Math Praxis Practice Test (5003)
If two fair six-sided number cubes are thrown, in which region will the sum of the two number cubes most likely to appear? blue region: 1-4 green region: 5-8 yellow region: 9-12 a. green b. blue c. all regions are equally likely to appear d. yellow
answer: a. green The probability of getting between 1 and 4 is 6 out of 36. The probability of getting between 9 and 12 is 10 out of 36. The probability of getting between 5 and 8 is 20 out of 36. The green region has the highest likelihood to appear.
Know what parallel and perpendicular lines are.
Parallel: Have the same slope, never touch Perpendicular: Have the opposite, inverse slope (example: 2, -1/2), and form a 90 degree angle where they intersect
The weights of twenty trouts were recorded: 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 18, and 34. If the weight of the heaviest trout is removed from the data, which statistical parameter will drastically change? a. range b. median c. mean d. mode
answer: a. range Since the mean, median, and mode are measures of center, outliers will not have much effect. The range will be greatly affected since it measures the difference between the highest and lowest.
What shape is obtained by drawing the polygon whose vertices are the points of coordinates (2,0), (0,2), (-2,0), and (0,-2)? a. square b. rectangle c. parallelogram d. trapezoid
answer: a. square The polygon determined by the four points is a square
What is the definition of a regular shape? What is the definition of an irregular shape?
The definition of a regular shape is that all the sides are equal and all the inside angles are equal. An irregular shape doesn't have equal sides or equal angles. For example, an equilateral triangle is a regular shape because all the sides are equal AND all the angles are equal.
Know how to find volume, area, and surface area of a triangle, triangular prism, rectangle, rectangular prism, circle, sphere, and trapezoid
Google and memorize formulas
Which of the following statements regarding basic operations in numbers is not always true? a. the product of two odd numbers is odd b. the product of two composite numbers is even c. the product of an even number and another number is even d. the product of two prime numbers is odd
answer: d. the product of two prime numbers is odd By using inductive reasoning, we can either prove or disprove a given statement. A counterexample for the statement, ''the product of two prime numbers is odd,'' is using any prime number and the number 2. Multiplying any number by 2 will result in an even number.
Draw the solution to 2x-(12x+5)>-x-32.
answer: on a number line, there is an open circle at 3, with an arrow going to the left (negative, smaller numbers) The inequality becomes 2x-12x-5 > -x - 32 and simplifies to - 9x > -27 . By dividing by -9 both sides of the inequality, we obtain 'x < 3'.
Know what obtuse, acute, and right angles are.
Obtuse: Greater than 90 degrees Right: Exactly 90 degrees Acute: Less than 90 degrees
The difference between 11 times a number and 161 is twice the sum of the number and 5. What is the number? a. 18 b. 19 c. 151/13 d. 171/13
answer: 19 Let x denote the unknown number. The difference of 11 times x and 161 translates as 11x-161. The phrase "twice the sum of the number and 5" translates as 2(x+5). Therefore, the following linear equation is obtained for the unknown number: 11x-161=2(x+5). By applying the distributive property, the equation becomes 11x-161=2x+10. Isolating the unknown x on the left-hand side, we have 11x-2x=161+10 or, equivalently, 9x=171. The unknown number is obtain by dividing both sides by 9. Thus, x=19.
Six children have collected these amounts in their piggy banks: $10, $33, $45, $23, $1, and $68. What is the median of their savings? a. $28 b. $33 c. $23 d. $66
answer: a. $28 Rearrange the numbers in increasing order: 1, 10, 23, 33, 45, and 68. The median of a sequence of numbers is the middle value. Since there are six numbers, there are two values in the middle 23 and 33 and, therefore, the median is the average of these values. The median is 28.
There are 429 children in Greenville. If the number of boys is twice as the number of girls, what is the difference between the number of boys and girls in the city? a. 143 b. 100 c. 286 d. 43
answer: a. 143 If x denotes the number of girls, then 2x represents the number of boys. In total, there are 429 children, and that means that 2x+x=429. Thus, 3x=429 implies x=143. There are 143 girls and 286 boys. The difference is 286-143=143 children.
A number of 321 children went on a school field trip to a zoo. At the end of the trip, a third of the number of children went to the gift shop. How many students did not go to the gift shop? a. 214 b. 224 c. 284 d. 107
answer: a. 214 A third of 321 is 321/3=107. Only 107 children went to the gift shop. Subtract 107 from 321 to find the number of children who did not go to the gift shop. The answer is 321-107=214
Diego has 48 pages to encode, and he is only 25% through. How many more pages does he need to encode? a. 36 b. 12 c. 6 d. 24
answer: a. 36 With twenty five percent of the work done, there is still seventy five percent of the work to be finished. Convert seventy-five percent to its ratio form, which is ¾, then multiply it by 48.
Tom has $2.35 in quarters, dimes, nickels, and cents. If he has 5 quarters, 6 dimes, and 5 cents, what percentage of all of his coins are nickels? a. 36% b. 9% c. 25% d. 64%
answer: a. 36% Tom has 5 quarters, 6 dimes, and 5 cents that total $1.25 + $0.60 +$0.05 = $1.90. Since he has $2.35, the difference of $2.35 - $1.90 = $0.45 consists of nickels. Thus, Tom has 0.45/0.05=45/5=9 nickels. Since he has a total of 5+6+5+9 = 25 coins, the percentage of nickels is 9/25 = 0.36. Thus, Tom has approximately 36% nickels.
There are 612 applicants for a manufacturing firm but only one-twelfth of the applicants will be interviewed for the second screening. How many applicants did not reach the second screening? a. 561 b. 510 c. 51 d. 102
answer: a. 561 Out of the 612, only a twelfth of them will reach the second screening, which is 612 divided by 12 = 51. We subtract 51 from 612 to get 561.
The cost y of buying x pieces of chocolate bars is represented by the linear equation y = 2x - 8. If this is converted to a graph, what part of the graph of this linear function is useful? a. the part that will appear on the first quadrant b. the part where x is less than 4 c. the part that will appear on the third quadrant d. the part that will appear on the fourth quadrant
answer: a. the part that will appear on the first quadrant The number of chocolate bars purchased, as well as cost of purchasing chocolate bars, must have positive values. Therefore, the linear model will only make sense as long as x is greater than 4. The graph when x > 4 lie along the first quadrant.
There is a pattern: red triangle, white square, red square, white pentagon, red pentagon, _____, _____, white hexagon, red hexagon, white hexagon. Which of the following will fit perfectly in the sequence? a. white pentagon, red hexagon b. red pentagon, white hexagon c. white pentagon, red pentagon d. red hexagon, white hexagon
answer: a. white pentagon, red hexagon The pattern involves an increase in the number of sides. As the number of sides increases, the number of copies of the figures increase as well. The figures also have an alternating pattern of red and white versions.
A rectangular solid has dimensions of 12 in, 8 in, and 10 in. It has a mass of 288 pounds. What is its density in pounds per cubic inch? a. 1.2 b. 0.3 c. 30 d. 10
answer: b. 0.3 The formula for density is mass divided by volume. The volume of a rectangular solid is the product of its length, width, and height.
Ms. Sanders is teaching map reading in class. She uses the map of their school, and draws grids along the map that resembles the Cartesian plane. She sets the flagpole to be the origin and other school landmarks are labeled with their corresponding coordinates. If the playground has coordinates of (-2, 8), and the school cafeteria has coordinates of (3, -4), what is the distance between the two landmarks? a. 10 b. 13 c. 18 d. 15
answer: b. 13 Distance between two points can be computed by using the distance formula. Even if the coordinates have negative values, it will still end up being positive after squaring the differences in the x and y coordinates.
In a candy factory, 85 pounds of sugar is needed to make 200 bags of candies. How many bags of candies can be made with 68 pounds of sugar? a. 140 b. 160 c. 250 d. 220
answer: b. 160 The ratio of sugar used in the new setup compared to the original setup is 68:85. It can be simplified and converted to a fraction, which is equal to ⅘ . Now multiply the result to 200, we will get 160 bags of candy made.
The number of mangoes is thrice the number of oranges. If there are 88 mangoes and oranges, how many oranges are there? a. 66 b. 22 c. 33 d. 11
answer: b. 22 We let the number of oranges to be x and the number of mangoes to be 3x. We get the equation x + 3x = 88, and x = 22
a ^ b Which of the following is a correct representation of the image if set A is the set of prime integers from 1 to 20, and set B is the set of all odd numbers? a. empty set b. 3, 5, 7, 11, 13, 17, 19 c. 2, 3, 5, 7, 11, 13, 17, 19 d. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
answer: b. 3, 5, 7, 11, 13, 17, 19 The inverted V is the symbol for conjunction. The conjunction between two sets are the elements that are common to both sets A and B.
Which of the following gives the area covered by a triangle with coordinates at (3, 7), (12, 7), and (1, -1)? a. 72 b. 36 c. 120 d. 48
answer: b. 36 If the points are plotted in the Cartesian plane, it can be easily identified that it has a base of 9 and a height of 8. Using the formula base times height divided by two, we will get 36 square units.
Which of the following is the probability of drawing a king or a heart if you randomly pick 1 card from a regular deck of cards? a. 17/52 b. 4/13 c. 9/26 d. 1/52
answer: b. 4/13 The probability of getting a heart or a king is equal to the probability of getting a king plus the probability of getting a heart minus the probability of getting the king of hearts. Since this is an overlapping probability, we need to subtract the intersection between the two events.
Jean and Pierre went on a trip to France. They traveled from Paris to Grenoble by car a distance of 575.4 km and then from Grenoble to Lyon other 111.4 km. If 1 km = 0.6214 miles, how many miles did the two friends traveled? Round your answer to the nearest integer. a. 687 miles b. 427 miles c. 1105 miles d. 428 miles
answer: b. 427 miles The total trip was 575.4 + 111.4 = 686.8 km. 686.8 km x (0.6214 miles / 1 km) = 426.5 ≈ 427 miles
Which of the following is an algebraic expression? a. 4x + 5y + z = 0 b. 4x + 5y - z + 1 c. 4x + 5y = -z + 1 d. 4x + 5y = z + 1
answer: b. 4x + 5y - z + 1 An algebraic expression is a mathematical phrase that contains numbers and variables together with at least one arithmetic operation. The correct answer is 4x + 5y - z + 1. All of the other choices are equations because they contain an = sign.
From 2 cups of pancake mix, 12 to 18 waffles can be made. Which number of waffles is it possible to make from 8 cups of mix? a. 40 b. 60 c. 30 d. 80
answer: b. 60 Since the number of waffles made from 2 cups of mix is between 12 and 18, then from 8 cups, 48 to 72 waffles can be made. Therefore, a reasonable answer is 60
A Math teacher gives a lecture about using nets in representing three dimensional figures. She asks the class to site a real-life object that can show the surface area of a cylinder. Which of the following is the best visual representation of a cylinder's surface area? a. a cylinder-shaped paper weight b. a can of soup with both ends open, and its body cut along the vertical c. writing the dimensions of the cylinder and plugging the values in the formula d. drawing a cylinder on the board and labeling its dimensions
answer: b. a can of soup with both ends open, and its body cut along the vertical Writing the dimensions on the board and drawing a cylinder are not real-life materials to represent the cylinder. The paper weight might be cylindrical in shape, but it is more of a visual representation of a cylinder's volume.
What do you call questions that have more than one possible answer, and require collection of data to reach a valid answer? a. probing questions b. statistical questions c. non-statistical questions b. rhetorical questions
answer: b. statistical questions A non-statistical question just has one answer that does not change. A rhetorical question does not require to be answered. Probing questions require elaboration of the topic.
Changes in the data may or may not affect the mean or the range. Which of the following statement is true? a. the median remains the same if the number 3 is added to the entire data set b. the mean is tripled if the entire data set is multiplied by 3 c. the mean is doubled if the entire data set is multiplied by 1/2 d. the range is tripled if the entire data set is multiplied by 1/3
answer: b. the mean is tripled if the entire data set is multiplied by 3 The correct answer is that the mean is tripled if the entire data set is multiplied by 3. For instance, if the data is 1, 2, and 3, the new data becomes 3, 6, 9. The mean of the first set is 2 while the mean of the second set is 6.
Which of the following linear inequalities is equivalent to 5(x+1)<6x+3? a. x<-1 b. x>2 c. x>-2 d. x<2
answer: b. x>2 Use the distributive property to simplify the left-hand side 5x+5<6x+3. Subtract 6x from each side and next subtract 5 from both side to isolate the term with x: -x<-2. Divide by -1 both sides and reverse the inequality symbol since -1 is a negative number: x>2.
Here is a receipt: T-Shirt: $5 Cookies: $2.50 Notebook: $1 Book: $2.25 Sales tax is 6% What is the total amount due? a. $12 b. $11 c. $11.40 d. $10.75
answer: c. $11.40 The sum of the costs of the items is $10.75. The sales tax is 6% of 10.75, that is $0.65. The sales tax is then added to $10.75. Therefore, the total amount is $11.40.
A large square pizza was divided into 48 square slices. How many slices is equivalent to 25% of the whole pizza? a. 16 slices b. 8 slices c. 12 slices d. 4 slices
answer: c. 12 slices Multiplying 48 by 0.25 without a calculator will be tedious. Instead, we can convert 0.25 to ¼ and we can simply multiply 48 by ¼ , which is equal to 12.
How many hours are there in 9000 seconds? a. 1.5 b. 2 c. 2.5 d. 3
answer: c. 2.5 Since there are 60 minutes per hour and there are 60 seconds per minute, then an hour has 3600 seconds. We can divide 9000 by 3600 to get 2.5.
There is a right triangle. Side a has a length of 9, side c has a length of 41. Which of the following is the measurement of side b? a. 27 b. 36 c. 40 d. 39
answer: c. 40 Using the Pythagorean theorem where side a = 9 and side c = 41, we will get that side b = 40.
Elizabeth has a collection of nickels and quarters in her purse, and its total value is 7 dollars. If the number of her nickels is twenty less than three times the number of her quarters, how many coins are there overall? a. 40 b. 30 c. 60 d. 20
answer: c. 60 If we represent the number of quarters as x, then the number of nickels can be represented as 3x - 20. The equation will be 0.05*(3x-20) + 0.25*x = 7. The value of x is 20. Since we are looking for the total number of coins, then it is 20 quarters plus 40 nickels. There are 60 coins overall.
3x^3 - 7x + (square root sign) 17 Which statement does not accurately describe the given polynomial? a. it is an algebraic expression with -7 as the coefficient of x b. the given has a constant term of (square root side) 17 c. it is an algebraic equation with a degree of 2 d. the given has three terms
answer: c. it is an algebraic equation with a degree of 2 A collection of variables and numerical coefficients, combined with a ''+'' or a ''-'', comprises an algebraic expression. If the terms are separated by an equal sign, it becomes an algebraic equation. Since there is no equal sign in the given, it is not an equation.
What quadrant or axis does the point A= (0, -2) belong to? a. first quadrant b. second quadrant c. y-axis d. third quadrant
answer: c. y-axis The point A=(0,-2) lies on the negative direction of the y-axis. Therefore, it does not belong to any quadrant.
A ten-sided dice is thrown three times. What is the probability that the die will fall on the same number? a. 2/1000 b. 3/100 c. 3/1000 d. 1/1000
answer: d. 1/1000 The three events of throwing the die are independent. Each probability of obtaining a specific face is 1/10. Therefore, the probability of obtaining the same number is (1/10)(1/10)(1/10)=1/1000.
Jordan has a chocolate bar. The chocolate bar consists of squares of chocolate; it has a length of 6 squares and a width of 4 squares. For the first three days, Jordan eats the largest possible square off of the chocolate bar. What fractions of the chocolate does she eat each day? a. 2/3, 16/24, 1/4 b. 16/24, 1/6, 3/24 c. 1/3, 16/24, 1/4 d. 2/3, 1/6, 1/6
answer: d. 2/3, 1/6, 1/6 The chocolate bar has 24 rectangles. The largest possible square is a 4 by 4 square that contains 16 squares out of 24. Therefore, Jordan eats 16/24 = 2/3 in the first day. The remaining part is a 4 by 2 rectangle. The largest possible square is a 2 by 2 square that represents 4/24 = 1/6 of the chocolate bar. The remaining part is a 2 by 2 square that, similarly, represents 4/24 = 1/6 of the chocolate bar. In conclusion, she ate 2/3, 1/6, and 1/6 of the chocolate bar.
Which of the following is equal to 11 + 39 + 38 - 29 + 21 - 50? a. 35 b. 4 c. 25 d. 30
answer: d. 30 Adding the first two numbers is equal to 50, which can be cancelled by the other 50. We can round off the remaining numbers to .40, 30, and 20. 40 - 30 + 20 = 30
There are two cars, a and b. After 30 minutes, car a has travelled 25 miles and car b has travelled 30 miles. The two cars are initially 550 miles apart and they move towards each other. How much time will it take for them to meet? a. 6 hours b. 11 hours c. 10 hours d. 5 hours
answer: d. 5 hours Since the two cars are moving towards each other, we can say add their rates and use it to divide the distance separating them to get time. Take note that the time given is in minutes, so convert it to hours.
x = 3 and 3/10 + 1 and 1/5 Plot x on the number line. a. at 5 b. between 2 and 3 c. between 1 and 2 d. between 4 and 5
answer: d. between 4 and 5 Add the two mixed fractions by adding the whole numbers first, then adding the two fractions. In adding the fractions, get the ''LCD'' of the fractions to make them similar.
Which of the following is the term used for the intersection of the x-axis and the y-axis? a. quadrant b. coordinate c. abscissa d. origin
answer: d. origin Abscissa refers to the x-axis, while ordinate refers to the y-axis. Quadrant refers to the four sections in the Cartesian plane that are divided by the two axes.
