Praxis 1

Sarah rolls a fair, six-sided number cube, numbered 1 -6, five times and rolls a 3,4,1,4 in that order. What is the probability that she will roll a 4 on her sixth roll

1/6

The figure above shows a right circular cone with base radius 6 and height 20. The shaded portion of the figure is a right circular cone with height 10. The volume of the smaller cone is what fraction of the volume of the larger cone? ( the volume of the right circular cone with base radius of r and height h is 1/3Pir^2h.) Fraction. NOT COMPLETED

1/8 On the larger cone, the radius r1 is 6 when h1 is 20. The smaller shaded cone is similar to the larger cone, so rules for similarity can be used to determine the radius of the smaller cone. Since the height of the smaller cone h2 given is 10, which is half of the larger cone's height of 20, the radius of the smaller cone r2 should be half the radius of the larger cone, which is half of 6, or 3. The questions asks what fraction of the volume of the smaller cone is compared to the larger cone, which leads to the following ratio, set up using the volume formula for each cone that was given in the problem.

The graph of the line l is shown in the xy-plane above. The point of line l that has x coordinate 75 is not shown. What is the y coordinate of that point? A) 100 B) 95 C) 75 D) 70 E) 65

100 The change in the y value was 20 when the x value changed from 0 to 15, and from 15 to 30. For every change in 15 for x value of a coordinate, the y value of the coordinate will change by 20. When x changes from 0 to 75, it would have five increases of 15, so the y value also must have 5 increases of 20, or a change of 100.

If 5(2x + 1) = 3(x + 4) - 5 what is the value of x? Give your answer in fraction.

2/7 Solve the equation first using the distributive property 5(2x +1)=3(x+4)-5 becomes 10x + 5 = 3x +12 -5. Combining similar terms yields the equation 10x + 5 = 3x + 7, subtracting 5 from both sides yields the equivalent equation 7x=2. The answer is found by diving each side of the equation by 7.

If 1/7x - 2 = 1 then x = A) -7 B) 3 C) 9 D) 15 E) 21

21 Solve the equation by first adding 2 to both sides, resulting in an equivalent equation 1/7x = 3. Multiplying both sides of this equation by 7 yields 7(1/7x) = 7(3) or x = 21

The ratio of the number of adults to the number of children on a certain bus tour was 4 to 22. If the total number of passengers on the bus tour was 91, how many adults were on the tour? A) 14 B) 28 C) 65 D) 69 E) 77

A The ratio of 4 to 22 can also be expressed as 2 to 11, or 2x to 11x, where 2x represents the number of adults and 11x represents the number of children. Since the total number of adults and children is 2x + 11x = 91, solving the equation yields x=7, and the number of adults is 2(7) = 14

The five numbers shown above are listed in order from least to greatest. Which of the following could be the value of k? 1/4, 9/8, 23/12, k, PI A) 2 B) 5/16 C) 23/8 D) square root of 7 E) square root of 17

A,C,D The problem can be answered using estimation. The value of k lies between 23/12 (a number slightly less than 2) and pi (a number slightly more than 3). Since 5/16 < 1 and square root of 17 > 4 they can be estimated easily. the other three choices are greater than or equal to 2 and less than 3, which are in the necessary interval

4r + 10b The expression above represents the total amount, in dollars, earned by selling r rolls of gift wrap and b boxes of greeting cards. A freshmen class earned a total of $958 by selling both gift wrap and greeting cards. The amount earned by selling the greeting cards is what fraction of the total amount earned? A) b/958 B) 10b/ 958 C) r/ 958 D) 4r/ 958 E) 4r + 10b/ 958

B A freshmen class earned a total of $958 selling gift wrap and greeting cards. Using the expression given, r rolls plus b boxes of greeting cards equals total dollars earned : 4r + 10b = 958. Amount earned by selling the greeting card is 10b/958

If the speed of light is 1,080,000,000 kilometers per hour, how far does light travel in 100 hours? A) 1.08 X 10^9 km B) 1.08 X 10^11 km C) 1.08 X 10^13 km D) 10.8 X 10^14 km E) 108 X 10^15 km

B The number 1,080,000,000 can be written in scientific notation as 1.08 X 10^9. Multiplying any number by 100 would have have same effect as adding two zeros to the number, thus increasing the exponent by 2, so light travels 1.08 X 10^11 km in 100 hours.

Which of the following expressions is equivalent to the expression 21-6x for all values of x? A) 5-2(8-3x) B) 6 + 3(5-2x) C) 25 - (4-6x) D) 3(4-2x) - 9 E) 7(3-2x) -8x

B Using the distributive property 6 + 3 (5-2x) = 6 + 15 - 6x = 21 - 6x None of the other selections is equivalent to this

A right circular cylinder with base B is shown. If a place that is neither parallel nor perpendicular to bas B passes through the cylinder, which of the following could be the shape of the intersection of the plane and the cylinder? A) an ellipse with circumference less than the circumference of B B) an ellipse with circumference greater than the circumference of B C) an ellipse with circumference equal to the circumference of B D) a circle with circumference less than the circumference of B E)a circle with circumference greater than the circumference of B

B- A plane that is parallel to the base intersects the cylinder in a circle, but because the intersecting plane is not parallel, the intersection is an ellipse. One of the axes of the ellipse is equal to the diameter of the base, but the other axis (in the direction of the tilt) is larger than the diameter. That means that the circumference of the ellipse is greater than the circumference of the base

The triangle has sides of 4, 7, and x. Which of the following could be the value of x? Indicate all such values. A) 2.9 B) 4.5 C) 6.25 D) 7 E) 12

B/C/D The triangle inequality states that the length of the longest side of a triangle must be less than the sum of the length of the other two sides. Examination of each case is required. If x= 2.9 then the sum of 2.9 + 4 = 6.9, which is less than the longer side of 7, so A cannot be a value of x. If x= 4.5 then the sum of 4.5 + 4 = 8, which is longer than the longest side of 7, so b could be a value of x. If 6.25, then the sum of 6.25 + 4 = 10.25, which is longer, so C could be the value of x. If x=7 then it would be an isosceles triangle with lengths of 7 for two of the sides, and a length of 4 for the other side, so D could be a value of x. If x=12, then the longest side of the triangle would now be 12 and the other two sides would have to sum to be larger than 12. Since 4 + 7 = 11, which is less than 12, E cannot be the value of x.

Which of the following sequence of steps, when completed, will solve the equation -6 + 3y =1 for y? A) Subtract 1 from both sides of the equation, then divide both sides of the new equation by -6 B) Subtract 1 from both sides of the equation, then divide both sides by 6 C) Add 6 to both sides of the equation, then divide both sides by 3 D) Add 6 to both sides, then subtract 3 from both sides E) Divide both sides of the equation by 3, then subtract 6 from both sides

C

Christina, Greg, Lisa, and Job are coin collectors, and together they have a total of 2,250 coins, They decided to meet and trade coins, The pie chart above shows the distribution of the 2250 coins before trading. At the end of trading, Christina has 32 %, Lisa has 22 %, and Jon has 26 % of the total number of coins owned by the four collectors. How many more coins does Greg have at the end of trading than he had before the trading began? A) 115 B) 120 C) 135 D) 140 E) 145

C Before trading coins, Greg had 14% of the 2250 coins, or he had 0.14(2,250)=315 coins. After trading, the combined percentages of coins owned by Christina, Lisa, and Jon are 32+22+26%= 80%. So Greg must have 100%-80% = 20%, or Greg now has 20% of all of the 2250 coins. After trading Greg has 0.20(2250) =450 coins. To figure out how many more coins he had after trading than before subtract 450-315= 135

Which of the following best approximates the area of the circle shown in the graph above? A) 8 B) 13 C) 18 D) 23 E) 28

C From the xy-plane in which the circle is graphed, it can be concluded that the radius is approximately 2.4. The formula for the area of a circle is A=r^2PI, were A is the area, and r is the radius, and Pi is approximately 3.14. If 2.4 is substituted into the formula for the radius and 3.14 for Pi, A= (2.4)^2 (3.14) = 18.0864

The number line above shows 7 points, each of them labeled with a letter of the alphabet. The product of the coordinate of point P and the coordinate of point Q is closest to the coordinate of which of the following points? A) a B) b C) c D) d E) e

C point p is -1.75 on the number line and point q is -0.50 on the number line. The product of these is (-1.75)(-0.50) = 0.875. This would be slightly to the right of point c which is at .75 thus making it the closest point to the result

James walked 2 1/2 miles in 2/3 of an hour. What was his average speed, in miles per hour? A) 3 1/4 B) 3 1/2 C) 3 3/4 D) 3 7/8 E) 4 1/4

C 3 3/4 2 1/2 5/2 5/2 (3/2) 15/4 15 ----- = ---- = ------- = ------= ---= 3 3/4 2/3 2/3 2/3(3/2) 1 . 4

P is 6 times Q, and Q is less than 9 times R. Which of the following statements describes the relationship between p and r? A) P is 2 less than 15 times R B) P is 2 less than 54 times R C) P is 12 less than 15 times R D) P is 12 less than 54 times R E) P is 18 less than 15 times R

D By translating each word expression, P is 6 times Q, or P =6Q and Q is 2 less than 9 times R, which means Q = 9R -2. To describe the relationship between P and R, substitute the value of Q into P's equation. P=6Q P=6(9R-2) P=54R-12 Therefore, P is 12 less than 54 times R

Jeramaine promised to donate a total of z dollar to a charity by donating x dollars immediately and then donating a fixed constant amount of dollars each month for m months. Which of the following expressions represents the fixed constant amount of dollars Jeramine promised to donate each month? A) z-xm B) z-m ------ x C) z -- - m x D) z-x ----- m E) z --- - x m

D The total amount that Jeramine promised to donate is z dollars. He will donate x dollars immediately and a fixed amount monthly over m months. The amount he will have left to pay after donating x dollars can be expressed as z-x. This amount is to be spread out of m months, so each month Jer would own z-x/ m dollars to the charity

The arch above is constructed of 5 nearly congruent stones, each of which is in the shape of a right prism with trapezoid bases. Based on the approximate measurements provided, which of the following best approximates the volume of the entire arch? ( The area of the trapezoid with bases b1 and b2 and height h is 1/2(b1+b2)h A) 900 cubic feet B) 1050 cubic feet C) 1140 cubic feet D) 2160 cubic feet E) 4320 cubic feet

D The volume of a right trapezoid prism is equal to the height of the prism times the base area of the trapezoid and is give by the formula v= 1/2 (b1 + b2) X h v= 1/2 (14 + 10) X 12 v= 432 One trapezoidial stone is 432 cubic feet. Since there are 5 nearly congruent stones, 432 X 5 = 2160 cubic feet

A large wheel has a diameter of 30 inches, and a small wheel has a diameter of 20 inches. How many revolutions does the small wheel need to make to travel the same distance that the large wheel travels in 240 revolutions. A) 160 B) 240 C) 320 D) 360 E) 420

D For each revolution of either wheel, the distance that they wheel would travel is equal to the wheel's cirumference, which can be found using either C= 2PIR or c =PID, where C is the circumference, r is the radius, and d is the diameter. Since we are given the diameter, the latter will be used. The larger the wheel travels a total distance of 240 times the circumference of the larger wheel is 240 (30PI) = 7200PI. The smaller wheel has a circumference of 20PI. To figure out how many revolutions the smaller wheel would need to go so that it would travel the same distance of 7200Pi that that larger wheel travelled, 7200Pi/ 20Pi = 360. Or the smaller wheel would need to make 360 revolutions to travel the same distance that the larger wheel could travel in 240 revolutions

A carpenter wants to build a diagnoal brace for a rectangle that is 5 feet wide and 7 feet high, as shown in the figure. Approximately what is the length, in feet, of the diagonal brace? A) 5.5 b) 6.5 C) 7.5 D) 8.5 E) 9.5

D Pythagorean theory A^2 + B^2 = c^2 7^2 + 5^2 = c^2 49 + 25 = c^2 74 = c^2 square root of 74 = c c= 8.6 feet

A total of 54 business letters at a certain company were inspected for errors. The graph above shows the number of letters with either 0, 1, 2, 3, or 4 more errors. How many of the 54 letters contained at most 2 errors? A) 6 B) 12 C) 24 D) 42 E) 48

E According to the graph, the three columns with 0,1, and 2 errors are the only letters that need to be considered of the 54 buisness letters. There are 27 letters with 0 errors, 15 letters with 1 error, and 6 with two errors. 27+ 15 + 6= 48

The median and the range of 15 measurements are 18 and 5, respectively. If 3 is subtracted from each of the 15 measurements, which of the following statements regarding the median and range of the modified measurements must be true? A) The median and range will both decrease B) The median and range both stay the same C) The median will stay the same, but the range will decrease D) the median will stay the same, but the range will increase E) the median will decrease, but the range will stay the same

E The given median is 18 and the range is 5 for a set of measurements. If each number were to be reduced by 3, and since the median is a member of the set, it too would be reduced by 3. So the new median would be would be 15. The range is the largest number in the set minus the smallest number in the set, the range should still be 5 for the new set of numbers. The difference would be the same, hence the range is still 5.

Which of the following statements is true about right triangle ABC above? A) The measure of A is 45 B) the sum of the measures of angel a and angle b is 70 degrees C) the area of the triangle is 60 D) the length of side AB is 17 E) the perimeter of the triangle is 30

E The triangle shown is a right triangle with sides of length 5 and 12. This is recognized as a 5 - 12 - 13 right triangle. Of the Pythagorean theory could be used to find the length of the missing side. The Pythagorean theory is c^2 = a^2 + b^2, where c is the length of the hypotenuse and sides a and b are the lengths of the other two sides. c^2= (5)^2 + (12)^2 = 25 + 144 = 169. Then square root of c^2 and square root of 169 is c = 13 . The perimeter would be 12 + 5 + 13, or 30. None of the other options are true.

Which of the following is equivalent to x/2 + y/3? A) x+y/5 B) x+y/6 C) 3x + 2y D) 3x + 2y/5 E) 3x +2y/6

E To add fractions they must have a common denominator. The least common denominator for 2 and 3 is 6. Each fraction can be written in an equivalent form with the common denominator of 6 thus, x(3)/2(3) = 3x/6 and y(2)/3(2) = 2y/6. Adding the two equivalent forms of the fractions gives 3x+2y/6

If x + z = 15 and w + y = 10, what is the value of (3w + 3y) (2x+2z)? A) 150 B) 300 C) 450 D) 600 E) 900

E In the expressions (3w + 3y)(2x + 2z), a factor of 3 can be factored from the first parenthetical and a factor of 2 can be factored from the second parenthetical. 3(w + y) X 2(x + z) The values of x + z and w + y can be substituted so that : 3(w+y) X 2(x+z) = 3(10) X 2(15) = 30 X 30 = 900

4 miles X 5280 feet 12 inches ----------- X ---------- 1 mile 1 foot Which of the following conversions is he performing? A) Miles to feet B) Miles to inches C) Feet to miles D) inches to miles E) inches to feet

b

On a map that is drawn to scale, 6 inches represents a distance of d miles. Which of the following represents the distance, in inches, of d + 1 miles on the map? A) d(d+1)/ 6 B) 6(d+1)/ 6 C) d+1/6d D) 6d/ d+1 E) 6/ d(d+1)

b The given ratio of 6 inches represents d miles can be written as 6/d . Another ratio must be written for the distance d +1, but since the distance for d+1 is not known, it can be called x, since that is what is being solved for in the problem. This leads to the equation 6/d = x/ d+1. Cross multiply can be used to solve and gives 6(d +1) = dx. Diving both sides by d to isolate x, gives x= 6(d+1)/d

Which of the following questions are statistical questions indicate all answers. A) how long is mikes foot? B) when do university students eat lunch ? C) what is the weight of johns math textbook D) how many coffee drinks do customers at a coffee shop order

b/d A statistical question is a question that one would expect to get a variety of answers for and not just a single answer

Of the following, which is most likely to be the height of a high school athlete? A) 3 yards B) 10 feet C) 124 inches D) 200 centimeters E) 400 millimeters

d 200 centimeters is approximately 6.5 feet, which would be a reasonable height for a high school athlete. A-C are 9 feet or greater and 400 millimeters is 2 small

A principal of a certain high school wants to ask a sample of students how they feel about a new school policy that will drop football as a varsity sport. Which of the following methods of selecting will yield the most valid information about the feelings of all the students at the school? A) Interviewing twelfth grade students on campus at random as they change classes B)Selecting a random sample of current football players C) Choosing two students at random from each science class on a given day D) Sending a questionnaire to all students currently enrolled and using the returned questionnaires as a sample E) Selecting a random sample from a list of all students currently enrolled at the school

e- A list of students currently enrolled gives a population where the group of students fit a particular description or set of conditions. Since the principal wants to ask a sample of students, a random sample where each member of this population has an equal chance of being included will give the principal an idea of what the entire population might look like.