Practice Exam
Let function represent the position of a particle in meters after t seconds. What is the velocity of this particle when its acceleration equals zero?
-3m/sec
The change in the population of a city is million people, where t is the time in years from now. What is the instantaneous rate of change of the population 3 years from now?
-4 million
Which of the following is an irrational number?
/7
Sal and his 3 friends went to a restaurant. At the end of the dinner, their check included food and 8.25% tax only. They added 15% of the check as gratuity and then split it equally. If Sal paid $34.75 in total, how much was the total cost of food before tax and gratuity were added?
$111.66
Sally has a total of 22 coins in her piggy bank. There are six more dimes than quarters. How much total money does she have?
$3.40
Jack has inherited a land that was purchased for $30,000 in 1960. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2017?
$484,000.
Sam will deposit a total of $750 into two separate bank accounts:· $300 will be in an account which earns 3.18% annual simple interest· The rest of the money will be deposited into another account which earns 3.09% annual compound interest. If he doesn't make any additional deposits or withdrawals, which of these amounts will be closest to the total amount of money earned in 3 years?
$821.64
Triangle ∆XYZ (4,4)(4,-2)(1,-2) is rotated 1800, where the center of rotation is point B(1,1). What are its coordinates after the rotation?
(-2,-2)(-2, 4)(1, 4)
A rational function is given as At what coordinates does that rational function have a removable discontinuity?
(6, 2.25)
During a field study, 6th-grade math students measured the width of a sidewalk as 42.5", using a tape measure that has the smallest unit of ⅛ of an inch. What is the greatest possible error the teacher would expect from this measurement?
1/16th of an inch
Macy's stock prices have increased from $29.07 to $32.73 from January 30th to February 3rd. What is the approximate percent gain in stock prices within these 5 days?
12.59%
Martha Main Middle School has 10 students in Math Olympiad Club. A 5-member team and a captain will be selected out of these 10 students. How many different selections can be made?
1260
Frank has a lavender field which has an area of 16 cm2 on the map. The scale of a map is 1 cm = 40 feet. He will apply fertilizer at a rate of ½ lbs. of fertilizer for every 100 square feet of the field. How many pounds of fertilizer does he need to fertilize the entire field?
128 lbs.
There are 20 male and 12 female dancers in a dance school. How many pairs of dance partners can be arranged?
12i
Students are writing all of the possible 4 letter words by using the letters in word MATH, such that no word repeats. After that, they arrange these words in ascending alphabetical order. What is the rank of the word MATH in that group?
14
What is the measure of angle B?
145
The top third of a square-based pyramid was cut off. The side of the square base is 15 cm, and the height is 14 cm. What is the volume of this truncated pyramid?
1516.67 cm3
The radius of circle O is 34 cm. The arc formed by angle β is 3.4πcm long. What is the measure of angle β to the nearest whole?
18
A group of sixth-grade students designed a pencil box as part of their math project. The volume of their box is 552π cm3. The diameter of the cylinder is 12cm, and its height is 14 cm. What is the total height of the pencil box?
18 cm
Mr. Fray's students' STAAR scores are as given below. What is the standard deviation to the nearest tenth? 34, 45, 78, 100, 48, 87, 56, 75, 86, 93, 100, 95, 98, 40, 67, 76, 70, 73, 67, 96, 56, 86, 88, 78
19.3 Mean
The 12th and 18th terms of a geometric series are given as: and . What is the 30th term of this geometric series?
2-25
A basketball player has a chance of making 70% of his free shots. What is his probability of making exactly 6 out of 10 shots?
20%
Duran rode her bike from her house (-4,5) to the library (-3,2). After the library, she stopped by the grocery store (2,-3) and then went back home (-4,5). Assuming she took the shortest distance between each stop, how many units did she travel overall?
20.23units
The radius of a ripple in a lake, which always remains circular, expands at a rate of 6 in/min. When the radius is 18 inches away from the center, what is the rate of change of the area covered by this ripple with respect to time?
216π in/min
A 6th-grade teacher is creating a formative assessment about equivalent forms of fractions, decimals, and percents. One of the questions asks students to convert a set of percents to decimals. Which of these sets of percent values would help him determine common misconceptions?
24%, 136%, 0.08%, 1.2%
Triangle ∆SEL is a right triangle. What is the length of the hypotenuse SE?
25
In an 80-mile relay race, each team had two cyclists and cyclists exchange at the mid-point of the race. The winning team crossed the finish line at 3 hours and 36 minutes. What was the speed of each cyclist of the winning team, if cyclist two was 5 mph slower than cyclist one?
25 mph and 20 mph
A ball is thrown straight up from the top of a 192-foot-tall building with an initial speed of 64 feet per second. The height of the ball as a function of time can be modeled by the function h(t) = -16t2 + 64t + 192. What is the maximum height the ball will reach with respect to the ground?
256 feet
Scientists started an experiment with 100,000,000 cells. 35% of the remaining cells died every minute throughout the experiment. How long did it take for the number of cells to drop below 1000?
27 minutes
A 7th-grade math class is working with similar figures. The two right cones shown below are similar. Mr. Kenney told the class that the surface area of the cones are 180 and 320 square units, and the volume of the smaller cone is 151 cubic units. He challenged his class to find the volume of the bigger cone. What is the volume of the bigger cone?
358 cubic units
What is the measure of angle β, to the nearest degree?
37
A triangle is formed inside a square by joining corner C with the mid points of sides AD and AB. If a point in the square is chosen randomly, what is the probability that the point will be inside the triangle as well?
37.5%
Campsites X and Y are on the opposite sides of the forest. A scout group measured the area as shown below. What is the distance between two campsites?
376 m
What is the simplest form of the algebraic expression?
3x(x-2)
A "Fermi question" is a question in physics which seeks a fast, rough estimate of a quantity which is either difficult or impossible to measure directly. An 8th-grade math teacher posts a Fermi question on her blog every Monday. At the end of the week, students share their estimation, discuss their reasoning, and find out whose answer is the closest to the actual solution. This week's question is given below:There are 3 time zones in the US. The average distance across the US (east to west) is about 3000 miles. Estimate the radius of the Earth.Which of these is the best estimate for this Fermi question?
4,000 miles
What is the probability of drawing a seven or a heart from a deck of 52 cards?
4/13
During a game, students randomly select two digit numbers and use divisibility rules to determine if it is divisible by 2, 3, 4 and 5. What is the probability of a number being divisible by 3 but not by 5?
4/15
The area of a rug is 7,920 in2. What is the approximate area of this rug in squared meters?
5.11m2
Two ladders are leaning against a wall as shown below. What is the angle below the shorter ladder?
54.86
Students in a 6th-grade classroom are learning about experimental and theoretical probability by using geometric models. Ms. Day brings a dart board as shown below. After calculating the experiment by throwing darts, they proceed to calculate the theoretical probability. What is the theoretical probability that the dart hit the shaded region?
59.5%
As part of an interdisciplinary unit in math and science, students are recording their daily caloric intake for a week. Sally ate two slices out of a 16" diameter pizza. The whole pizza is 1478 cal. She measured the angle of the slices for her calculation. How many calories will she record in her journal?
591 cal
An item that costs $28 to purchase is sold for 12% profit. About how many items need to be sold to make $20,000 in profit?
6000
The distance between Houston and Austin is 160 miles. Sarah and Sam left their home in Houston at 3:00 pm and drove at an average speed of 80 km per hour. When did they arrive in Austin?
6:12 pm
A 10 faced die is rolled over and over until it lands on a 7. What is the probability to the nearest whole that it takes exactly 5 rolls for it to land on a 7?
7%
There are 2 green and 3 red marbles in one bag, and 4 green and 2 red marbles in the other. A bag and a marble are picked at random. What is the probability that the marble will be red?
7/15
Researchers measured the reaction time of 18 adults. Results are given in milliseconds. What is the interquartile range of this data? 25, 30, 31, 34, 35, 35, 35, 36, 38, 39, 40, 40, 42, 43, 44, 46, 48, 64
8.5. IQR=Q1-Q3
There are 5 multiple choice questions on a math test. Each question has 4 answer choices and only one of those is the correct answer. If each question is answered at random, what is the probability of having 3 correct answers?
8.79%.
Darya asked her teacher how she did on the last math test. Her teacher showed her a list of grades without any names. She only told her that she is in the 80th percentile. Grades are given below. What is Darya's grade on the math test? 67, 78, 54, 95, 87, 75, 80, 76, 80, 82, 97, 65, 74, 84
87. 80th
What is the approximate value of the integral using 5 subintervals and left-end point Riemann summation?
9
Which statement best describes the two straight lines AB and CD?
Are not parallel because the two given alternate interior angles are not equal
A 4th-grade teacher observes a student using a division algorithm she has never seen before. When she asks him, he explains that he was very confused about the algorithm used in the classroom, so his mom taught him this shortcut. What is the best approach for the situation?
Asking Mike to teach her this new method so that she can help him
How is the repeating decimal expressed as a fraction in simplest form?
Correct answer is 1 7/30
What is the modulus of the complex number ?
Correct answer is 2 /5
A 4th-grade teacher is reviewing her students' work samples to diagnose what they are struggling with. The students' work is shown below. How should she form her small groups?
Daisy and Sam in one group, and Karen in another.
Which of these represents the domain and range of y=x2- x - 2?
Domain (-∞,+∞), Range [-, +∞)
Mrs. Dawson observes a student finding the measure of the missing angle in a right triangle by subtracting the given angle from 900. Which of these questions is the best to identify the problem?
How does subtracting 250 from 900give you the measure of the missing angle
Which statement is the missing statement in this two-column proof? Given ∆ABC and ∆ADC are right triangles Given Prove ∆ABC∆ADC
Hypotenuse Leg Postulate
Which of these statement is not true?
Imaginary numbers are subsets of irrational numbers
As part of the surface area of 3D figures study, a 7thgrade classroom is creating nets for square-based pyramids. Which of these students did not create a correct net?
Karen only
In sample statistics, small confidence intervals indicate which of these conditions?
Low variation
An 8th-grade teacher notices that one of her ELL students is struggling with lengthy word problems. Which of these is the most effective way to approach this issue?
Modeling how to look for important information, key words and eliminating unnecessary information.
A fourth grade teacher uses the bars shown during fractions and decimals unit. Which of these expressions cannot be modeled by this representation?
Multiplying decimals 3x0.6=1.8
Sam and Sarah shopped at the nursery. Sam bought 5 perennials and 2 trees and paid $54. Sarah bought 4 perennials and 3 trees and paid $60. How much did each perennial and tree cost?
Perennial= $6, Tree= $12.
Which postulate explains why ∆ABC ≅ ∆XYZ are congruent?
SAS
Joe has a total of $20,000 in three different investments: a savings account paying 5% annual interest, a bond paying 10%, and a stock market account paying 13%. He earns a total annual interest of $2005, and he has three times as much invested in the bond as in the savings account. What amount does he have invested in each account?
Savings=$3,500, Bond=$10,500, Stock=$6,000.
Triangle ∆DEF has side measures of 6, 12, and 15. Which of these best describes this triangle?
Scalene obtuse
Mrs. Kay, a 5th-grade math teacher, guides her students while they are modeling multiplication of decimals on base 10 grids. Which of these statements best explains purpose her teaching practice?
She communicates the multiplication process by providing students with a variety of representations
A 7th grade teacher uses student portfolios as summative assessment where they keep certain activities they have worked on in class and at home. Each student has a self-assessment sheet where they report their own portfolio grades. At the end of the unit, the teacher agrees or disagrees with the grades they give to themselves. What kind of behavior is best promoted by this kind of assessment?
Students take responsibility of their own learning by analyzing and evaluating their mathematical thinking.
Assuming students have no prior knowledge, which of these shows the proper continuum of instruction?
Students use decimal blocks to model decimal additions →use base 10 grids and color to model decimal additions → use the algorithm to add decimals
Determine whether the given argument is valid and sound. -All triangles have three sides. -Shape ABC has three sides. -Therefore, shape ABC is a triangle.
The argument is invalid and unsound
(1.32 x 10-3 ) + (3.44 x 10-4) =What is this sum expressed in scientific notation?
The correct answer is 1.664x10-3
What is number 407 in base 4?
The correct answer is 12113.
Mandy and Jeff start running around the track in the same direction at the same time. Mandy runs one lap in 2 minutes and 30 seconds; Jeff runs it at 2 minutes and 15 seconds. If they both start at 8:30 am, at what time will they be side-by-side again?
The correct answer is 8:52:30
Joe has two pieces of wood: one is 90 inches long and the other is 72 inches long. He wants to cut both pieces of wood into smaller pieces so that all pieces are the same length. If he wants the pieces to be as long as possible and doesn't want to have any lumber left over, how many total pieces of lumber will he have?
The correct answer is 9
If a is odd and b is even, then a+b is odd.What is the first assumption to construct an indirect proof of this result for all integers?
a+b is even
During a Data and Statistics Unit, students are asked to create a survey to determine the common interests of the students in their school and to display their results using the most appropriate means. Which of these process standards TEKS is addressed?
create and use representations to organize, record, and communicate mathematical ideas.
The age of people in a hospital lobby are displayed by the box plot as given below. Which of these statements describes the distribution of this data set?
data is negatively skewed and the median is higher than the mean
For the statistics and data analysis unit, students recorded following temperatures (in F0) each day for 15 days: 82, 72, 83, 75, 80, 78, 82, 73, 65, 63, 79, 80, 78, 83, 81. They are asked to represent data by choosing one of the central measures. Which of these statements explains the reasoning for choosing the best representative for this data set?
There are no outliers, therefore mean is the best representative.
In 7th grade classroom, students are starting the linear equations unit. Mr. Heart gives a brief introduction about specific requirements for the steepness of ramps by The Americans with Disabilities Act (ADA) of 1990. After explaining the rise and the run, he takes the students outside. Students determine the slope for each ramp around the school and then state whether or not each satisfies the ADA requirements. Which of these statements best explains the purpose of this activity?
To relate mathematics to students' lives.
Sarah studied the sequence given below and made a conjecture about the rule of the sequence. Which of these statements best explains her reasoning?Sequence: -3, -1, 1, 3, ...Conjecture: nth number in the sequence= 2n-5
inductive reasoning because she made observations based on the given terms of the sequence and made a generalization
When these numbers are ordered on a number line, which will be closest to 2?
is closest to 2
Karen built a rectangular bulletin board that has an area of 72 inches and a perimeter of 44 inches. The board is wider than it is long. Which of these is not a proper strategy to solve this problem?
looking for a pattern
A 7th-grade math teacher is planning a demonstration to teach the volume of a cone. She fills a cylinder with water. She empties the water into three cones that have the same radius and height as the cylinder. Which of the following is the teacher demonstrating with this activity?
making connections to the prior knowledge
A 7th-grade teacher uses the figure below to investigate the properties of parallel and perpendicular lines. Which statement explains best why QPR and SPT are congruent?
opposite angles formed by the intersection of two lines are equal
A 7th-grade teacher is planning a summative assessment for the Statistics and Data Unit. Throughout the unit, students will work on experimental and theoretical probability by using manipulatives to compare the outcomes. They will also conduct an internet research on different probability games around the world. Which of these is the most appropriate summative assessment for this unit study?
project where they design and create a probability game
6th-grade students are assigned a task whereby they plan their dream vacation. They choose a destination and research and calculate the expenses including travel, food, sights to see, hotels etc. to create a budget. At the end, they make a display of their choices and share with the rest of the class. Which learning model is being implemented?
project-based learning
6th-grade students worked on concrete and pictorial models of dividing fractions. Some students already discovered the rule invert-and-multiply by looking at the patterns while working on the concrete and pictorial tasks. The teacher is planning to teach them why the invert-and-multiply procedure works. She would like to show the example below. Which of the concepts is best for her to review before this example to make connections with what students learned before?
reciprocals of fractions
At the beginning of the school year, a 4th-grade teacher sets up three stations. One of these stations has laptops where students watch a video about prime numbers. A second station has textbooks where students read about adding fractions with unlike denominators. A third station has decimal block manipulatives with decimal multiplication problems. Students are not familiar with any of these concepts. At the end of each station, students answer a set of questions about their experiences and then move to the next station. Which of these best explains the teacher's purpose?
she is determining her students' learning styles so that she can create her small groups accordingly
On a summative assessment, a third of the students answered the question as shown below. What is the best way to modify instruction?
small groups
Mr. Kenney is planning a lesson about the sum of the interior angles of a triangle. Which of these is the most appropriate activity for the introduction of this concept?
vertices of paper triangle cutouts
Martha is baking cupcakes and cookies for a fundraiser. She wants to bake at least 50 items to raise at least $75. She will sell each cupcake for $5, and each cookie for $3. Which of these systems of inequalities represents the problem?
x+y≥50; 5y+3x≥75
Which of these is the point-slope form of the line that passes through points (-1, -2) and (1, 4)?
y+2=3(x+1)
