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mathematics
mcgraw hills conquering sat math
McGraw Hills Conquering SAT Math 2nd Edition Robert Postman, Ryan Postman - Solutions
John buys a cake at a bakery and a hammer at a hardware store. If there are five hardware stores and three bakeries, in how many different combinations of stores can he purchase the cake and the hammer?A. 20B. 15C. 8D. 5E. 3
Thirty students are asked if they play soccer or basketball. Every student plays at least one of the two sports. Twenty students said they play soccer and 15 said they play basketball. How many students play both sports?
Seventy people are seated at a dinner party. Each table at the party can seat eight people. What is the minimum number of tables needed for the party?A. 12B. 11C. 10D. 9E. 8
Five people, all different ages, are arranged in a row so that the oldest person is in the middle and the two youngest people are on the ends. How many different arrangements of this type exist?A. 32B. 16C. 8D. 4E. 2
A teacher gives stickers to students as a reward for good work. The stickers are on a long strip and repeat in a regular order: Balloon, Happy Face, Clown Face, and Spaceship. What are the 63rd and 65th stickers handed out by the teacher? A. Balloon and Happy FaceB. Clown face and BalloonC.
Frank scored 26 points in a basketball game. All of his points came from either a two-point or threepoint basket. If Frank scored at least one three-point basket, what is the maximum number of two-point baskets that Frank could have scored?A. 11B. 10C. 9D. 8E. 7
A jar contains 10 blue, 8 green, and 6 red marbles. Every time a marble is removed from the jar, it is not replaced. What is the probability, to the nearest hundredth,that the second marble chosen is green if the first marble chosen is green?A. 0.28B. 0.29C. 0.30D. 0.31E. 0.32
Three coins are tossed at the same time. What is the probability that exactly two heads are face up? A. B. C. D. E. -|∞ 1400 5100
How many 5-digit numerals have 9 as the first digit, 3 or 6 as the third digit, and no digit repeated?
There are 10 orange sodas, 15 cream sodas, and 7 cherry sodas in an ice chest. How many sodas must be removed from the ice chest to guarantee that one of each type of soda has been chosen?A. 16B. 18C. 23D. 25E. 26
There are 15 students on the Prom Committee and 20 students on the Yearbook Committee. If 10 students are on both committees, how many students are ononly one committee?A. 5B. 10C. 15D. 20E. 25
Five people want to rent the last two copies of a movie. How many ways can these five people rent the two movies?A. 10B. 9C. 8D. 7E. 6
The table below displays people’s opinion, by age, about a school referendum.What percent of the people, rounded to the nearest whole number, are for the referendum? For Against Undecided Total 18-25 26-40 85 85 50 220 56 47 77 180 41-60 64 70 36 170 61 and over x 24 63 140 Total 258 226 226 710
The table below displays people’s opinion, by age, about a school referendum.What percent of the 18–25 age group, rounded to the nearest whole number, are undecided? For Against Undecided Total 18-25 26-40 85 85 50 220 56 47 77 180 41-60 64 70 36 170 61 and over x 24 63 140 Total 258 226 226 710
The table below displays people’s opinion, by age, about a school referendum.What percent of those against the referendum, rounded to the nearest whole number, are in the 41–60 age group? For Against Undecided Total 18-25 26-40 85 85 50 220 56 47 77 180 41-60 64 70 36 170 61
The scatterplot below shows a student’s grade on a test against the numbers of hours that student spend studying each night.Which of the labeled points above represents the highest grade on the test?A. AB. BC. CD. DE. E Grade on Test 100- 90- 80- 70- 60- 50- 40. 30- 20- 10- 0- 0 Grade on
The scatterplot below shows a student’s grade on a test against the numbers of hours that student spend studying each night.Based on the correlation of the data, which would most likely be the test grade of a student who studies 3 hours a day?A. 50B. 60C. 70D. 80E. 90 Grade on
The table below displays the expected ticket sales for a concert.Which ticket price produces the most revenue?A. $15B. $20C. $25D. $30E. $35 Price per Ticket $15 $20 $25 $30 $35 Expected Number of Tickets Sold 8,500 8,000 7,000 5,000 4,500
The table below displays the expected ticket sales for a concert.How much more money would be made for tickets priced $35 than for tickets price $30?A. $5,000B. $7,500C. $10,000D. $12,500E. $15,000 Price per Ticket $15 $20 $25 $30 $35 Expected Number of Tickets Sold 8,500 8,000 7,000 5,000 4,500
The appraised price of a house is shown in the line graph below.What is the percent decrease in the price of the house from 2002 to 2003 to the nearest hundredth of a percent? Price (Hundred Thousand) 400 350 300 250 200 150 100 Appraised House Price 310 325 300 310 350 380 +370 50- 0- 1997 1998
The appraised price of a house is shown in the line graph below.What is the average increase in the price of the house per year?A. $5,000B. $10,000C. $14,000D. $35,000E. $70,000 Price (Hundred Thousand) 400 350 300 250 200 150 100 Appraised House Price 310 325 300 310 350 380 +370 50- 0- 1997 1998
The bar graph below compares the average monthly temperatures for Charlotte, NC, and Los Angeles, CAIn how many months is Charlotte’s average temperature greater than Los Angeles’s average temperature?A. 3B. 4C. 5D. 6E. 7 Temperature (Degrees) 90 80 70 60 50 40 30 20 10 Average Monthly
The bar graph below compares the average monthly temperatures for Charlotte, NC, and Los Angeles, CAIn how many months are both cities’ average temperature above 60 degrees?A. 5B. 6C. 7D. 8E. 9 Temperature (Degrees) 90 80 70 60 50 40 30 20 10 Average Monthly Temperature Month Charlotte, NC Los
Of the total number of subscribers in City N, what percent more subscribers does Company A have than Company C? Total Number of Cell Phone Subscribers in City N Company A Company B Company C Company D Company E = 10,000 subscribers w... COXXX .... www .... BO C O 1000 CO 10000 CO 9.00 CO DOD DOD CO
The circle graphs below show the production numbers for certain Ford Mustangs in 1965 and 1971.Approximately how many more two-door hardtop coupes were made in 1971 than in 1965?A. 36,000B. 38,303C. 44,960D. 74,303E. 83,263 1965 Mustang Production Numbers 174,103 38% 46% 9% 13% 12% 40% 17% 63A
What two companies account for 60% of all cell phone subscribers in this city?A. Company B and Company CB. Company B and Company DC. Company A and Company BD. Company A and Company EE. Company D and Company E Total Number of Cell Phone Subscribers in City N Company A Company B Company C Company
Below is a scatter plot showing the number of acres of land a house is on compared to the price of the house. What percentage of the houses on more than 4 acres cost less than $400,000? Price ($100,000) In 5 4 ترا 2 1 1 ● + + + 2 3 4 Land Area (acres) 5 6
A. 2B. 3C. 4D. 5E. 6 = 2,y = x², (y2 . 31 好 3y)
A. −4B. 4C. −4 and 4D. 1 and 4E. 1 X = x2 – 5x + 6, a = 2, a =
A. m # nB. m − nC. m × nD. m + nE. m m#n m#n= m² n²,- - m - n
A. x + yB. 2x − 3yC. 2x + 3yD. x + yE. x + y 4x² = 9(y² + 2), 18 2x - 3y
A. −6B. −10C. −15D. −18E. −21 a q b C S = ax² + bx+c = (2x + 7)(3x - 5) q+r+s=
Below is a population graph for a certain species of fox. At what point is the population growing the fastest?A. Point AB. Point BC. Point CD. Point DE. Point E Population A B Time E
What is the range of f (x) = (x + 2)2 − 3?A. All real numbers greater than or equal to 3B. All real numbers greater than or equal to 2C. All real numbers greater than or equal to −3D. All real numbers greater than or equal to −2E. All real numbers greater than or equal to −1
The graph of f(x) is seen below. Which of the following choices is the graph of f(x − 2) + 4? Graph of f(x) N
The initial population of deer is 50. If the deer increase by 25 each year write an equation that will show the number of deer, y, after x years.
f(x) = 2x3 − 3x2 + 5, f (4) =A. 81B. 82C. 83D. 84E. 85
−5t − 7 ≤ 8. What are all possible values of t?A. t ≤ 2B. t ≤ −2C. t ≥ −3D. t ≤ −3E. t ≥ 3
α =⎟⎟ x⎟ 3 −⎟ x − y⎟ 2 − y + x⎟ . If x = −2 and y = 5, a =A. 47B. 48C. 49D. 50E. 51
⎟ x − y⎟ = d and x > y, which of the following cannot be the value of y − x?I. dII. −dIII. ⎟ y − x⎟A. IB. IIC. I and IID. I and IIIE. II and III
⎟ 3x − 15⎟ = 18. What is the product of all possible values of x?A. −11B. −10C. −9D. −8
x = ab2/3 ,27 x3A. ab2B. a3b3C. a3b6D. a2b6E. a6b2
(x − 2)(x + 3)(x − 4) = 24. What is the sum of the possible values of x?A. 9B. 7C. 5D. 3E. 1
(2x2 + 3x − 5)(x + 2) = ax3 + bx2 + cx + d, ac − bd =A. 70B. 71C. 72D. 73E. 74
6b2 − 24b + 24 =A. 6(b − 4)B. 6(b − 4)2C. (b − 2)2D. 6(b − 2)2E. 6(b − 2)
4x = 52, x2 − 52 =A. 81B. 9C. 144D. 12E. 169
3(x − 10) = 5(x + 20), x =A. −65B. −50C. −35D. −20E. −15
x2 − 25 = 12, x + 5 = 4, x − 5 =A. 2B. 3C. 4D. 6E. 12
Which of the following statements is true?I. 4x2 − 9y2 = (2x − 3y)2.II. (x − 4)2 = x2 − 16.III. x2 + 2xy + y2 = (x + y)2.A. IB. IIC. IIID. I and IIE. I and III
5a2 − 4a − 3 − 3(a2 + a + 4) = 0. What is the sum of the possible value of a?A. 3sB. 3.5C. 4D. 4.5E. 5
(3x − 4)(2x − 5) − (x + 3)(4x − 7) =A. 2x2 − 28x + 1B. 2x2 − 28x + 41C. 2x2 − 14x + 41D. x2 − 14x + 1E. 2x2 − 14x + 1
x2 − 3x = 0, x =A. 0 and 3B. 3C. 6D. 0 and 6E. 3 and 6
If a + b = 5, then a2 + 2ab + b2 =A. 5B. 10C. 15D. 20E. 25
If y = 4 and x = 3, then y3 − 3x2 + 3y − 2xy + x =A. 24B. 25C. 26D. 27E. 28
9√x - 7 √x - 36 = -16,x =A. 5B. 10C. 20D. 50E. 100
√x + c√y = d√y, x/y =A. d − cB. √d - cC. c - dD. (d - c)2E. √c - d
3 √x − 7 = 5, x
274/x = 81, x = A. 2B. 3C. 4D. 5E. 6
Mike has a goal to bench press 220 pounds. When he started working out, Mike was able to lift 150 pounds. He has currently increased that amount by 20%. What percent of his current lifting amount must Mike increase to reach his goal of 220 pounds? A. 22-% 2 B. 22% C. 22.22% D. 22=% 2_% E. 22-
Find the mean, median, and mode for each set of dataA. {8,2,6,8,4,2,3,4,8}B. {97,65,58,67,87,42,34,57}C. {15,13,19,17,25,13,23,18,19,17}
n3 ≥ n2 for which of the following?I. n = 1II. n = 0III. n = −1A. IB. IIC. IIID. I and IIE. II and III
Which of the following is equal to 58x?I. (54x)4II. (54x)2III. (54x)(54x)A. IB. IIC. IIID. I and IIE. II and III
812 = 2x, x =A. 4B. 12C. 24D. 36E. 42
94x/273x =A. 9xB. 1/3xC. 1/9xD. 3xE. 1/4x
What is the sum of the mean, median, and mode(s) of the set{2,4,8,7,4,6,8,9}?A. 12.5B. 16.5C. 20.5D. 24.5E. 26.5
The average (arithmetic mean) of three numbers is 90. The sum of two of the numbers is 150. What is the value of the third number?A. 90B. 100C. 110D. 120E. 130
On three of the first four geometry tests Jim earned the following scores: 84, 92, and 88. If Jim’s average for all four tests is 87.5, what score did Jim earn on his fourth test?
4√18 x 11√12 = A. 12√6 B. 34√6 C. 264√6 D. 264√3 E. 264√2
y−5 = 1,024, y =A. 5B. 4C. 3D. 1/5E. 1/4
√x = 4a2bc3, x = A. 16a4b2c9B. 16a4b2c6C. 16a2bc3D. 8a4b2c6E. 2ab1/2 c 2/3
5√8 + 7√32 = A. 18√2 B. 38√√2 C. 23√4 D. 33√3 E. 38√3
What is the average (arithmetic mean) of a set of 20 numbers if the sum is 340?
4−a = 64, a =A. 4B. −4C. 3D. −3E. 2
There are 24 students in period 1 gym class and 20 students in a Period 2 gym class. The students ran an obstacle course during gym class. The average time in period 1 was 165 seconds, and the average time in Period 2 was 180 seconds. What is the average time for the two combined gym classes?
Using the data set, {30,70,40,50,90,40,60}, which of the following statements is correct?A. Median <mean <modeB. Mode <mean <medianC. Mode <median <meanD. Mean <mode <medianE. Median <mean <mode
Mark, Danielle, Peter, and Kendra have an average height of 71 inches. What is the sum of all of their heights?
The average (arithmetic mean) of four numbers is 50. Two of the numbers are 30 and 60. What is the average of the other two numbers?A. 70B. 65C. 60D. 55E. 50
How many points did Ed score during the fourth game?A. 12B. 11C. 10D. 9E. 8 Jay's points 20 16 25 15 14 Ed's points 15 21 17
Say that Ed scored 16 points in the fourth game. What should be added to Jay’s median score to equal the median of Ed’s scores? Jay's points 20 16 25 15 14 Ed's points 15 21 17
Blaire, Chen, Erin, Liz, and Mauro all participate in a 1-mile race. The average (arithmetic mean) for the times of all girls is 6.5 minutes. If the average time for Blaire, Chen, and Erin is 6.7 minutes, what is the average time for Liz and Mauro?A. 6.1 minutesB. 6.2 minutesC. 6.3 minutesD. 6.4
What is the median of the modes in the dataset {−5, 4, 3, 7, 2, 1, 3, 4, 5, −1, 7, 8, −4, 2, 6}?A. 2B. 2.5C. 3D. 3.5E. 4
The average of x and y is 7, and z = 3x + 2. What is the average of y and z?A. 2x + 8B. 2x − 16C. 2x + 16D. x − 8E. x + 8
The average of a set of n numbers is x. If each number is increased by y, then what is the average of the new set of numbers?A. xB. yC. n(x + y)D. x + yE. x + y/n
Mr. Jones administered a test to the students in each of his three Algebra II classes. The average (arithmetic mean) of all the students in his classes was 82.8. What is the average for his Period 8 class? Number of students Class average A. 80 B. 81 C. 82 D. 83 E. 84 Period 1 16 85 Period
If the average of a, b, c, d, and e is 14, what is the value of e?A. 14B. 16C. 18D. 20E. 22 a+b+c+d 4 12.
Frank took 4 history tests. Frank earned an 85, 92, and 89 on the first three tests. If Frank’s average (arithmetic mean) for all 4 tests is 91, what did he earn on his last test?A. 100B. 99C. 98D. 97E. 96
a, b, and c are all positive integers such that a + b + c = 150, and none of these values are equal to each other. What is the smallest possible value for the median of a, b, and c?A. 5B. 4C. 3D. 2E. 1
s and t are positive integers whose average (arithmetic mean) is 9. If s < t, what is the median of all possible values of s?A. 6.5B. 6C. 5.5D. 5E. 4.5
The modes of a set of 9 numbers are x, y, and z, and the average (arithmetic mean) of the 9 numbers is 20. Three of the 9 numbers are 2x + 5, 2y, and 2z − 3. What is the value of 4(x + y + z)?A. 178B. 179C. 180D. 181E. 182
⎟ 3x − 4⎟ > 20. Which of the following choices is not a possible value for x? A. -5.3 B. 8.2 C. -5.4 D. 8.1 E. -5.5
x − 5y = 2 and 3x + y = 6, (xy)2 =A. 0B. 1C. 4D. 9E. 16
Points R = (6,4), Q = (4,3), and P = (−2,b) are colinear. What is the value of b?A. 4B. 3C. 2D. 1E. 0
Points A, B, and C are co-linear. ĀB̄ ≅ B̄C̄ and A = (−2,3), B = (2,−4), then C = A. B. (0.−1) C. D. (0.--) E. (-) (글) (0.--)
On the graph below, L̄N̄ is 4 times the length of L̄M̄. How long is L̄M̄? N = (2,4) A M=(-4,-2) L
If M= (5,2.5), is the midpoint of X̄Ȳ with X = (−4,1) and Y = (a,4), what is the value of a?A. 6B. 8C. 10D. 12E. 14
Let M = (x, y) be the midpoint of ĀB̄ with A = (3,7) and B = (−1,3). What is the product of x and y?
PQ || XY P = (−3,6), Q = (4,3), and X = (−2,−5). Which of the following are the possible coordinates of Y?A. (11,−12)B. (11,12)C. (−12,−11)D. (12,−11)E. (−12,11)
What is the perimeter of the triangle with vertices L = (1,5), M = (−3,−3), and N = (3,1)? A. 6√10 +4√13 B. 6√5 +2√13 C. 4√5 +2√18 D. 8 √18 E. 24√2
What is the length of ĀD̄ in the graph below? (-2,1)= A (-2,-1) = C B = (2,1) D = (2,-1)
A is the midpoint of P̄Q̄ and B is the midpoint of X̄Ȳ P = (2,4) Q = (6,10) X = (−8,2), and Y = (4,−6). What is the slope of AB? E. D. C. U B. دان مان ال - A. نا أننا
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