Handy formulas to memorize
Area of a circle
Area of a parallelogram
Area of a rectangle (including a square)
Area of a trapezoid
Area of a triangle
Volume of a rectangular prism (such as a box)
Area
Base
Congruent
Coordinate grid
Depth
Dimension
Greatest common factor
Height
Least common multiple
Mean
Median
Parallelogram
Perimeter
Rhombus (pl. is rhombi)
Trapezoid
Width
Number sense
1. Which number leaves a remainder of 1 when divided by 5 and also when divided by 7?
A) 671
B) 761
C) 176
D) 716
2. 1 + 2 + 3 + 4 + 5 =
1x2x3x4x5
3. (2 x 1/100) + (3 x 1/1000) + (7 x 1/10,000) =
A) 2.37
B) 0.237
C) 0.0237
D) 0.00237
4. The digits 1986 are written in order from largest to smallest. Next they’re written in
order from smallest to largest. What number is halfway between these two numbers?
5. Jack has 6 1/2 dozen pencils and Jill has 8 1/3 dozen pencils. How many more pencils
does Jill have
than Jack?
Measurement
1. A circus clown buys balloons at $1.44 per dozen and sells the
balloons for 20 cents each. What will be his profit on a day when he
buys and sells 20 dozen balloons?
2. 51/3 tablespoons equal 1/3 of a cup. How many tablespoons are in a
cup?
3. Thirty-three minutes after 11 a.m. is _____ minutes before 1 p.m.?
4. A Fun Run is ten kilometers (km) long (about six miles). How many
centimeters (cm) long is the Fun Run? _____
5. Today is Saturday, May 5, 2001. One year from today will be May 5, 2002.
What day of the week will that be? (Note: 2001 is not a leap year.)
geometry
1. In the diagram, there is an equilateral triangle
and a square. If the perimeter of the triangle is
24 m, find the area of the square.
2. One angle of an isosceles triangle has a measure of 108º.
Another angle of this triangle must have a measure of how many
degrees?
3. The perimeter of the rectangle shown in the diagram is 20
inches. The width of this rectangle is 4¼. What is the length of
this rectangle?
4 ¼ inches
4. ABCF is a trapezoid. ABDE is a square. Line segments FE, ED,
and DC are all equal in length. Line segment AB is 5 cm in
length. What is the area of trapezoid ABCF?
5. Square ABCD has a perimeter of 8 cm. If a
circle is inscribed in the square as shown, what is the area of
the circle?
probability & statistics
1. Four children line up at the lunch counter. In how
many different orders can they arrange themselves in
line?
2.After five tests, a student’s average was 80. After
taking another examination which counted as two test
grades, his average dropped to 76. What was his grade
on that examination?
3. A set of markers is numbered consecutively from 12
through 50. If you draw one marker randomly from the
collection, what is the probability that you draw a
prime number?
4. If the pattern of the first six letters in
CIRCUSCIRCUS… continues, then the pattern’s 500th
letter is?
5. I was paid $2.80 on the first day, and my salary
doubled each day thereafter. I earned a total of $714.
How many days did I work?
algebraic sense
1.
In a camel herd with 80 legs, half the camels have one hump
and half have two. How many humps are there in this herd?
2. If two dogs weigh as much as three cats, and two cats weigh
as much as 15 mice, how many dogs weigh as much as 45 mice?
3. The triplet plant grows one leaf during the first month, and
then it triples its total number of leaves each month
thereafter. If the plant must have more than 90 leaves before it
can be picked, during which month at the earliest would the tree
have enough leaves to be picked?
4. Mary is ten years. Mary is three years older than Mark, and
John is twice as old as Mary. How many years older than Mark is
John?
5. I shipped some books by Stork Express. I sent 1/3 of all the
books on Monday, eight books on Tuesday, and ½ of all the books
on Wednesday. How many books did I ship altogether?
Number Sense
1) A rat runs in a 2 meter tube that has a number line below it marking
off the lengths as shown on the number line. A goofy student who likes math takes
data of the rat’s position every few seconds. She writes the following. The rat starts
at 1/4 meter. Add 0.95m to get to its next point. To find its next point on the number
line take this last value and multiply it by 150%. From this point subtract the sum
of 1/3 + 1/6 meter. Where is the rat now located on the number line?
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
2) A bank teller doesn’t realize that on his computer screen the digit in the ones
place is not
printing. So he reads $12.00 when the actual number could be $126.00, he doesn’t
see the 6. A customer makes him aware of the problem when she doesn’t get the
right amount of cash. What’s the most the teller could owe his customer if the
number he saw on his screen looked like more than $10 but less than $100?
3) PINs, or personal identification numbers, are needed everywhere once you start setting up
accounts for just about anything. Eric decides he needs a plan for the PINs he will need. His first
PIN will be 7862 for reasons known only to him. After that every new PIN will be obtained from
7862 by adding the next prime number, for example 7864 is his second pin (he added 2). All he needs
to remember is where he is in the list of prime numbers, and he knows all his PINs. Where in the list
is the first PIN that doesn’t have an 8 in it?
4) A small country prints only two kinds of stamps, 7 cent stamps and 13 cent stamps. One letter
requires 64 cents postage. How many of each stamp should you ask for so that you can mail the
letter and spend the least amount of money?
5) Sonja swims in races. This season she notices that she drops in time for her butterfly at each race
by 1/3 of the time she dropped at the previous race. She began the season at 1 minute and 25
seconds, the second race she did 1 minute and 7 seconds, an 18 second drop. What should her time be
in the 5th race? Express you answer to the nearest one hundredth of a second.
Measurement
1) What is the area of the garden here
in which all the
corners are right angles and the
dimensions shown are in
feet?
2) Eugene and Florence are both reading
books and they read for 20 minutes a day
during an after school program that runs
Monday through Friday. Eugene reads 3 pages every 6 minutes and
Florence reads 2 pages every 5 minutes. If it takes Eugene 4
whole weeks to finish his book, and Florence takes 6 whole
weeks, whose book is longer and by how many pages?
3) A room is 25% full. If 900 more people enter the room it will
be at full capacity. Full capacity is determined by one person
per 1.5 square meters. The length of the room is 60 meters. What
is the width of the room?
4) Aleisha is exercising her business talents as the go to
classmate to get things from. She trades:
2 Bag of chips = 1 candy bar
1 Bag of chips = 5 brand new pencils
3 brand new pencils = 2 gel pens
If she’s successful at trading how many gel pens can she get for
1 candy bar?
5) The Telinos are tiling their bathroom. Part of the
design will be a
zigzag band all around the room. To create this they
will need to cut
white triangles and grey parallelograms from rectangle
tiles. The
rectangles have dimensions 4 cm by 12 cm as
labeled. The triangles have height 7 cm.
What is the area of a parallelogram piece?
Geometric Sense
1) The stained glass window design is a rhombus
subdivided into four congruent rhombi. If the small angle at
point M is 40° as shown then what is angle DAB?
2) A polygon has the two perpendicular lines of symmetry shown. One
quarter of the interior of the polygon is the shaded trapezoid drawn in.
Sketch the completed polygon and give its geometric name based on
the number of sides or angles it has.
3) Two congruent isosceles triangles are joined together along a side to
create a kite as shown. The perimeter of one of the triangles is 30 units. The
lengths of the sides of the triangle are all whole numbers. What is the length
of the longest side of the triangle if the perimeter of the kite is as long as
possible?
4) Rosie builds a large cube out of sugar cubes. Her large cube has a width of 4 cubes, height
of 4 cubes and length of 4 cubes. She wants to add one more layer of cubes all around to
make an even larger cube that will have height, width and length 6 cubes. How many cubes
does she need?
5) The formula for the area of a triangle is often gotten by
looking at a related parallelogram. For triangle ABC shown on
the coordinate grid what are the coordinates of the vertices of a
parallelogram in the first quadrant that has twice the area of the
triangle and contains the triangle? The coordinates should all
be positive.
Probability & Statistics
1) Katie and Jim play a game with 2 six sided number cubes numbered 1 through
6. When the number cubes are rolled, Katie gets a point if the sum of the two
is even and Jim gets a point if the product is even. What is the likelihood
that on one roll of both cubes both Katie and Jim get a
point?
2) Randy opens up a bag of jelly beans after mixing them up. He pours out 10
and counts 4 red ones in the bunch. He wants to practice his knowledge of
statistics and has his brother count all the jelly beans in the bag in another
room. There are 160 according to his brother. Based on Randy’s sample, about
how many red jelly beans should be in the bag?
3) The students in Mr. Beloshi’s class are
working in groups to draw a life size average
fifth grader for their class of 25 students.
Group A has gathered data about all the fifth
graders in their class. Heights to the nearest
inch are shown in the bar graph. To the
nearest inch, what is the mean height and what
is the median height?
4) Mr. Zee just can’t play it straight. He’s asked you to come over and help
him paint his fence.He’ll pay you based on the flip of 3 coins. If they all
come up heads you get $100. If two heads,then $75, if one head $50 and no
heads $25. What’s the likelihood you will earn more than $50 for
this job?
5) Lelani is on a track team and wants to win in the 100 yard dash. Every day
she runs as fast as she can. Her personal coach shows her the following table
of her times over a 10 day period, but as you can see there isn’t data for
every day. Plot the points on a grid on your answer sheet.
Based on the overall trend in
your graph how fast do you think
Lelani will run on the 12th day?
Algebraic sense
1.) Jim likes to text message. The cell phone family plan his parents have
allows for 250 text messages per month for $5.00 as part of the plan and
additional text messages cost 15 cents per message both incoming and outgoing.
What is the total number of messages Jim can send and receive for less than
$10.00 if no one else in his family texts?
2) Hannah has some pencils in her pencil case. She loans 1/6 of the pencils to
Tommy and then 3 pencils to Marc. On her way home from school Hannah loses 50%
of her remaining pencils through a hole in her bag. When she gets home she
realizes that she only has 6 pencils left. How many pencils did Hannah start
the day with?
3) Pictured is a sequence of growing chairs.
The first chair is made of 6 squares. How
many more squares are in the 8th chair in the
sequence than in the first?
4) A boy lives on the same road as his school and the road is straight. He
bikes to school. When he reaches halfway he notices he has dropped his math
book. He bikes back 400 yards to pick it up. He is now 1300 yards from school.
How far is his house from school?
5) Mr. Jones takes three taxi cab rides with the same cab driver. The table
shows how many mileshe traveled and what the taxi fare was. Plot the points on
a coordinate grid and use the information to decide what the base fare without
tip is for a trip that is 6 miles long.
i
Number Sense
1) A grocery store sells three different-sized cans of orange
juice. A 6-oz can costs 55 cents. A 16-oz can costs $1.15. A 32oz can costs $2.79. Which is the best buy?
2) In Kendra's school, 2 out of every 5 seventh graders went to
a movie theater over the weekend. If there are 80 students in
the seventh grade, how many of them saw a movie?
3) A food stand buys ice cream cones in packages of 8. Each
carton of ice cream will make 12 cones. What is the least number
of packages of ice cream cones and cartons of ice cream that
need to be bought to have no leftover ice cream and no leftover
cones?
4) Mr. Zipher sells fresh walnuts at his farm stand and charges
by the pound. Stella fills a small bag and Mr. Zipher tells her
it weighs 3/16 lb and asks for 47 cents. She decides she has
just enough for
½ lb of walnuts. How much is ½ lb of walnuts to the nearest five
cents?
5) Guess this number from the clues:
The least common multiple of this number and 42 is 630.
The greatest common factor of this number and 42 is 6.
Measurement
1) How much carpeting is needed to cover the floor of an L
shaped room with the dimensions shown in the figure?
2) The right triangle BAC has a base of 4 centimeters and a height of
5 centimeters. A new triangle is created by increasing the angle at A
by 60° and moving point C
to point D. AD has the same length as AC. What is the sum of the
angles DBA and BDA in triangle BAD?
3) A loop of rope has a total length of 30 feet. Stevie creates a
rectangle with the loop that has length 8 ft. Taneisha takes the loop
and creates a rectangle that has length 10 ft. What is the difference in the area between Stevie’s and
Taneisha’s rectangles?
4) Tina’s walk home from work is 2 miles. After leaving work she walks 1000 feet and stops to get a
drink of water. Tina then walks an additional quarter of a mile and gets her mail. How much further does
she need to walk? Give your answer in feet. 1mile = 5280 feet.
5) Rocks are being put in an empty well
at a rate of 5 rocks per second. After
one hour and fifteen minutes how many rocks are in the well?
geometric sense
1) A pinwheel is made of four identical shapes each with a different color arranged counterclockwise in color order red, blue,
green, and gold. They are evenly spaced. The wind spins the pinwheel counterclockwise, and when it stops, the red shape is now
where the blue shape used to be. If the pinwheel went through two complete rotations before red ended up where blue used to
be, how many total degrees did the red shape travel?
2) John is trying to make a rectangle on the given coordinate
grid. He has already labeled the point A at (-1, 3), the point
B at (1, -1), and point C at (-2, 2). Where should he plot
point D to complete the rectangle?
3) Toleen’s math teacher makes a model of a solid rectangular prism out of white one centimeter
cubes to explore surface area and volume. She paints the entire outside surface red. If the
dimensions of the prism are 3 cm by 4 cm by 6 cm, how many of the cubes have exactly two sides
painted red?
4) In Latoya’s class they are cutting out snowflakes from square paper folded in half and then in
half again to make a folded square. Latoya cuts along the three lines shown in the picture of the
folded square. When she unfolds her paper what shape will fall out of her square?
5) In right triangle AMC (see diagram) triangles ANP and PLC
are congruent. MNPL is a square and segment LC has length 2
cm. What is the perimeter of the square MNPL?
Probability & Statistics
1) A dart hits the dartboard shown at
random. Find the probability of the dart
landing in the shaded region.
2) Jazmin has a coin and Sue a 6 sided number cube labeled 1 through 6. They have
decided to playa game. What is the probability that Jazmin will flip a head and Sue will
roll an even number?
3) Four friends, Amber, Becky, Callie, and Darcy went to a party. If Callie was the third
to arrive,how many different orders could the other three friends have arrived in?
4) 4) After three tests Max has a test average of 83. He is nervous for the fourth test
and wants to keep an average of at least 80. What is the lowest score he can get on the
fourth test if each test is worth 100 points?
5) A class of 21 children goes to the gym to
measure its length in paces. The bar graph
shows the distribution for the number of paces
it took to traverse the gym lengthwise. All
numbers are whole numbers. From the graph
which bar contains the median number of
paces?
Algebraic sense
1)Tina and Jeff each bike 3 miles to school. Jeff bikes a steady ¼ of a mile per minute.
Tina bikes a steady 1/6 of a mile per minute. When Jeff arrives at school, how far does
Tina still have left to bike?
2) The boy scouts are building bird houses. Michael buys screws and nails for the
project. Screws go for 65 cents per pound and the nails go for 30 cents per pound.
Michael bought 3 pounds of screws and he spent a total of $4.05. How many pounds of
nails did he buy?
3) The colored stripes pattern Red, Blue, Blue, Green, Yellow repeats on wall paper.
What will be the color of the 32nd stripe?
4) Tran loves jellybeans. Every day he eats one more jellybean than the previous day. If
Tran ate 15 jellybeans on Saturday, how many total jellybeans did he eat that week if his
week began on Monday and ended Saturday?
5) Sosna is moving. She can carry 16 books at once in her arms to the car. She can also
carry 26 DVDs in one load. She doesn’t mix books and DVDs to keep things organized.
Sosna made 7 trips to the car with arms fully loaded and carried a total of 142 objects.
How many DVDs did she carry to the car?
number sense
1. C) 176
2. 15/120 = 3/24 = 1/8 = .125
3. C) 0.0237
4. 5775
5. 22 or 15/6 dozen
MEASUREMENT
1. $19.20
2. 16
3. 87
4. 1,000,000
5. Sunday
geometry
1.
2.
3.
4.
5.
64 m2
36
5 ¾ inches or 5.75 inches
50 cm2
_ cm2 or 3.14 cm2 (Accept any number between
3.14 and 3.1416 cm2.)
PROBABILITY & STATISTICS
1. 24
2. 66
3. 10/39 or 10 out of 39
4. The letter “I” (The answer of “I” is
sufficient.)
5. 8
Algebraic Sense
1.
2.
3.
4.
5.
30
4
Month 6 (An answer of “6” is sufficient.)
13
48
Number Sense
1. 1.3m
2. $900
3. 13 (corresponding to prime number 41) or 14 (corresponding to the PIN number)
4. five 13 cents stamps and zero 7 cent stamps
5. 58.33 sec
Measurement
1. 75 ft.
2. Florence by 40 pages
3. 30 m.
4. 6 gel pens
5. 20 cm
Geometric Sense
1. 140°
2. hexagon
3. 14 units
4. 152 cubes
5. ((2,1), (4,7), (3,9), (1,3)) or ((1,3), (2,1), (5, 5), (4,7))
Probability & Statistics
1. 1/4
2. 64
3. Mean: 55 in., Median: 54 in.
4. 1/8
5. Possible answers: 9.3 – 9.5
Algebraic Sense
1.
2.
3.
4.
5.
283
18 pencils
28 squares
1800 yards
$20.50
i
1.
2.
3.
4.
5.
Number Sense
16 oz can
32
3 packages of ice cream and 2 cartons of ice cream
125 cents or $1.25
90
measurement
1. 264 square feet
2. 30 degrees
3. 56 – 50 = 6 square feet
4. 8240 feet
5. 22,500 rocks
Geometric Sense
1. 810°
2. (-4, 0)
3. 28
4. Octagon
5. 8 cm
Probability & Statistics
1. 1/3
2. 1/4
3. 6
4. 71
5. 46-50 bar
Algebraic Sense
1. 1 mile
2. 7 pounds
3. Blue
4. 75 jellybeans
5. 78 DVDs