny’s
8.
Sometimes milk is stamped
with a date.
The store
shouldn’t sell the milk after
that date.
The later the
date, the fresher the milk.
Which milk do you think is
fresher?
a) Dec 14
b) Dec 17
9.
This chicken pie thawed
when the electricity went off.
Now the electricity is fixed.
What should you do with the
pie?
a) Eat is tonight for
dinner
b) Put it back in the
freezer
10.
What can’t you do with this
fish?
a) Cook it right away
b) Leave it on the
table overnight
c) Put
it
in
the
refrigerator
6
QUESTIONS:
1.
Wish detergent may hurt your;
a) Eyes
b) Skin
2.
How much Wish goes into each of
these washing machines? Write your
answer above each picture.
3.
Sani-Sink fixes stopped up sinks.
The label says POISON. Which should
you be more careful with?
a) Sani-Sink
b) Wish
7
4.
To get the top off this can;
a) Squeeze, pull, and twist
b) Turn left and unscrew
5.
This spray is not food for:
a) Ants
b) Flies
c) Roaches
6.
The Cautions at the right are
numbered. Write the numbers
below to show what each
Caution means. (The first one
is done for you.)
__6__ Catches fire easily
_____ Be sure there is a lot of fresh air
_____ Don’t breath product
_____ Don’t throw empty can in garbage
to be burned
_____ Lock it up when not using it
_____ Try not to get it on skin
_____ If swallowed, see a doctor right
away.
8
QUESTIONS;
1.
The shirt on Page 10 is red.
Can you wash it with your white
sheets?
a) Yes
b) No
2.
COLORFAST is on the label
of another red shirt. If you
wash it with your white
sheets will they turn pink?
a)
b)
3.
Which pair of pants is more likely
to need ironing?
a)
1
b)
2
4.
Which pair of pants will probably
look worse if you let them out
at the bottom.
a)
1
b)
2
5.
Which jacket will keep water out
even in a heavy storm?
a)
1
b)
2
6.
How
a)
b)
c)
7.
Which shirt will probably shrink the most?
a) 1
b) 2
c) 3
8.
Which shirt will probably shrink the least?
a) 1
b) 2
c) 3
9.
Which shirt is largest?
a) 1
b) 2
c) 3
10.
Which shirt was made in America?
a) 1
b) 2
c) 3
Yes
No
can you clean Jacket 1?
at the dry cleaners
in a washing machine
by hand
9
THE STORY OF AIRCRAFT
Man Invents the Balloon. The
first balloon was invented by
Jacques and Joseph Montgolfier in
1783. Their father was a paperdealer who lived near Paris.
Whenever there was wastepaper to
be destroyed, he would have it
burned.
The brothers used to
watch the smoke rise into the air
from the fires. It occurred to them
that if they could capture the
smoke in a bag, the smoke would
make the bag rise into the air and
fly.
On June 5, 1783, they placed a
huge linen bag several feet above
a pile of straw and set fire to the
straw. When the bag had filled
with smoke and hot air, they cut
the ropes that held it down. It
rose into the sky. On this first
flight it traveled 1 ½ miles in 10
minutes.
This first flight created a sensation,
and even the King heard about it.
He asked the Montgolfier brothers
to prepare a balloon so that he
could watch a flight.
The First Man Goes Up in a
Balloon.
After the Montgolfiers
had experimented by sending a
balloon up with some animals,
people began to wonder if a man
could go up in a balloon.
The
King’s historian, a man named de
Rozier, volunteered to go up in a
balloon. A pan of burning coals
was placed in a big basket under
the balloon to feed it hot air, and
de Rosier went up! He remained
aloft 4 ½ minutes and went as high
as 80 feet. He proved that man
could fly in balloons!
Man Learns How to Steer
Balloons. The next step in the
progress of aircraft was the
invention of a way to steer
balloons. The round balloons you
have been reading about just
drifted along wherever the wind
carried them.
In their first attempt to steer
balloons, men took along oars and
tried to row the big gas bags
floating in air, much as you would
row a boat floating on a lake. The
method, however, didn’t work.
Finally, a propeller driven by an
engine was attached to the basket
of a balloon. Once this was done,
man found that he could steer a
balloon and travel from place to
place in the ocean of air that
surround us.
Balloons Begin to Use Hydrogen.
These flights were followed by an
immediate
improvement
in
balloons. Another Frenchman, a
scientist named J. A. Charles, knew
that balloons rise because the hot
air in them weighs less than the
cooler air outside. He also knew
that hydrogen gas weighs less than
air. He decided to fill a silk balloon
with hydrogen.
This kind of
balloon could stay in the air much
longer than hot-air balloons.
It
10
didn’t burn coal, and it was not
affected by air temperature.
Charles’s balloon is also famous
because when it landed after its
first flight, it came down in a place
where people didn’t know about
balloons. They thought it was a
monster.
It frightened them so
much that they destroyed it.
Airplanes
Replace
Balloons.
More than 100 years passed before
the first successful airplane took
place. On December 19, 1903, the
Wright brothers went up in the first
heavier-than-air plane at Kitty
Hawk, North Carolina.
Planes
quickly replaced balloons.
They
could fly in all kinds of weather,
carry heavy loads, and go long
distances.
Space Rockets Are Here.
In
1926, only 23 years after the
Wrights’ first plane, the first
workable liquid-fuel rocket was
developed by Robert H. Goddard.
Today, rockets have been built that
not only fly from continent to
continent, but are also sent around
the earth, to the moon, and even
to some planets. Very soon, men
will leave the earth and start on a
great exploration of the solar
system.
Underline the word or phrase under
each sentence that should go in
the blank space in the sentence.
1.
The
first
balloon
was
invented by _____________.
a) Charles
b) Goddard
c) The Montgolfiers
2.
The first balloon was sent up
in ___________________.
a) 1903
b) 1783
c) 1926
3.
The first balloon flight lasted
_____________________.
a) 1 minutes
b) 4 ½ minutes
c) 10 minutes
4.
The first man to go up in a
balloon was _____________.
a) Charles
b) Montgolfier
c) De Rozier
5.
The gas first used for lifting
balloons was ____________.
a) hot air
b) oxygen
c) hydrogen
6.
The first way that man tried
to steer balloons was by
using ________________.
a) oxygen
b) ropes
c) oars
7.
Men were finally able to steer
balloons by using ________.
a) hydrogen
b) propeller-driven
engine
c) oars
11
8.
The airplane was invented by
_________________.
a) Charles
b) The Wright brothers
c) Goddard
9.
The first airplane was flown
at ________________.
a) Paris
b) London
c) Kitty Hawk
10.
The first airplane flight was in
_______________.
a) 1803
b) 19903
c) 1926
11.
The first liquid-fuel rocket
was invented in __________.
a) 1726
b) 1826
c) 1926
12.
The liquid-fuel rocket was
invented by _____________.
a) de Rozier
b) Charles
c) Goddard
12
YOUNG VIKING SAILOR
A blow from a rough hand sent
Thorfin spinning across the beach.
Slowly the boy rose to his feet and
stood facing Magnus, the gigantic
red-bearded sailor who had struck
him. Magnus scowled at the boy,
at the stout oaken galley being
prepared for her voyage, and at
the stone houses edging the
sparkling cove in Greenland.
“You’re no sailor,” Magnus said
scornfully. Shaking his head, he
said, “You belong in the fields.
Aye, Leif must be crazy to begin a
voyage with the likes of a farmer’s
boy.”
“I am a sailor,” replied Thorfin
angrily, “or I will be by the time we
return.”
“If we return,” sneered Magnus.
“I was a fool to come on this
voyage. Who knows what dangers
lie ahead?
Leif Ericson is
headstrong and proud, like his
father, Eric the Red. He will have
us all killed just so he can prove
there is land across this dark sea.”
As the coast of Greenland faded
from view the next day, Thorfin
watched the oarsmen pull the
dragon ship swiftly toward the
west. Some day, he thought, he
would be a sailor too – a real
sailor.
He was grateful to the
mighty Leif for taking him along,
although he knew he would only be
mending badly torn nets. Thinking
of his job suddenly reminded
Thorfin that there was work to do.
He awoke from his daydreams with
a start. He would show them how
good a sailor he could be!
That night, after he could no
longer see well enough to work,
Thorfin stood beside the prow.
“A calm night,” said a voice
coming out of the darkness.
Thorfin peered into the half-light
and made out the figure of a tall
man. It was the captain!
“Aye, a calm night, sir,” Thorfin
replied.
“The sun set red.
It
should be fair in the morning.
“So our boy is a sailor!” Leif’s
laughter sounded out over the
entire one-hundred-foot length of
the ship. “It’s all right, boy,” he
said, patting Thorfin on the back.
“You will be a good sailor!”
“Thank you, sir,” said Thorfin
quietly. “But there is so much I do
not know. There is so much I have
to learn.”
“You can learn now,” Lief said.
Thorfin listened carefully as the
great Viking hero pointed to the
North Star.
“Yonder is the
mariner’s friend.
When the sun
does not shine during the day, we
rely on the North Star at night to
give us our direction. Right now
we are going westward.”
“And what lies there, sir?”
Thorfin asked eagerly.
“I do not know. But of this I am
sure. There is a land there.
A
land that no Northman has seen
before.
Thorfin nodded his head. If Lief
Ericson, the most skillful sailor is
all of Norway and Greenland,
believed in this unknown land, that
was good enough for him!
The days that followed were
thrilling ones for Thorfin. First had
come the excitement when they
13
sighted the land with forests. This
probably was the country we now
know as Labrador. Then a fierce
gale sprang up from the north. It
filled the ship’s one sail and sent
the little wooden boat skimming
southward far away from the land
that they had seen. Huge waves
crashed down on them and shook
the tiny ship from bow to stern.
Thorfin had not minded the
storm, but oh how upset he was
the first time he saw porpoises!
“Look!” he shouted fearfully.
“There are sea serpents alongside
the ship!”
How Magnus and the others
laughed! “I said you would never
be a sailor!” Magnus snarled.
Thorfin’s ears burned all that day.
Yet is was Thorfin, ever watchful,
who first spotted the birds and the
seaweed which were the evidence
that the ship was nearing land.
Leif himself praised the boy.
Thorfin, reddening with pride,
made up his mind that he would
not close his eyes until he saw
land.
The hours that followed were
long and trying. Thorfin tried very
hard to stay awake but at last
sleep closed his eyelids. When he
awoke, it was to find the ship
gliding into a pleasant cove.
“What happened?” he cried.
Then he remembered.
He had
planned to stay awake like a good
sailor, but he had failed. Tears fell
from his eyes.
“Ah, Thorfin,” said Leif, “you
weep? And no wonder. Tears of
joy should be yours for was it not
you who saw the birds and the
seaweed? You are a good sailor,
Thorfin. Come, I am taking you
with me to explore the new land.
Magnus scowled, but the others
patted Thorfin in a friendly was as
he walked proudly between the
rowing benches at the great
Viking’s side.
Thorfin no longer
cared what Magnus thought.
It
was good enough to know that Leif
had called him a good sailor and
that he was about to set foot onto
this unknown land.
Five hundred years later, men
would call this land America!
FACT QUESTIONS
Underline the right answer to each
of the questions below;
1.
From what country did Leif’s
ships sail?
a) England
b) Russia
c) Greenland
2.
Who was Leif Ericson’s father?
a) Magnus
b) Eric the Red
c) Columbus
3.
What was Thorfin’s job on the
ship?
a) new mender
b) lookout
c) oarsman
4.
What gave Leif his
direction at night?
a) a c compass
b) a magnet
c) the North Star
sailing
14
5.
Thorfin mistook these animals
for sea serpents:
a) whales
b) sharks
c) porpoises
6.
The first person to see birds
and seaweed was:
a) Thorfin
b) Magnus
c) Leif
7.
The country where Leif and his
men landed was later called;
a) Alaska
b) America
c) Canada
4.
Was Thorfin faithful to his
work?
________________________
________________________
5.
Why did Leif laugh at what
Thorfin said when they were
standing together at the prow
of the boat?
________________________
________________________
________________________
________________________
________________________
6.
Do you think Leif Ericson was
wise to make a trip into the
unknown? ______________
Why? ___________________
________________________
________________________
________________________
________________________
7.
Compare Thorfin with Norman
Muscarello.
Which
one
deserves more credit for
seeing something important.
________________________
Why? __________________
________________________
________________________
________________________
________________________
THOUGHT QUESTIONS
1.
Why did Magnus hit Thorfin?
________________________
________________________
2.
Why did Magnus say he was a
fool to go on this trip?
________________________
________________________
3.
Do
you
think
Thorfin
appreciated Leif’s taking him
along? _________________.
What proof have you?
________________________
_______________________
15
BLESSINGS
RAINTREE*
FROM
THE
José watched the dark clouds as
they formed across the valley.
“The raintree is gathering more
water for us,” he thought happily.
José and his pretty little sister,
Maria, lived with their parents on
the island of Ferro.
It is the
farthest west of the Canary
Islands, a small volcanic speck in
the sea. There are no rivers or
lakes in the fields and hills of black
lava, so rain must be stored in
tanks cut in the volcanic rock. The
people of Ferro were proud of their
famous raintree, which gave the
seed pods for their cattle and fresh
water when they needed it.
Every day José and Maria
carried jugs of water from the
raintree. Their path twisted along
the fig orchard s of Señor Rafael.
The Señor was a wealthy man who
was not too friendly with his
neighbors.
One morning he met them on
the path. “My little girl is sick,” he
said anxiously.
“She is burning
with fever and must be bathed in
cool water many times a day. Will
you bring water from the wonderful
raintree to my home?”
“Gladly, Señor,” José answered.
“Good,” the Señor sighed in
relief. “I will leave my water jug
with you.”
José and Maria climbed higher
and higher up the steep hill until
the cloud mist felt cold upon their
faces. At last they reached the
huge raintree, standing all alone.
Moisture dripped from its thick
dark leaves and fell in a cistern,
which men of long ago had carved
in the hard lava.
José set Señor Rafael’s beautiful
jug under the low-lying branches
beside his own plain one. As he
filled the jugs, his little pet goat,
Poco, came prancing up the path.
“Go away from here, Poco!”
Maria call.
“You always make
trouble.”
“Let him come,” said José.
“Poco only wants a drink from the
raintree, too.”
“What if he breaks Señor
Rafael’s jug?”
“Don’t worry, I will watch him,”
José replied.
But just as José finished filling
Señor Rafael’s jug, Poco came up
behind him and gave him a playful
butt. José stumbled and felt the
jug slip from his hands.
He
watched in horror as it rolled down
the rocky path.
“Catch it, Maria!” he shouted.
Just in time, she kept it from
smashing on a huge rock. José
rushed down the path, picked up
the jug, and saw that it was
crocked from top to bottom.
“I knew this would happen,”
Maria sobbed.
José was worried until he
remembered how clever his mother
was at mending broken pottery.
There was no time to take it to her
now, however, for they must hurry
with the water for the sick child.
José had an idea. Stripping off his
shirt, he tied it around the cracked
clay jar.
“Maybe I can squeeze the crack
together,” he said. But when he
16
poured some water in the jug, it
seeped right through, wetting the
cloth.
Suddenly they heard a branch
snap. “Now Poco is after Señor
Rafael’s figs,” cried Maria.
“More trouble,” José thought as
he jerked Poco away from the tree.
Then he stopped and stared at the
fig leaves. “I knew the blessed
saints would help me!” he said.
Quickly he gathered a handful of
leaves and put a layer of them
over the crack on the inside of the
jug. When he poured more water
in it, the water pressed the leaves
tightly against the jug. It held!
When the jug again was full, José
carefully carried it to the home of
Señor Rafael.
José was tempted to say
nothing to the Señor about having
cracked his jug, but he reminded
himself that this would not be
honest.
So he told what had
happened.
Don’t worry,” Señor Rafael
reassured him.
“Accidents will
happen. I can use a smart boy like
you. Would you be willing to bring
water every day for my child until
she is well?”
“Yes, Señor. And I know my
mother can mend your jug so it will
be as good as new.”
“Take it to her, then,” he said.
“But first, please bring more water
from the raintree.”
José carried their own large jug
filled with water to the Señor’s
home. Then he took the cracked
jug to his mother, who gladly
mended it.
The Señor paid José for carrying
water. When his child was well, he
invited José’s family to his home
for dinner. “We must be friends as
well as neighbors,” he said. “You
see, José, sometimes accidents
bring unlooked-for blessing.”
*Adapted from a story prepared for this
book by Olive Rambo Cook and Margaret
Allison Johnson.
FACT QUESTIONS
Underline the word or phrase that
best completes each of the
following sentences.
1.
Raintrees are found in;
a) Japan
b) Africa
c) The Canary Islands
2.
The raintree gets its water
from:
a) a spring
b) clouds
c) a lake
3.
The island in the story was
named:
a) Ferro
b) Haiti
c) Black Island
4.
The island has:
a) rivers
b) lakes
c) hills of black lava
17
5.
6.
The path to the raintree
passed;
a) desert
b) Señor
Rafael’s
fig
trees
c) Pastures
1.
Would you have consented to
bring water for Señor Rafael,
even though he had always
been unfriendly to you in the
past? ___________________
Why? ___________________
________________________
________________________
________________________
2.
If you had been José, what
would you have done when
you saw that the jug was
cracked?
________________________
________________________
________________________
________________________
________________________
________________________
3.
If you had been José, would
you have told Señor Rafael
that you had broke the jug?
________________________
Why? ___________________
________________________
________________________
________________________
________________________
4.
What did Señor Rafael mean
when he said, “Sometimes
accidents bring unlooked-for
blessings?”
________________________
________________________
________________________
________________________
________________________
Señor Rafael’s attitude toward
neighbors had been;
a) kind
b) unfriendly
c) generous
7.
The one who was to blame for
breaking the jug was;
a) Maria
b) José
c) Poco
8.
José covered the crack in the
jug with;
a) cabbage leaves
b) fig leave
c) raintree leaves
9.
THOUGHT QUESTIONS
José had the broken
mended by;
a) Señor Rafael
b) His mother
c) A servant
10. Señor Rafael invited
family to:
a) his fig orchard
b) his garden
c) his home
jug
José
18
5.
On a separate piece of paper,
write a short paragraph telling
how you think this story might
have ended if Maria had had
her way in sending Poco home.
19
Study Package – Math
The following package has been organized into different components. Each
component has been explained in easy to follow steps with practice
questions at the end of each component.
After completing all the
components the student should try all the practice tests at the end of the
booklet. Remember, there are no calculators allowed on the exam, so the
student should do this booklet without a calculator as well.
PLACE VALUE
4 3 2 .
Example: 432.567
The 2 is in the
The 3 is in the
The 4 is in the
To the right of
The 5 is in the
The 6 is in the
The 7 is in the
ones place.
tens place.
hundreds place
the decimal place…
tenths place.
hundredths place.
thousandths place.
H
U
N
D
R
E
D
S
T
E
N
T
H
S
O
E
N
E
S
D
D
E
C
I
M
A
L
P
O
I
N
T
5 6 7
T
E
N
T
H
S
H
U
N
D
R
E
D
T
H
S
T
H
O
U
S
A
N
D
T
H
S
T
E
N
T
H
O
U
S
A
N
D
T
H
S
H
U
N
D
R
E
D
T
H
O
U
S
A
N
D
T
H
S
M
I
L
L
O
N
T
H
S
The number is read as:
“Four hundred thirty-two and five hundred sixty seven thousandths.”
ROUNDING:
1. Round 67.1275 to the nearest tenth =
2. Round 67.1275 to the nearest hundredth =
3. Round 67.1275 to the nearest thousandth =
4. Round 67.1275 to the nearest tens =
5. Round 67.1275 to the nearest ones =
PLACE VALUE, SHOW:
1. three thousandths =
2. fifty-seven ten thousandths =
3. two and one tenth =
4. thirty tens =
5. 23 hundredths =
20
BASIC OPERATIONS:
ADDITION
Line up the numbers according to the place value and add vertically from right
to left.
Example: 35647 + 64537 + 235
1
1
1
1
Example: 54.78 + 3.660
1
1
3 5 6 4 7
6 4 5 3 7
+
2 3 5
1 0 0 4 1 9
5 4
+ 3
5 8
1
.
.
.
7 8 0
6 6 0
4 4 0
SOLVE:
1. 477.075 + 64 + 709.999 =
2. 37.2 + 26.555 + 64 =
3. 206.25 + 1.0026 + 0.6009 =
4. 125.345 + 1654 + 2.12 =
5. 7.0036 + 5.24 + 0.00089 =
SUBTRACTION
Line-up the numbers according to place value and subtract vertically from
right to left.
Example:
8 4 7
- 2 5
8 2 1
borrow
5
8
6
5
6
9
5 4 .
- 3 .
5 1 .
7 8 0
6 6 0
1 2 0
SOLVE:
1.
2.
3.
4.
5.
7986 – 1039 =
897.2333 – 129.345 =
786.33 – 291.003 =
189.303 – 6.79 =
400.36 – 126.002 =
21
MULTIPLICATION
Place one number above the other so that the hundred’s, tenths, and one’s
places are lined up. Draw a line under the bottom number.
45036
X 12
Multiply the furthest number to the right through every number on the top.
1
1
45036
X 12
90072
The cross off the 2 and place a 0 at the bottom of the one’s column.
45036
X 12
90072
0
Then multiply the next number through all the top numbers.
45036
X 12
1
90072
+450360 add both lines together
540432
If there is a decimal in the question, count how many decimal places there
are in the question and move the decimal that many places from the left.
450.36 – there are two decimal places
X 1.2 – there is one decimal place
90072
+450360 -- add both lines together
540.432 – there will be three decimal places in the answer
SOLVE:
22
1. 183 x 152 =
2. 1985 x 230 =
3. 0.25 x 0.375 =
4. 45.230 x 0.36 =
5. 75.2 x 1.3 =
DIVISION
425 ÷ 25 = 17
Dividend ÷Divisor = Quotient
-
The number to be divided into is known as the dividend (425 from
above)
The number which divides the other number is known as the
divisor (25 from above)
Quotient
Divisor Divident
17
25 425
0
See if the divisor will go into the first number – 25 425 (25 does not go into 4)
See if the divisor will go into the first and second number combined;
01
25 425 (25 goes into 42 once)
Subtract 42 from 25 and apply the remainder
to the next number
Now divide 25 into the new number, 175 and
place it up top
− 25 ↓
17 5
_017_
25)425
− 25 ↓
175
175
0
When your remainder is 0, then you have completed the question and the
answer is 17.
SOLVE:
1. 14 294
23
2. 16 256
3. 125 3375
4. 162 2916
5. 72 2448
DIVISION WITH DECIMALS
When dividing decimals, remove the decimal from the divisor. What you do
to the divisor, you must apply it to the dividend.
0.34 912 →
034 91200 (to remove the decimal, move the decimal 2
places to the right on the divisor, therefore move the decimal 2 places to the
right on the dividend and fill in those places with 0’s). Then divide.
SOLVE;
1. 3.2 6452 =
2. 4.75 3325 =
3. 18.5 231.25 =
4. 67.2 ÷ 0.24 =
5. 481.92 ÷ 0.024 =
24
NEGATIVE AND POSITIVE QUANTITIES
Negative numbers mean that they are below zero.
-5
|
-4
|
-3
|
-2
|
-1
|
0
|
1
|
2
|
3
|
4
|
5
|
Rules to determine (-) or (+)
Adding negative numbers – A negative plus a negative will be negative ex.
(-5) + (-6) = -11
A negative plus a positive will be which ever one is a higher number ex.
(-9) + (6) = -3
(13) + (-6) = 7
Subtracting negative numbers – 2 negatives together make a positive ex.
7 – (-5), the five becomes positive 7 + 5 = 12
A negative subtract a number will be negative ex. -8 – 4 = -12
Multiplying negative numbers – A negative times a positive will be
negative ex. 8 x (-3) = -24. A negative times a negative will be a positive ex.
(-5) x (-3) = 15
SOLVE;
1. (-1) + 2 =
2. (-3) – (-4) =
3. (-9) + (-10) =
4. (-6) x 4 =
5. (-7) x (-3) =
25
EXPONENTS
3 – exponent
8
The exponent tells you how many times to multiply, and the 8
tells you what number to multiply. This means 8 multiplied by
itself 3 times. 8 x 8 x 8 = 512
If the exponent is zero or the number is zero, then the answer will be zero.
SOLVE:
1. 73
2. 35
3. 82
4. 26
5. 63
MULTIPLYING AND DIVIDING EXPONENTS
(3+5)
A3 x A5
= Add the exponents
A8
(6-4)
B6 x B4
= Subtract the exponents
B2
SOLVE:
1. X3 x X3 =
2. R6 x R9 =
3. Y4 ÷ Y1 =
4. Z8 ÷ Z5 =
5. B6 x B3 =
26
SQUARE ROOTS
A square root ( 25 ) undoes squaring (52). 5 x 5 = 25
25 = 5
SOLVE:
1. 81
2.
36
3.
16
4.
49
5.
144
POWERS OF 10
102 x 104
= Using the same exponent rules as above = 106 =
1,000,000 (the exponent represents the number of zeros)
SOLVE:
1. 105
2. 102
3. 104 x 102 =
4. 109 x 103 =
5. 107 ÷ 103 =
SCIENTIFIC NOTATION
Scientific Notation is always written as: number x a power of 10
3.42 x 105 =
Using the power of 10 rules from above;
The exponent represents the number of places to move the decimal.
105 = 100 000
The decimal must move 5 places to the right. 3.42 = 342 000
SOLVE:
1. 4.56 x 103
2. 4.7 x 105
3. 38.05 x 106
4. 25.003 x 102
5. 7.92 x 105
27
CONVERTING BETWEEN PERCENTAGE AND DECIMAL
Percentage means “per 100”, so 50% means 50 per 100, or simply 50
If you divide 50 by 100 you get 0.5 (a decimal number).
100
.
So, to convert from percentage to decimal: divide by 100 (and
remove the “ 0 ” sign).
0
The easiest way to divide by 100 is to move the decimal point 2 places
to the left.
So:
75%
0.7.5.
0.75
Move 2 places to the left
Move the decimal point 2 places to the left, and remove the “ 0 ” sign.
0
Change the percent to a decimal;
SOLVE;
1. 45%
2. 65%
3. 125%
4. 33%
5. 20%
Change the decimal to a percent;
SOLVE;
1. 0.65
2. 0.45
3. 0.33
4. 0.025
5. 0.80
28
PERCENTAGES
For all percentage questions use the “is over of” method.
%
is
=
(percent is always out of 100)
100
of
What is 30% of 75?
Is = ?
is
of
Of = 75
75 x 30 = 100(?) = 2250 = 100(?) =
% = 30 out of 100
? = 22.5
?
30
=
= cross multiply
75
100
2250 100(?)
=
100
100
18 is 24% of what number?
Is = 18
is
of
Of = ?
18 x 100 = 24 (?) = 1800 = 24(?) =
18
24
=
= cross multiply
?
100
1800 24(?)
=
100
24
What percent is 41 out of 93?
Is = 41
is
of
Of = 93
14 x 100 = 93(%) = 1400 = 93(%) =
%=?
% = 15.0537 = 15%
14
%
=
= cross multiply
93
100
1400
93(%)
=
93
93
SOLVE:
1. What is 12% of 240?
2. What is 60% of 350?
3. 15 is 50% of what number?
4. 26 is 50% of what number?
5. What percent is 35 out of 105?
6. What percent is 60 out of 135?
29
A FRACTION TO A PERCENTAGE
Use the “is over of” method
is
of
1
%
=
*percent is always out of 100
100
4
Cross multiply to solve for x. 1(100) = 4(x)
Get x by itself – 100 =
4x
(what you do to one side you must do to the other)
4
100
4x
=
4
4
X = 25 add the percent
1
= 25%
4
Convert the fraction into a percent
SOLVE;
1.
1
5
2.
22
88
3.
15
90
4.
2
3
5.
6
20
30
CONVERTING A PERCENT TO A FRACTION
Put the percent into a fraction-percent is always out of 100 and reduce
35% =
35
To reduce, find a number that goes into both numbers evenly
100
Rules to reduce:
First try: if top can be divided evenly into the bottom ex
1
36(÷36)
=
2
72(÷36)
Second try: if both are even divide by 2 (ends in 0,2,4,6,8)
Third try: if both end in 5 or a 0 then divide by 5
SOLVE:
1. 75%
2. 60%
3. 88%
4. 15%
5. 124%
31
A FRACTION TO A DECIMAL
The fraction bar (between the numbers) means divide.
Divide the
denominator (the bottom part into the numerator (the top part):
1
= 1.00 ÷ 4.00 =
4
0.25
4 1.00
− 0 ↓↓
10
8
20
− 20
0
Change the fraction to a decimal. (to 3 decimal places)
SOLVE:
1.
1
5
2.
1
7
3.
2
7
4.
4
9
5.
1
8
6.
5
12
32
DECIMAL TO A FRACTION
0.0625
Put the number within the decimal on the top of a fraction – 0.0625
625
10000
The bottom number will start with a 1 and then count the number of spaces
after the decimal and replace those with zeros. Reduce to lowest terms.
625 ÷ 625 = 1
1000 ÷ 625
16
SOLVE:
1. 0.75
2. 0.1875
3. 0.65
4. 0.036
5. 0.092
33
ORDER OF OPERATIONS
BEDMAS
B = Brackets
E = Exponents
D = Division
M = Multiplication
A = Addition
S = Subtraction
This is the order of which you would solve a question that has more than one
operation. Starting from the top, do brackets first, followed by exponents,
then division, multiplication, addition and subtraction.
Example
(21 + 2) + 7 x 2 = y
8
Brackets – 21 + 3 = 24
24 + 7 x 2 = y
8
Exponents – there are no exponents, so move on to the next operation
Division – 24 ÷ 8 = 3
3+7x2=y
Multiplicaton – 7 x 2 = 14
3 + 14 = y
Addition – 3 + 14 = 17
3 + 14 = y
Subtraction – there is no subtraction
The solution is y = 17
SOLVE;
1. 36 ÷ 6 X 3 – 2 =
2. 14 + 2 (5-3) =
3. 32 – 22 + 3 X 2 =
4. 14 (5-3) + 5 X 2 =
5.
6−4+8
=
5 − 15
6. 3 X 8 ÷6 + 6 ÷ 3 X 2 =
7. 18 – 32 + 4 X 3 =
34
SOLVING EQUATIONS
When solving an equation, you are always trying to get the variable by itself.
Solve for n: 4n – 5 = 3 get n by itself on one side of the equation and move
everything else to the other side.
Add 5 to both sides of the equation to eliminate the (-5)
4n-5 (+5) = 3 (÷5)
4n = 8
Now divide both sides by 4 to eliminate the 4
4n
8
=
4
4
n=2
SOLVE FOR N:
1. 3n – 4 = 17
2. 9 + 2n = 23
3. 11n = 8 = 14
4. 45 = 3n + 15
5. 27 = 2 + 5n
SUBSTITUTING
Plug in the numbers for the letter variables and use Order of Operations (BEDMAS)
to solve the equation
A = 5n + 3p where n = 2 and p = 4
Plug the 2 in the equation for n A = 5(2) + 3p
Plug the 4 in the equation for p A = 5(2) + 3(4)
And solve:
A = 10 + 12
A = 22
SOLVE FOR A:
1. A = L x W
L = 16
W=4
2. A =
b = 12
h=6
a=6
b=9
1
bh
2
1
3. A = (a + b)h
2
4. A = 3.14r2
r=3
5. A =
b=7
bh
2
h = 10
h=4
35
FRACTIONS
Fraction Rules
33 − numerator
4 − deno min ator
RULES
1. Change mixed (8 ¼) fractions to an improper fraction (33/4).
2. Adding and Subtracting – you need to have the same number on the
bottom of the fractions – this is a common denominator.
3. Multiplying – You do not need a common denominator. Multiply across.
4. Dividing – You do not need a common denominator.
Flip the second
fraction and then multiply.
5. Reduce Fractions.
1.
-8
Change mixed (8
1
33
) fractions to an improper fraction ( ).
4
4
1
take the denominator (bottom number) of the fraction and multiply it by
4
the whole number, then add the numerator (top number) 4 x 8 + 1 = 33 (will
give you the new numerator). The denominator stays the same. Therefore
8
33
1
becomes
4
4
Change the mixed fraction to an improper fraction.
SOLVE:
1. 3
1
5
2. 5
3
7
3. 2
1
2
4. 10
5. 6
1
5
2
9
36
2.
Adding and Subtracting – you need to have the same number on the
bottom of the fractions – this is a common denominator.
2
3
+
= Make the denominators the same
3
4
3 – 3,6,9,12
4 – 4,8,12
Multiply both top and bottom by the same number
Add the numerators
8+9=
8
9
2( x 4) 3( x3)
+
= + =
3( x 4) 4( x3) 12 12
17
12
The denominator stays the same
Change into a mixed number
17
=
12
1
5
12
- The same rules apply for subtraction SOLVE;
1.
8
5
+
=
9
18
2.
3
1
+
=
5
15
3.
1
9
=
6
12
4.
12
1
=
14
7
5. 5
1
1
+2 =
3
6
6. 7
1
5
-1
2
12
37
3.
Multiplying – You do not need a common denominator. Multiply across
– Multiply the top numbers and then multiply the bottom numbers;
2
5
x
=
3
10
If it is a mixed fraction change it to an improper fraction
Multiply the top numbers
Multiply the bottom
Reduce
10
2
5
x
=
3
10
5
2
10
x
=
10
3
30
1
10(÷10)
=
3
30(÷10)
SOLVE:
1.
1
2
x
=
2
9
2.
5
3
x
=
7
4
3. 3
1
2
x4 =
2
5
4. 1
3
7
x2 =
5
8
5. 3
2
3
x4 =
7
9
38
4.
Dividing – You do not need a common denominator.
3
5
+
=
5
9
Flip the second fraction and then change the sign to multiplication.
3
5
3
9
+
=
x
=
5
9
5
5
Multiply across
3
9
27
x
=
5
5
25
Reduce the fraction and/or put into a mixed number
27
2
=1
25
25
SOLVE;
1.
32
4
÷
=
7
14
2.
5
13
+
=
8
2
3.
4
9
÷
=
9
4
4. 1
3
7
÷2
=
5
10
5. 3
1
3
÷1 =
4
4
39
PRACTICE #1
1.
2.
54.58
72.24
+ 8.04
94.75
78.65
+ 8.06
3.
67.43 x 0.94 =
4.
5.64 ÷ 1.6 =
5.
45 mm = ________cm
6.
1.9kg = _________g
7.
4∧2 =
8.
3∧4 =
9.
144 =
10.
If 31 = 6N-5 then N =
11.
4x
- 2 = 10 then x =
5
12.
1
A = (c + d)B
3
B=5
13.
12 is 40% of ____________
14.
20 is what % of 80?
15.
15% of 62 is ____________
16.
5
17.
2
8
=
12
2
18.
7
1
x2 =
10
2
19.
3
1
÷
=
4
2
20.
4
2
÷
=
9
3
21.
6
as a decimal
8
22.
3.65 x 10 ∧ 4 =
23.
9 –(-3) =
24.
(-4) – 9 =
1
1
+2 =
4
3
c = 2, d = 4,
40
PRACTICE TEST #2
a)
b)
c)
a3 x a6 =
x8 ÷ x5 =
p7 ÷ p3 =
2.
a)
b)
43 =
26 =
3.
a)
b)
2.42 x 103=
1.6 x 205 =
1.
b)
c)
d)
e)
f)
4.
5.
a)
b)
c)
d)
856 + 391 =
2608 – 7529 =
3624 ÷ 8 =
610 x 515 =
a)
b)
c)
d)
92.34 – 51.75 =
14.0 x 2.6 =
6.35 x 0.41 =
4.2 ÷ 0.3 =
10.
a)
b)
c)
4
=
10
9
=
20
1
=
4
1
4
÷
=
4
9
1
2
÷
=
9
3
9x2
2
9
+4
=
3
12
6
1
=
15 5
13 x 21 =
4
2
2
11.
a)
What is 20% of 88?
________
b)
5.5 is 10% of what?
________
c)
19 is what % of 95?
________
(2a – 3b) + (4a + b) =
(4a +5) + (2 + 3a) =
(-a + 6) – (3a – 2) =
12.
a)
81 =
b)
25 =
8.
If a = 2
Then what does 3a(-2a+5) =
13.
9.
Write as a decimal
6.
Solve, if m = -3 and n = 4
a)
5m – 4n =
b)
2(m + n) =
c)
-(3m+ 2m) – (4m – n) =
7.
a)
b)
c)
a)
1
=
3
a)
40%
b)
25%
What is this as a fraction?
____________
What is this as a fraction?
____________
41
PRACTICE #3
1.
(-32) ÷ 7 =
11. (9÷3) x (8÷4) =
2.
(-37) + (-47) =
12. 7.95 ÷ 1.5 =
3.
(-9) – 2 =
13. 5.36 x 0.21 =
4.
12 ÷3 – 4 – 81 =
14. 35% of what number is 70?
5.
16 =
15. What # is 5% of 200?
6.
25 + 119 =
16. What % of 90 is 27?
7.
Solve for x
3 (2x + 5) = 16
8.
18. reduce
Evaluate; (x – y)3
X=2
9.
17. 41% = what as a decimal?
y = (-2)
Evaluate:
19.
2
1
+
=
3
4
20.
5
3
=
6
4
21.
3
2
x
=
4
3
22.
3
4
÷
=
5
5
A=2, b=1, c=3, d=2
a (b + c) =
2d
10. 0.98 + 45.1012 + 32.333 +
0.0009 =
25
=
30
23. 4
7
2
-3 =
12
3
42
PRACTICE TEST A
1. The number 9,060,900
is written;
a) Nine
million
six
hundred nine thousand
b) Nine million sixty nine
thousand
c) Nine
million
sixty
thousand nine hundred
d) Nine
hundred
six
thousand nine hundred
e) Nine billion six million
nine hundred
2. 2 ∧ 4 means;
a)
b)
c)
d)
e)
2
2
4
2
2
x4
x2x2
x4
x2x2x2
+2+2+2
3. Which
is
statement?
a
a)
b)
c)
d)
e)
(3 ÷ 1) + 0 = 1/3
(3 + 0) – 1 = 1
(3 + 0) x 1 = 3
(0 – 3) x 1 = 3
3 + (0 x 1) = 0
4.
2
is
5
equal
to
6. 45% is the same as 10. 578
which fraction:
X
a)
b)
c)
d)
e)
7. Which
sentence
always true?
a) (a+b)d = d + (ab)
b) x(a-b) = (ab) –x
c) (cd) + t = c(d+t)
d) fg – a = a-fg
e) cb – cd = c(b-d)
true 8.
what
decimal?
a) 0.4
b) 0.25
c) 0.04
d) 0.2
e) 0.52
5. 3.14 x 10 ∧ 3 is equal
to;
a) 0.314
b) 3140
c) 31.4
d) 0.00314
e) 9.42
3/5
9/20
45/10
4/5
NG
a)
b)
c)
d)
e)
9.
23
196
905
+ 58
1062
1182
1082
1181
NG
24067
-18392
a) 5775
b) 14335
c) 5675
d) 42459
e) NG
a)
b)
c)
d)
e)
is 11.
57
254956
3596
32946
32900
NG
467
X 208
a) 69377
b) 97136
c) 13076
d) 97130
e) NG
12. 6255 ÷ 5 =
a)
b)
c)
d)
e)
125
121
1250
1251
NG
13.
36916 ÷ 29 =
a)
b)
c)
d)
e)
204
1204
2104
1240
NG
43
PRACTICE TEST A CON’T
14.
4
a)
5
b)
6
c)
3
d)
e)
15.
a)
b)
c)
d)
16.
a)
b)
c)
d)
e)
1
6
+1 =
4
8
7
8
1
2
7
5
12
NG
11 1
=
18 6
10
12
10
18
4
9
17. What is C when d=2, 20. 25 is related to 5 and
15 is related to 3 in the
e=1, f=6?
same way that 20 is
1
C= (d-e)f
related to;
4
a) 24
1
b) 1
2
1
c)
4
d) 6
e) NG
18.1.03+25.021+198.2 =
a)
b)
c)
d)
e)
5
15
4
19
NG
21. 13 is 20% of;
a) 225.251
a)
65
b) 56.141
b)
2.6
c) 0.225251
c)
0.65
d) 225251
d)
26
e) NG
e)
NG
19.
22. (-19) + 7 =
NG
4
1
x3 =
6
4
10
12
4
3
24
1
3
6
3
44
26.48 – 8.319 =
a) 22.179
a)
-26
b) 18.179
b)
12
c) 6329
c)
26
d) 18.161
d)
-12
e) NG
e)
NG
NG
23. (-3) – 14 =
a)
b)
c)
d)
e)
-6
-22
22
112
NG
44
PRATICE TEST A CON’T
24.
13 x 2
1
a) 26
4
1
4
b) 117
c) 26
d) 29
1
4
27.
a)
b)
c)
d)
e)
If
49
16
7
24
NG
4
n
=
7
28
30. (-4) x (-3) =
a)
b)
c)
d)
e)
12
-12
-7
7
NG
e) NG
1
5
÷
=
3
9
25.
a)
b)
c)
45
3
2
1
3
5
27
d) 15
e) NG
26. y=4x -7
What is y if x = 4
a)
9
b)
3
(- )
4
c)
4
d)
7
e)
NG
28.
25% of 90 =
a) 2250
5
b)
18
c) 22.5
d) 0.28
e) NG
144
31.
a)
b)
c)
d)
e)
62
0.12
14.4
12
NG
a∧6 x a∧2 =
d
f
29. If
=
then f =
e
g
32.
de
g
e
b)
gd
dg
c)
e
a)
12a
b)
2a ∧ 6
c)
a∧8
d)
a ∧ 12
e)
NG
a)
d) NG
45
PRACTICE TEST B
1. The number 23,062,400 6. 60% is the same 11.
is written;
as what fraction?
a) two million three hundred
thousand
six
hundred
twenty-four
b) twenty-three million sixtytwo
thousand
four
hundred
c) twenty-three million six
hundred
twenty-four
thousand
d) two hundred thousand
three hundred sixty-two
and four hundred
e) twenty-three million six
thousand two hundred
forty
2. 64 means;
a) 6 + 4
b) 4x4x4x4x4x4
c) 6x4
d) 6+6+6+6
e) 6x6x6x6
3. Which is a true statement
a) 6x1=1
b) 6x0-6
c) 6-6=0
d) 6+1=6
e) 6/0=6
a) 6/100
b) 3/10
c) 2/5
d) 3/5
e) NG
a)
b)
c)
d)
e)
629
X 230
14467
31250
3145
144670
NG
7. Which sentence is 12. 3624 ÷ 8 =
always true?
a) 453
a) XY=Z=X(Y-Z)
b) 440 R4
b) M(N-P)=MN=MP
c) 449
c) (R+S)T=R+ST
d) 516 R4
d) XY+Z=X+YZ
e) NG
13. 11986 ÷ 26 =
8.
19
422
a) 479.44
36
+561
b) 461
c) 76.38
a) 938
d) 361
b) 41343
e) 46.1
c) 50243
d) 40343
e) NG
4. 5/8 is equal to what 9.
73401
14. 14003 ÷ 67 =
decimal;
+23158
a) 209
a) 0.625
b) 215
b) 0.58
a) 50357
c) 189
c) 0.5
b) 41343
d) 306
d) 1.6
c) 50243
e) NG
e) NG
d) 40343
e) NG
5. 3.42 x 103 is equal to;
15. 5 1/3 + 2 ½ =
10.
527
a) 0.0000342
X 35
b) 342
a) 7 2/5
a) 18440
c) 34.2
b) 7 2/6
b) 17445
d) 3420
c) 7 2/3
c) 4216
e) 342000
d) 7 1/6
d) 18445
e) 7 5/6
e) NG
46
PRACTICE TEST B CON’T
16.
a)
b)
c)
d)
e)
17.
a)
b)
c)
d)
e)
18.
a)
b)
c)
d)
e)
19.
a)
b)
c)
d)
9/10 – 4/5 =
5/5
5/10
1/10
5/15
3/10
2/5 x 1 ¾ =
1 6/20
1 8/15
8/35
7/10
NG
8 x 3 ¼=
24 ¼
26
13/32
6
8 3/4
2/5 ÷ 1/3 =
3/5
1 1/8
3/24
2/5
e)
1
20.
a)
b)
c)
d)
e)
3/8 ÷ 1/3
3/5
1 1/8
3/24
2/5
NG
21.
a)
b)
c)
d)
e)
22.
a)
b)
c)
d)
e)
1
5
4.732+2.610+0.109=
6.450
7.441
7.551
6.451
7.451
51.00 – 28.37 =
22.63
37.37
23.63
23.37
NG
23. 32.4 x 6.05 =
a) 3.564
b) 19602
c) 196.02
d) 19.602
e) NG
24. 6.50 x 0.39 =
a) 79.00
b) 2.535
c) 253.5
d) 7900
e) NG
25. 3.91 ÷ 0.34 =
a) 1.15
b) 11.5
c) 115
d) 0.115
e) NG
26. 4.6 ÷ 0.2 =
a) 23
b) 0.023
c) 2.3
d) 0.23
e) NG
30.
a)
b)
c)
d)
e)
31.
a)
b)
c)
d)
e)
32.
a)
b)
c)
d)
e)
33.
a)
b)
c)
d)
e)
9 is 40% of ___
2.25
225
0.225
22.5
NG
12 is what % of 60?
25
5
50
20
NG
(-9) + 15 =
24
6
-24
-6
NG
-8 – 3 =
-11
11
-5
5
NG
27. 5 is related to 15 and
3 is related to 9 in the
same way that 4 is related
to;
a) 14
b) 10
c) 12
d) 1
e) NG
28. If 3/8=15/n, then n=
a) 20
b) 40
c) 32
d) 35
e) NG
34.
a)
b)
c)
d)
e)
(-9) x (4) =
36
-5
-36
5
NG
29. 20% of 88 =
a) 1936
b) 176
c) 4.4
d) 17.6
e) NG
35.
a)
b)
c)
d)
e)
36.
a)
b)
c)
d)
e)
81
8.1
3
27
6561
9
X3 x X5 =
X15
X35
15X
X8
NG
47
PRACTICE TEST B CON’T
37. If 4n + 3 = 19, then
n=
a)
b)
c)
d)
e)
38.
a)
b)
c)
d)
e)
4
3
5
2
NG
If
BC
D
BCD
CD
B
BD
C
NG
39. A =
a)
b)
c)
d)
e)
40.
a)
b)
c)
d)
e)
A C
= , then A=
B D
1(a + b)h
2
What is A when a=3,
b=5 and h=9?
9½
8½
24
36
NG
18 − (6 + 8) x5 = B
7
What is B?
3
10
8
12
NG
48