Questions and Answers of McGraw Hills Conquering SAT Math

A complete network of size n is n points connected by line segments, as shown below. What is the minimum number of segments that must be removed from a complete network of size 5 so that one point
Jim’s and Al’s ages total 30. Doubling Jim’s age and adding it to Ed’s age equals 46. Subtracting Al’s age from Ed’s age equals 3. How old is Jim?A. 13B. 20C. 33D. 46E. 59
The sum of two numbers is 10, and the difference of the two numbers is 4. Which is the smaller of the two numbers?A. 3B. 4C. 6D. 7E. 8
In the graph of h(x) below, h(a) = 1, which of the following is not a possible value of a?A. −7B. −2C. 3D. 4E. 7 -76-54/3-2 -1 1 W - نیا 2 3 -4 6 7 8
A circle has a radius 8. A cone is formed by cutting out a 60° wedge and placing together the two ends of the remaining part of the circle (diagram below). What is the surface area of the cone
Below are the strikeout totals for two pitchers, Tom and Frank, during three games. How many strikeouts must Frank have on his next game so that Frank’s strikeout average for 4 games is equal to
The distance between adjacent marks on the number line is one unit. Use the number line below to determine which of the following points is not equal to |x − y|. a y b x A. |a - bl B. e-d C. c D.
Shawn can swim two laps every 100 seconds. Brian can swim four laps every 4 minutes. If both Shawn and Brian start swimming at the same time, Shawn will swim how many more laps than Brian in 5
The radius of the outer circle is twice the radius of the inner circle. What is the probability that a point chosen at random inside the outer circle will be inside the inner shaded region? ●
The total price of two items at a department store is $140. If the price of one item is increased by 20%, and the price of the other item is decreased by 25%, the average price of the two items is
When a number is increased by 8, the original value is 75% of the new value. What is the original value of the number?A. 2B. 3C. 6D. 18E. 24
John traveled 600 miles in 9 hours. Which of the following is John’s average speed? 1 A. 33 mph 3 B. 45 mph 2 C. 66 mph 66²3 D. 75 mph E. 90 mph
There are 4 blue, 6 red, and 8 green marbles in a jar. What is the least number of marbles that can be removed, without replacing, guarantee that a chosen marble is red?A. 3B. 12C. 13D. 14E. 15
What is the value of x?A. 36B. 72C. 90D. 120E. 240 P мы\ Х 3x a
In the expression an, n is an even power. Which of the following expressions does not have even power?A. an+1B. a2nC. an+2D. a3nE. an+4
What is the area of the figure below?A. 10B. 20C. 30D. 40E. 50 V65 in 5
In the parallelogram below, m∠ABC = A B (10x)⁰ (9x + 12)° D C
The measure of the angles is a quadrilateral are in a ratio of 2:4:5:7. What is the measure of each of the angles?
If the ratio of the area of a sector to the area of the circle is 3:5, what is the ratio of the length of the arc in the sector to the circumference of the circle? A. B. C. D. E. 3 5 - 2 013-14 25 3
The average score for 10 students on a math test is 85. If the average of 8 of the students is 88, what is the average of the other two students?
The table below shows the number of students in a high school who play varsity sports. Which of the following circle graphs displays the information shown in the table?
A bicycle company makes five styles of bikes in seven different colors. How different bicycles can the company make when considering both style and color?A. 35B. 12C. 7D. 5E. 2
A certain hat style comes in five different colors and three different sizes. How many different hats of this style are there?A. 2B. 3C. 5D. 8E. 15
In the rectangular prism below EF = 8 and FG = 6. What is the value of EG?A. 10B. 12C. 14D. 16E. 18 A E B H 1 1 1 1 D F C G
What is the next term in the sequence: 4,9,6,11,8, 13, . . . ?A. 18B. 16C. 10D. 9E. 8
The square of the sum of 2x and 3y is equal to the sum of the square of y and the square root of x. Which of the following represents this statement?A. 4x2 + 9y2 = y2 + x2.B. 4x2 + 9y2 = (y + x)2.C.
In a hardware store the ratio of shovels to rakes is 3:5. If there are 10 more rakes than shovels, how many rakes are there in the hardware store?A. 10B. 15C. 20D. 25E. 30
Which of the following statements is NOT true for the function f (x) = 2(x − 3)2?A. The domain is all real numbers.B. The range is all real numbers greater than or equal to zero.C. The graph of the
In the figure below l ∥ m. What is the value of x + y?A. 40B. 70C. 90D. 110E. 180 7 m ܘܬܐ ܂ 110°
In the rectangle ABCD below, M is the midpoint of C̄D̄. If the length of rectangle ABDC is 3 times the width, and the area of triangle AMB is 18, what is the length of C̄M̅? A D M B C
The amount of pancake mix required to make pancakes is proportional to the number of pancakes that are being made. The table below shows the required amount of pancake mix and water to make 6
x : 4 = 25 : x and x ≤ 0. Which of the following is equal to x?A. −10B. −5C. −2D. 5E. 10
In the figure below, points B and C are on circle O whose area is 81π. B̅Ā is tangent to circle O at point B and BA = 12. What is the length of C̄Ā.A. 6B. 9C. 15D. 16E. 25 в с A
In the following Ā ≈ B̄. Which of the following statements must be true? A AB = — - AC. 2 I. AB B II. B is the midpoint of AC. 1 III. - AB = BC. A. I only B. II only C. III only D. II and
In the xy-coordinate plane, line k passes through the point (2,4) and is perpendicular to the graph of the line whose equation is y = 2/3 x - 6. Whichof the following is the equation for line k? 3 A.
A company has two manufacturing plants, Plant A and Plant B. Three times Plant A’s production is equal to one half of the total produced by the company. If T represents the total produced by the
Two airplanes at 25,000 feet above the ground are flying toward the same airport. Airplane A is flying due south toward the airport at 200 miles per hour, and Airplane B is flying due west toward the
The function graphed below is a cubic function. f (a) = −f(2). Which of the following could be the value of a?A. −2B. - 1/2C. 0D. 1/2E. 2 -6 4 y 5 0 -5 2 X
There are a total of s seats in a movie theater. During a certain week there were a total of v viewings at the theater with an average of t unsold tickets for each viewing. Which of the following
If (x) = 2x2 + x + k is the equation of a quadratic function with a graph that passes through the x-axis when x = 3. What is the value of k?A. 21B. 18C. −21D. −18E. −3
In the figure below, a||b. What is the value of z?A. 120B. 60C. 40D. 30E. 20 a be zº 120°
Three couples host a dinner party. Each couple invites 4 guests, none of whom are the same. The tables for the party seat 5 people. If everyone attends the party, what is the minimum number of tables
Five groups of men, 10 men in each group, have the following average ages: 36,42,32,34, and 40. What is the sum of the ages of all 50 men?A. 184B. 368C. 552D. 1,840E. 3,680
For which points on the number line is the statement x3 > x2 true?I. x II. −1 III. x > 1A. IB. IIC. IIID. I and IIIE. I, II, and III -1 0 1
|2x − 3 | ≤ 7 and | x − 2 | ≤ 4. If x is an integer, what value of x is a solution for one inequality but not the other?
The sum of 10 consecutive integers is 105. What is the median of these 10 integers?
Let a represent the arithmetic mean of k numbers whose sum is S. Which of the following is equal to 1? A. B. C. a.k S E. S.a k S.k a D. S.a.k k a. S
4, 12, 36, 108, and 324 are the first five terms of a sequence. Each term in the sequence is formed by multiplying the preceding term by 3. 4(3)10 is what term in this sequence?A. 12B. 11C. 10D. 9E. 8
The circle graph below shows the percent of an exercise routine that is spent on each body part. If approximately 37 minutes is spent on shoulders and back, which of the following choices best
The ratio of Dan’s height to Phil’s height is proportional to the ratio of Jim’s height to Mike’s height. If Dan is 76 inches tall, Phil is 80 inches tall, and Mike is 74 inches tall, how
If there are no gaps between tiles used for a kitchen floor, how many 8-square-inch tiles are needed to cover a kitchen floor that is 10 feet wide and 14 feet long?A. 120B. 168C. 210D. 2,520E. 20,160
Jim’s and Al’s ages total 30. Doubling Jim’s age and adding it to Ed’s age equals 46. Subtracting Al’s age from Ed’s age equals 3. How old is Jim?A. 13B. 20C. 33D. 46E. 59
a2 + b2 + 72 = 74 − 2ab, a + b =A. 7B. 5C. 3D. 1E. 0
A survey of college freshmen asked them if they have decided on a major. Part of the information that was gathered is shown in the table below. What percent of the women surveyed said that they have
On a map 1/5 of an inch represents 15 miles. If John is taking a 700-mile trip, which of the following equations represents the distance left on the trip if he has traveled x inches on the map?A. 700
When half a number is increased by 13, the result is 74. What is the number?
When x is increased by 5, the result is 60% of increasing x by 15. What is the value of x?A. 6B. 8C. 10D. 12E. 14
What is the product of the x-coordinates for the intersection points of the graphs for functions f(x) = x2 − 5 and g(x) = −2x + 3?A. −8B. −4C. −2D. 2E. 8
The picture of a building is shown in a college architecture book. In the book, every half-inch represents 25 feet. How tall is the building in the book if the actual building is 350 feet tall?A. 175
What is the value of x + y?A. 30B. 50C. 80D. 110E. 130 xo 130° Do
A password is formed with two letters followed by three one-digit numbers (0–9). If no letter and no number can be repeated, how many passwords of this type can be formed?A. 676,000B. 650,000C.
2xy +√z = x2 .If x = −3 and y = 2 then z =
The scatter plot below shows the relationship between the weight of a car and average miles per gallon of the car. Which of the following accurately describes the relationship?A. As the weight of the
The rectangle below in the xy-coordinate plane has two points on the x-axis and two points on the graph of the function f (x) = −x2 + 11. What is the area of the rectangle? -3 3
x + 2y = 1 and 5x − 4y = −23. x − y =A. 2B. −3C. −5D. 5E. 3
In the xy-coordinate plane, line k is a reflection of the line l about the line y = x. If the slope of line l = -3/5, which of the following is the slope of line k? A. B. من أمن من
The table below gives values of a function which describes the path of an object that has been dropped from a height of 16 feet. Which of the following equations is equal to f(x)?A. f(x) = x2 −
In the figure below line a and line b are not parallel. If line t bisects the acute angle PQR, this means y cannot equal what number? a b- R 110° Q P S t
The graph of f (x) is shown below. Which of the following is the graph of |f (x)|? M 4 2 -51 2 X
The graph of f (x) below −f (a) = 2; which of the following is the value of a?A. −2B. −1C. 0D. 1E. 2 4 山 -2 -1 -1 Vo て w
X = x2 + 7x + 5. If 2a = 3a then what is a possible value of a?A. 1.4B. 1.2C. 0.7D. 0.6E. 0
The cube shown below has edges of length 4. Points A, B, and C are midpoints of three different edges. What is the area of triangle ABC? A C B
The perimeter of the regular hexagon below is 12. What is the length of ĀB̄, if A is equidistant from each vertex?A. 1B. 2C. 4D. 6E. 8 B A
At Jim’s Italian Restaurant, the early bird special includes one main course and two side items, no two of which are the same. There are four main courses to choose from and four side items to
There is an inverse relationship between the squirrel (s) and the fox (f) population in a certain wooded area. The point (s, f) represents the number of squirrels and foxes. If the point (200,100)
In the expression an, n is an even power. Which of the following expressions does not have even power?A. an+1B. a2nC. an+2D. a3nE. an+4
In the figure shown below l ⊥ m. What is the value of x?A. 30B. 45C. 60D. 90E. 120 m 2 2
Which segment in the figure below is the longest? A = (-6,4) E = (-2,-3) 4 B = (2,9) D = (2,-3) C = (6,4)
x − k = x, what is the value of k?A. −2B. −1C. 0D. 1E. 2
If x − 4 = 10, then 3x − 12 =A. 10B. 20C. 30D. 40E. 50
Which number below is between 0.15 and 0.20? A. B. C. D. E. - | T - -
If 2x + 5 ≥ 3, which of the following is not a possible value of x?A. −2B. −1C. 0D. 1E. 2
Four blocks are placed side-by-side.A full cycle is completed when the block in the furthest most right position is moved to the furthest most left position. But the full cycle must be completed
The figure below is the side view of a pool that is 10 feet wide. What is the volume of the water in the pool when it is filled to 2 feet below the top?A. 1,120B. 720C. 360D. 200E. 112 4 10 20 6 8
Phil has x quarters, y dimes, and z nickels and nothing else. Which of the following expressions represents the amount of money that Phil has, in dollars?A. 0.25x + 0.10y + 0.05z.B. 2.5x + 1.0y +
The standard deviation of a set of numbers is the average distance the set of numbers is from the mean of the set of numbers. If the standard deviation of a set of numbers is 6, which of the
A parabola whose equation is in the form y = 2x2 + bx + c passes through the points (3, 16) and (1, −12). What is the value of y when x = 4?
Every year Jack’s investment of $700 increases by 5%. In which year will his investment first exceed$1,000?A. 6B. 7C. 8D. 9E. 10
Let n = c · p, where p is a prime number, and c is a composite number less than p. The number c has three unique prime factors. How many unique prime factors does n2 have?
a ∥ b, x =A. 20B. 40C. 60D. 80E. 120 a Ь to 40° 120°
The table below gives values of a function which describes the path of an object that has been dropped from a height of 16 feet. Which of the following equations is equal to f(x)?A. f(x) = x2 −
Shawn can swim two laps every 100 seconds. Brian can swim four laps every 4 minutes. If both Shawn and Brian start swimming at the same time, Shawn will swim how many more laps than Brian in 5
What is the sixth term of the geometric sequence whose first three terms are 120, 60, and 30?
What is the product of the x-coordinates for the intersection points of the graphs for functions f(x) = x2 − 5 and g(x) = −2x + 3?A. −8B. −4C. −2D. 2E. 8
4:7 = a:28, a =
The picture of a building is shown in a college architecture book. In the book, every half-inch represents 25 feet. How tall is the building in the book if the actual building is 350 feet tall?A. 175
In the figure below, which of the following choices is the median of 100 and y? 100° ܘܙ
a = x3 and b = x2, for which of the following values of x is b > a?A. 0B. 0.5C. 1D. 2E. 3
A car travels 70 miles on x gallons of gasoline. Each gallon of gasoline costs y dollars. In terms of x and y, how much does it cost for the car to travel 1 mile?A. yx/70B. 70/xyC. 70y/xD. 70y/xE.
If y − 5 = 4(x − 2), what is the value of x if y = 13?A. 0B. 2C. 4D. 8E. 16

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