Praxis 5901 Math

Box plot

A graph that gives you a good indication of how the values in the data are spread out. A graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

3 dimensional shapes with nets

A net is a pattern that we can cut out and fold to model a 3D shape. Net= unfolded 3D shape. Net of rectangular prism has 6 faces. The net of a triangular pyramid made up of 4 triangles, 1 triangular base and 3 triangular lateral faces. Pyramids are named for the shape of their base.

Quadrants on a graph

A quadrant is the area contained by the x and y axes; thus, there are four quadrants in a graph. To explain, the two dimensional Cartesian plane is divided by the x and y axes into four quadrants. Starting in the top right right corner is Quadrant 1 and in a counterclockwise direction you will see Quadrants 2 through 4.

Rhombus

A quadrilateral whose four sides all have the same length. Sometimes referred to as a diamond.

Parallelogram

A simple quadrilateral with 2 pairs of parallel sides.

Algebraic expression vs equation

Algebraic expression= a number, a variable or a combination of numbers and variables and operation symbols. Equation= made up of two expressions connected by an equal sign.

Equilateral triangle

All angles have the same measure. 180 divide by 3 = 60

Formula for Area

Area of a rectangle: Area= L xW. Area of a square: Area = a(squared). Area of a triangle: Area = 1/2b x h. Area of a circle: Area= (pie) r (squared).

If y=2, what is the value of of 4-2 (4y) + 5y? A.-22. B. -2. C. 22. D. 26

B -2. Reason: 4-16+10= -2

2/3 divide 4/3 + 3/5 x (5/3)to the 2nd power. Which of the following is equivalent to the proceeding expression? A. 2/9 B. 1/6 C. 23/9 D 55/18

B The question requires an understanding of how to solve problems using the order of operations. By using the order of operations and the fact that dividing is equivalent;ent to multiplying by the inverse, the expression can be simplified to 2/3 x 3/4+ 3/5 x 25/9. Performing both multiplications yields 1/2 + 5/3, which is equivalent to 13/6.

A machine that works at a constant rate processes 18 pounds of fruit every 3 hours. At this rate, how many hours does it take the machine to process 72 pounds of fruit? A. 4. B. 10. C. 12. D. 15

C . 12 18divided by 3= 6 6 lbs per hour. 72divided by 6= 12

1 tablespoon = 1/16 cup. 1 teaspoon = 1/3 tablespoon. 1 fluid ounce = 2 tablespoons. Each of the preceding conversions shows equivalent measurements. Based on the equivalent measurements, which of the following quantities is greatest? A. 12 tablespoons B. 7/8 cup C. 8 fluid ounces D. 45 tablespoons

C. 8 fluid ounces The quantity in option A is already 12 tablespoons. The quantity in option B is 7/8 cup, which is equivalent to 7/8 x 16, or 14 tablespoons. The quantity in option C is 8 fluid ounces, which is equivalent to 8x2, or 16 tablespoons. Lastly, the quantity in option D is 45 teaspoons, which is equivalent to 45x1/3, or 15 tablespoons.

Types of triangles:

Equilateral: has 3 equal sides. Isosceles: has 2 equal sides. Scalene triangle: has no equal sides. Acute triangle: has 3 angles less than 90. Right triangle: has one 90 angle. Obtuse triangle: has 1 angle greater than 90.

Volume formula

Length x Width X Height. Volume is three dimensional

Acute angle

Measures less than 90 degrees, therefore all the angles of an equilateral triangle are all acute.

Independent Variable

A variable often denoted by x whose variation does not depend on that of another

Dependent Variable

A variable often denoted by y whose value depends on that of another.

What is the value of the following expression? 1-2 5/6 A. -1 5/6. B. -1/6. C. 1/6. D. 1 5/6

A. -1 5/6 The given expression is equivalent to 6/6- 17/6. That is -11/16, or -1 5/6

The surface area of a cube is 54 square inches. What is the volume of the cube? A. 27 cubic inches. B. 54 cubic inches. C. 81 cubic inches. D. 108 cubic inches

A. 27 cubic inches. The question requires an understanding of how to solve problems involving elapsed time, money, length, volume, and mass. If the length of the side of the cube is S inches, then its surface area is 6S squared inches. Since the surface area is 54 square inches, the length of the side of the cube, in inches can be found by solving the equation 6S squared = 54, which yields S=3. The volume of the cube can then be found by solving the equation V= S to the 3rd; this V=3 to the 3rd. Therefore, the volume is 27 cubic inches.

The cost to rent a bus for a field trip is $34.25 per hour, and the duration of the trip is 4hours and 45 mins. Which of the following expressions is best for doing a mental calculation to closely estimate the total cost, in dollars, or renting the bus for the trip? A. 34x5. B. 34x4.75. C. 34.25 x 4.75. D. 35x5

A. 34x5

Carlos makes an annual salary of $65,295. Which of the following is Carlos' salary rounded to the nearest thousand? A. 65,000. B. 65,300. C. 66,000. D. 70,000

A. 65,000

Which word describes each angle in a equilateral triangle? A. Acute B. Obtuse C. Right D. Straight

A. Acute

A certain polygon has the following attributes: 1. There are 2 pairs of parallel sides. 2. It is a quadrilateral 3. 1 pair of parallel sides has length 2, and the other pair of parallel sides has length 4. Which of the following types of polygons has all the attributes listed? A. Parallelogram B. Rhombus C. Triangle D. Square

A. Quadrilateral Reason: A quadrilateral is a polygon with 4 sides. A parallelogram is a quadrilateral with 2 pairs of parallel sides. A rhombus is a parallelogram with all sides of the same length. A square is a rhombus with at least one right angle. For attributes 1 and 2, the polygon is not a triangle. For attributes 3, the polygon is neither a rhombus nor a square. Therefore, the polygon must be a parallelogram.

(2x+5x-2) - (x+y-3y-5x+2) Which of the following is equivalent to the preceding expression? A. 11x+2y-4. B. 3x-2y-4. C. 11x-2y. D. X-2y

A. The question requires an understanding of how to add and subtract linear algebraic expressions. Adding terms in the given expressions yields the equivalent expression (7x-2) - (-4x-2y +2), which is equivalent to 7x-2 +4x +2y-2. Adding like terms again yields 11x +2y-4.

In a bag there are 28 candies, of which 17 are peppermint and the rest are caramel chews. What is the ration of the number of caramel chews to the number of peppermints in the bag? A. 11 to 17. B. 17 to 11. C. 17 to 28. D. 28 to 17

A. The question requires an understanding of how to apply the concept of ratios and unit rates to describe the relationships between 2 quantities. The total number of candies is 28, and 17 of them are peppermints. Therefore, there are 28-17, or 11 caramel chews. The ration of caramel chews or peppermints is 11 to 17.

Which of the following is an algebraic expression? A. 6x-4 B. 6y<4 C. 6z=4. D. 6+4

A. The question requires an understanding of how to differentiate between algebraic expressions and equations. An algebraic expression is made of constants, variables, and algebraic operations.

The following figure's are the first three figures in a pattern. Figure 1 is composed of 2 triangles and one square. Each figure after figure 1 is composed of 2 triangles and one square more than the preceding figure. How many line segments are in figure 10 of the pattern? A. 35 B. 38 C. 41 D. 44

A. The question requires and understanding of how to identify and extend a pattern. The first figure has 8 line segments. Adding a square to each figure is equivalent to adding 3 line segments. So the number of line segments of figure N in the pattern can be described by the expression 5 + 3n, with n = 1,2,3,.... Therefore figure 10 of the pattern has 5 + 3 x 10, or 35, line segments.

Which of the following inequalities is equivalent to the inequality 4x+4 <= 9x+8? A. X>= -4/5. B. X <= -4/5. C. X>= -12/5. D. X<= -12/5

A. X>= -4/5. Reason: When the addition property of inequality is used, the given equality is equivalent to 4x+4+ (-9x -4) <= 9x +8+ (-9x -4). Simplifying like terms yields -5x<=4. When the multiplication property of inequality is used and the sign is taken into account, -5x <=4 is equivalent to (-1/5) (-5x) >= (-1/5) (4). Simplifying yields x>= -4/5

A window's size is 8 feet by 4 feet. Which of the following units is most appropriate to use to convert the dimensions to in metric units? A. Kilometers B. Meters. C. Millimeters. D. Nanometers

B. Meters This question requires knowledge of relatives sizes in the US customary units and metric units. Since 1 meter is approximately 3.28 feet, meters are the most appropriate unit to use.

If r is a real number, which of the following illustrates the communities property of multiplication? A. (32)(r)=(3)(2r) B. (32)(r)=(r)(32). C. (32)(r) =(30)(r)+(2)(r). D. (32)(r)=(32)(r)(1)

B. The communicative property of multiplication states that given any two numbers k and m, Kim=make; that is, the order of the factors in the multiplication problem does not affect the product.

Two friends went out for lunch and decided to share the dessert. One of them ate 1/2 of the dessert, and the other ate 1/3 of the remaining part. What fraction of the dessert was left over? A. 1/6. B. 1/3. C. 2/3. D. 5/6.

B. 1/3 Reason: The first friend ate 1/2 of the dessert, while the second friend are 1/3 of the remaining part; that is, 1/3 (1-1/2), or 1/6. Altogether they are 1/2+ 1/6= 4/6, or 2/3 of the dessert. Therefore, the fraction left over is 1-2/3, or 1/3 of the dessert.

In the preceding figure, all small rectangles contained in rectangle EFGH shown have the same area. How many small rectangles must be shaded so that 38percent of the area of rectangle EFGH is shaded? A. 12 B. 19 C. 31 D. 38

B. 19 This question requires and understanding of percentage as a rate per 100. There are 50 congruent small rectangles in EFGH. If 38% of the area of EFGH is shaded, then 38/100 x50. Or 19 small rectangles, must be shaded.

Lily, Mathew, Natalie, and Owen each walked from their homes to the mall. Lily walked 1/4 mile, Matthew walked 3/8 mile, Natalie walked 5/6 mile, and Owen walked 7/12 mile. Which list shows these distances in order from least to greatest? A. Lily, Matthew, Natalie, Owen. B. Lily, Matthew, Owen, Natalie. C. Lily, Natalie, Matthew, Owen. D. Owen, Matthew, Natalie, Lily.

B. The question requires an understanding of how to compare, classify, and order rational numbers. The distances can be ordered by rewriting all fractions as equivalent fractions with the common denominator 24. Since 1/4=6/24, 3/8=9/24, 5/6= 20/24, and 7/12= 14/24, the correct order from least to greatest is

What is the least common multiple of 12, 20 and 30? A. 2. B. 60. C. 240. D. 360

B. The question requires an understanding of how to find factors and multiples of numbers. The prime factorization of 12 is 2Squared x 3, the prime factorization of 20 is 2Squared x 5, and the prime factorization of 30 is 2x3x5. Therefore, the least common multiple of the three numbers is 2 squared x3 x5, or 60.

The preceding figure is a net for which of the following three-dimensional figures? A. Cube. B. Triangular prism. C. Rectangular prism. D. Triangular pyramid.

B. Triangular prism Reason: The question requires an understanding of how to represent three-dimensional figures with nets. The net is composed of 2 triangles and 3 rectangles. The triangular prism is the only one of the listed three dimensional figures that has 2 triangular faces and 3 rectangular faces.

Table set up corresponding x and y. X 1,2,3,4. Y 1,4,9,16. Which of the following functions could be represented by the preceding table? A. Y=2to x power. B.y=x squared C. Y=2x D. Y=5x-4

B. Y=x squared

Which phrase describes the solution set to the inequality 18b-5 <20b+11? A All numbers that are less than -8. B. All numbers that are greater than -8. C. All numbers that are less than 8. D. All numbers that are greater than 8.

B.All numbers that are greater than -8. The question requires an understanding of how to interpret solutions to multi step one-variable linear equations and inequalities. The first step to find the solution set of the inequality is to use the addition property of inequality to add -20b+5 to both sides of the inequality. This yields 18b-5-20b+5. The second step is to add like terms. This yields -2b<16. The third step is to use the multiplication property of inequality to multiply both sides by -1/2. One must not forget to flip the direction of the inequality sign when multiplying by a negative number. This yields (-1/2) (-2b)>(-1/2) (16), which is equivalent to b>-8. The solution set to to inequality 18b-5<20b+11 is the set of all numbers that are greater than -8.

At an apple orchard between 280 and 300 bushels of apples are picked each day during the peak harvest season. There are between 42 and 48 pounds of apples in each bushel. Which of the following could be the number of pounds of apples picked at the orchard in each day during peak harvest season? A. 9,000. B. 11,000. C. 13,000. D. 15,000

C. 13,000 because 280 x 42= 11,760. And 300 x 48= 14,400. This number is the best choice.

At an apple orchard, between 280 to 300 bushels of apples are picked each day during peak harvest season. There are between 42 and 48 pounds of apples in each bushel. Which of the following could be the number of pounds of apples picked at the orchard in one day during peak harvest season? A. 9,000 B. 11,000 C. 13,000 D. 15,000

C. 13,000. Reason: 300x38= 14,400 300x42=12,600

The formula V=IR relates to the voltage V, in volts, to the current I, in amperes, and the resistance R, in ohms, in a circuit. What is the current produced by a 9-volt battery in a circuit with 4 ohms of resistance? A. 1.50 amperes. B. 2.00 amperes. C. 2.25 amperes. D. 2.5 amperes

C. 2.25 amperes. V=IR. 9=I(4)

3 less than 4 times the sum of the number x and 15. Which of the following expressions best represents the preceding verbal phrase? A.4x+15-3. B. 3-4x+15. C. 4(x+15)-3 D. 3-4(x+15)

C. 4(x+15)-3

The following table shows the population of four neighboring counties. Counties and Population: A. Brookhaven 74,702 B. Columbus 70,472 C. Davidson 74, 072. D. Washington 74,720. Queen lives in the county with a population of 70,000 + 4,000+ 70 + 2. In which county does Queen live?

C. Davidson

In a flower shop, there are 5 roses in every bouquet. The following equation gives the number of roses r used to make b bouquets. R=5b. Which of the following sentences best describes the variables r and b in the preceding equation? A.b is a dependent variable, and r is a dependent variable. B.b is a dependent variable, and r is an independent variable. C.b is an independent variable, and r is a dependent variable. D.b is an independent variable, and r is an independent variable.

C. In the given formula, there are two variables, b and r. Since the formula investigates how the number of roses r used increases depending on the number of bouquets b, the dependent variable is r and the independent variable is b.

The following list shows Caleb's scores for the first 6 quizzes in his algebra class. 90,90,95, 90, 85, 90. If he receives a score of 95 on the 7th quiz, which of the following statements will be true? A. The average (aritmetic mean) of the 7 scores is less than the average of the first 6 scores. B. The mode of the 7 quiz scores is greater than the mode of the first 6 quiz scores. C. The median of the 7 quiz scores is equal to the median of the first 6 quiz scores. D. The range of the 7 quiz scores is greater than the range of the first 6 quiz scores.

C. Placing the first 6 scores in order gives 85, 90, 90, 90,90, and 95. Since the two middle numbers are both 90, it is easy to see that the median is 90. The mode and mean are also 90, and the range is 10. After adding 95 to the list, the median remains 90, the mode remains 90, and the range remains 10. Only the mean is affected by adding 95 to the list. Since 95 is greater than 90, that is. The mean of the first 6 quiz scores, the mean of the 7 quiz scores is greater than the mean of the first 6 scores. Therefore, of the given statements, the only true statement is that the two medians are equal.

A=5,000 (1-r) The formula shown can be used to find the amount of money in dollars, a in an account at the end of the year when 5,000 is invested at simple annual interest rate 4 for a year. Which of the following represents the independent variable in the formula? A. A B. 5,000. C. R. D. 1+r

C. R reason: In any given formula, there are two different variables, a and r. The formula can be used to investigate how the amount of money a varies depending on interest rate r. Therefore, the dependent variable is a and the independent variable is r.

The following list shows the first 6 terms of a sequence. 1, 1, 2, 3, 5, 8. Which of the following formulas can be used to find the terms of the sequence? A. a1=1 an= an-1 for n>= 2. B. A1=1 an=an-1 +1 for n>=2. C a1=1 a2=1 an=an-2+an-1 for n>=3. D. A1=1 a2=1 an=an-2+an-1+n-3 for n>=3

C. Requires an understanding of how to make conjectures, predictions, or generalizations based on patterns. The only formula that yields a sequence whose terms are those shown is the one in option C, in which the first 2 terms are defined as 1and each subsequent term is the sum of the two terms immediately preceding it.

A painter used 1 and 1/2 cans of paint to paint 2/3 of a room. At this rate, how much more paint does the painter need to paint the remainder of the room? A 1/3 can. B. 1/2 can. C. 3/4 can. D. 1 can

C. Since the painter has already painted 2/3 of the room, the painter still needs to paint 1- 2/3, or 1/3 of the room. To determine the amount of paint P needed to paint the rest of the room, one can use the proportional relationship that 1 1/2 is to 2/3 as P is to 1/3 to set up an equation 2/3p= (1 1/2) x 1/3. Simplify the right side of the equation yields 2/3p = 1/2. Therefore, p= 3/2 x 1/2; that is, p= 3/4.

The preceding figures are squares. Each side in Figure 1 has a length 7, and Figure 2 has side lengths that are double those in Figure 1. How does the perimeter and area of Figure 1 compare to with the perimeter and area in Figure 2? A. The perimeter and area of Figure 2 are double the perimeter and area of Figure 1. B. The perimeter and area of Figure 2 are four times the perimeter and area of Figure 1. C. The perimeter of Figure 2 is double the perimeter of Figure 1, and the area of Figure 2 is four times the area of Figure 1. D. The perimeter of Figure 2 is four times the perimeter of Figure 1, and the area of Figure 2 is eight times the area of Figure 1.

C. The perimeter of figure 2 is the double the perimeter of figure 1 and the area of four times the area of figure 1. Because: This problem requires an understanding of how changes to dimension change area and volume. If the dimensions of a figure double, the ration of corresponding sides will be 1 to 2. The same ration will apply to the perimeter. In the figure shown, the perimeter of the smaller square is 28, and the perimeter of of the larger square is 56. The results of the ration of 28 to 56, which is equivalent to a ratio of 1 to 2. The ratio of the areas of the squares with a side ratio of 1 to 2 will be 1(squared) to 2(squared), or 1 to 4. The area of the smaller square is 49, and the area of the larger square is 196. This results in the ration of 49 to 196, which is equivalent to the ration 1 to 4. Thus the perimeter is doubled, and the area is quadrupled.

The following list shows the first 6 terms in a sequence . 1, 1, 2, 3, 5, 8,... Which of the following formulas can be used to find the terms of the sequence? A. A1=1 AN=AN-1 for n greater than equal

C. The question requires an understanding of how to make conjunctures, predictions or generalizations based on patterns. The only formula that yields a sequence whose terms are those shown is the one in option C in which the first two terms are defined as 1 and each subsequent term is the sum of the two terms immediately preceeding it.

Properties of Operations

Communicative example: 6 x 4= 4 x 6. Associative example: (75 + 81) + 34 = 156 + 34 the grouping of the numbers does not change their sum. Distributive example: 5 x 46 = 5 x 40 + 5 x 6

Converting between fractions, decimals and percents.

Convert to a decimal: move the decimal point to the left and drop the % symbol. Convert the fraction first to a decimal, then move the decimal point to the right and add the % symbol. Convert a fraction to a %: 1. Divide the numerator by the denominator. 2. Take the result and multiply by 100. 3. The result is the fraction as a %.

Mary has a rectangular garden in her backyard. The garden measures 5.75 feed wide by 7.5 feet long. What is the area of the garden? A. 26.5 square feet B. 35 3/8 C. 36 1/8 D. 43 1/8

D 43 1/8 The question requires an understanding of how to find the area and perimeter of polygons. If a rectangle has a length of L units and width of of 2 units, then its area is LxW square units. Since the garden has a length of 7.5 feet and a width of 5.75 feet, the area is 7.5 x 5.75 = 15/2 x 23/4= 345/8 square feet, that is 43 1/8 square feet.

At a flower shop, there are 5 different kinds of flowers: tulips, Lillie's, daises, carnations, and roses. There are also 3 different colors of vases to hold the flowers: blue, green, and pink. If one kind of flower and one color vase to hold them are to be selected at random, what is the probability that the selection will be Lillie's held in a pink vase? A. 2/8. B. 2/15. C. 1/8. D. 1/15.

D. 1/15 There are 15 possibilities (5 different kinds of flowers times 3 different colors of vases), so the probability of selecting Lillie's held in a pink vase is 1/15.

What is the prime factorization of 3,780? A. 2x5x6x7x9. B. 3x4x5x7x9. C. 2x3x6x7x15. D. 2x2x3x3x3x5x7

D. 2x2x3x3x3x5x7

0.7 is 1/1,000 of what number? A. 0.0007. B. 0.007. C. 70. D. 700

D. 700

Which of the following expressions is equivalent to -4(3-2x)? A. -2x-12. B. 2x-12. C. -8x-12. D. 8x-12.

D. 8x-12 Reason: This question requires the distributive property to generate equivalent linear algebraic expressions. Using the distributive property of multiplication over addition, -4(3-2x)= -4(3)- 4(-2x); that is, -12 + 8x. Using the communicative property of addition yields 8x-12

What value does the 8 represent in the number 5,836,303? A. Eight hundred B. Eight Thousand C. Eighty Thousand D. Eight hundred thousand

D. Eight hundred thousand

A unit square is partitioned into identical parts having equal areas. One of the parts is removed from the square, and a shape is formed by the parts that remain after the removal. For which of the following areas of the removed part will the shape that is formed have the greatest area? A. 1/4. B. 1/5. C. 1/6. D. 1/7.

D. If the unit square is partitioned into n parts having equal area, the area of each part is 1/n. Therefore the area of the shape that is formed when removing one of the identical parts is 1- 1/n. The smaller the area of the removed part, the greater the area of the shape that is left. Since 1/7 is the smallest of the four fractions listed, the shape that has the greatest area is the one that is left by removing a part with area 1/7.

4x(3x+2y). What does 2y represent in the expression shown? A. A binomial B. A factor C. A coefficient D. A monomial

D. Monomial Reason: a monomial is an algebraic expression that consists of one term that is a number, a variable, or a product of a number and a variable, where all exponents are whole numbers.

Which of the following is a statistical question? Select all that apply. A. What is the daily high temperature for an August day in Cheyenne, Wyoming. B. How many speeches did George Washington make during his life? C. How many minutes did Hannah spend talking on her phone on August 28, 2016? D. What is the average number of miles a week run by the members of the Hereford High School cross country team last month?

D. What is the average number of miles a week run by the members of the Hereford High School cross country team last month.

Prime vs Composite numbers

Prime numbers = have only 2 factors, number x 1 eg: 3= 3x1. Composite numbers has at least 3 factors and sometimes more eg: 12. 12 x 1, 2 x 6, 3 x 4.

(0x10 to 4th) + (4x10 to 3rd) + (0x10 to the 2nd) + (5x10 to 1st) + (2x10 to 0 power) What number is represented by these base -10 expression shown?

The correct answer is 4052. The question requires an understanding of how to write numbers using base-10 numerals, number names, and expanded form. Since 10 to 3rd = 1,000. 10 to 2nd = 100 and 10 to 0 power= 1, the expression shown is equivalent to (0) + (4x1,000) + (0) + (5x10) + (2x1) = 4,000 + 50 +2

Which of the following is an algebraic expression? A. 6x-4. B. 6y<4. C. 6z=4. D. 6+4

The question requires an understanding of how to differentiate between algebraic expressions and equations. An algebraic expression is made of constants, variables, and algebraic operations.

Volume of a Cylinder Formula

V= (pie) (radius squared) (height) Example: A cylinder with a radius of 4 and height of 8. V= 3.14 x 4(squared) x 8= 402.123

Finding the volume of a cube

V=a to the third power (a x a x a). The a is equal to the measurement of one of the sides.