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mathematics
mcgraw hills conquering sat math

McGraw Hills Conquering SAT Math 2nd Edition Robert Postman, Ryan Postman - Solutions

In the xy-coordinate plane which of the following is a true statement about the graph of f(x) = x2 − 2x + 2?A. The graph never crosses the y-axis.B. The graph crosses the y-axis at y = −2.C. The graph crosses the y-axis at two points.D. The graph crosses the x-axis at x = 2.E. The graph never
On the graph below point B is symmetric to point A about the y-axis and point C is symmetric to point B across the x-axis. What is the area of triangle ABC?A. 2B. 4C. 8D. 16E. 24 B A = (2,4)
A translation in the xy-coordinate plane is as follows: for every positive horizontal move of 4 there is a positive vertical move of 2. Starting at the point (5,7) the translation goes to (x,31). What is the value of x?A. 12B. 17C. 24D. 48E. 53
Let a be an even integer and b be an odd integer.Which of the following is odd?I. a + bII. abIII. baA. I onlyB. II onlyC. I and IID. I and IIIE. II and III
The sum of the heights of six people is 336 inches. No two people are the same height. What is the mean height of the third and fourth tallest people if the mean and the median height of all six people are equal?A. 84B. 67.2C. 56D. 56.5E. 57
If x(x − y) > 0 (x > 0, y > 0), which of the following lists all the true statements?I. x > yII. x = yIII. x < yA. I onlyB. II onlyC. III onlyD. I and IIIE. I, II, and III
Let c be the number of distinct prime factors of 34. Let k be the number of distinct prime factors of 37. What is the value of ck?A. 1B. 2C. 4D. 6E. 8
A 120-foot-long rope is cut in half. One of those two pieces is cut in half and the process continues. What is the maximum number of cuts so the length of the remaining piece of rope is a whole number?A. 64π − 128B. 64πC. 128D. 32π − 64E. 96π
The area of the circle shown below is 81π. What is the length of arc PQR?A. 18πB. 15πC. 12πD. 6πE. 3π P 60° R
Over a 3-year period, a car company manufactured 50% more cars in the second year than in the first year, and twice as many cars in the third year than in the first year. What is the probability that a car produced in this 3-year period was built in the second year? A. D. E. -13+9 la almala
When Mr. Mayer went to the grocery store he spent $5 on grapes and $4.50 on peaches. If grapes cost 2 per pound and peaches cost $1.50 per pound, how many total pounds of grapes and peaches did Mr. Mayer purchase?A. 2.5 poundsB. 3 poundsC. 5.5 poundsD. 8 poundsE. 8.5 pounds
Which of the following statements is true about the lengths of the sides of triangle ABC below?A. AB B. AB C. BC D. AC E. BC A B 80° 140° с
2x − y = 4 and −x + y = 2, x =A. 2B. 3C. 4D. 6E. 8
A, B, and C are points on a line, and B is the midpoint of ĀC̄. If AB = 15, then AC =A. 60B. 30C. 15D. 10E. 7.5
2x + 4 = 8, 6x + 12 =A. 2B. 4C. 8D. 16E. 24
Which of the following points on the number line below has the same value as ⎟ x − y⎟ ?A. AB. BC. CD. DE. E A B C -2 -1.5 -1 X D Y -0.5 0 0.5 1 1.5 E 2
The average of six consecutive positive integers is 4.5. What is the median of these six integers?A. 3B. 3.5C. 4D. 4.5E. 5
The radius in the cylinder below is one fourth the height. Which of the following is a formula for the volume of this cylinder?
Let A be the set of all numbers in the form 2n, where n is an even integer. Which of the following numbers is not in set A?A.1/4B. 1C. 2D. 4E. 16
The height and the base of triangle ABC are equal and the change in the x-value from A to C is one-fourth the base. Which of these could be the coordinates of point C?A. (−1,−3)B. (−3,−1)C. (−2,−2)D. (−2,−3)E. (−3,−2) A = (-3,1) C B = (1,1)
There are six soccer teams in a league. Every team must play every other team twice. How many games must be played?A. 6B. 12C. 15D. 30E. 60
The table below gives the value of a function, f (x), for a certain value of x. Which of the following could be equal to f (x)?A. f (x) = 3x − 1.B. f (x) = 3x + 1.C. f (x) = x3 + 1.D. f (x) = x3 − 1.E. f (x) = x2 − 3. R fox) -2 -7 -1 0 0 1 1 2 2 9
How many distinct prime factors does 700 have?
The square of a number equals the sum of 21 and 4 times the number. Which of the following could be the number?A. −7B. −4C. −3D. 3E. 4
The diagram below represents the cost to set up a computer network, in thousands of dollars. What is the least amount of money it will cost to guarantee that there will be a connection between each point on the network?A. $180,000B. $150,000C. $120,000D. $90,000E. $70,000 C 50 20 B 30 A 60 40 70 D
John exercises 45 minutes a day, 3 days a week. How many hours does John exercise in 8 weeks?
The sale price of a television after a reduction of 15% is $357. What was the original price of the television set?
648 same-size cubes fill a rectangular box. The dimensions of the rectangular box are 18 inches by 27 inches by 36 inches. What is the length of the side of each cube?A. 3 inchesB. 6 inchesC. 9 inchesD. 18 inchesE. 27 inches
The volume of a rectangular prism with a square base is 128 cubic inches. If the height of the prism is 8, what is the perimeter of the base?
Lines p and q are perpendicular. Each line has a y-intercept of −4. If line p crosses through the x-axis at x = 3, at which value of x does line q cross the x-axis? D. E. lawlifiwbowle |
A copy center charges $0.07 per copy up to and including 100 copies, $0.05 for every copy over 100 up to and including 300 copies, and $0.03 for every copy over 300 copies. How much does it cost to make 500 copies?A. $6B. $7C. $10D. $15E. $23
x2 + 2xy + y2 = 121, ⎟ x + y⎟ =
In the function f (x) = ⎟ x − a⎟ + b, f (9) = f (−3), what is the value of a?
The table below shows the results of a survey about high school students’ support for reporting class rank to colleges. How many non seniors do not support reporting class rank to colleges? All Students Seniors Number of Students 800 225 Percent Who Support Reporting Class Rank 60% 80%
In the figure below, the two semicircles have centers that are midpoints of the side of the rectangle. What is the area of the shaded region?A. 16 − 4πB. 24 − 4πC. 32 − 4πD. 16 − 2πE. 32 − 2π 2 4 2
A circle with radius 10 has center (9,10). A new circle is formed by reflecting the center of the given circle across the y-axis. How many times do these two circles intersect?
What is the average of the lengths of the five segments seen below?A. 4.8B. 4.6C. 3.8D. 3.6E. 3.4 (2,5) A (5,4) B (5,1) D E (2,-3) (9,4) C F (9,-2)
A person’s weight on the moon is one-sixth of her or his weight on Earth. If a person weighs 30 pounds on the moon, how much would the person weigh on Earth?A. 5 poundsB. 30 poundsC. 60 poundsD. 150 poundsE. 180 pounds
Tickets at a movie theater cost $5 for children and $7 for adults. A total of 400 tickets were sold for $2,300. How many children’s tickets were sold?
For which of the following values of x is the relationship x < x2 < x3 true?A. -2B. -1/2C. 0D. 1/2E. 2
The volume of a cylinder is 32π. The height of the cylinder is equal to the square root of the radius. What is the radius of the cylinder?
The rectangle in the figure below is inscribed in a circle with a radius 5√5. If the height of the rectangle is twice its base, what is the area of the rectangle?A. 500B. 400C. 300D. 200E. 100
If c is equal to the sum of a and twice b, which of the following is the average (arithmetic mean) of a and c?A. cB. a + bC. aD. bE. a + c
The distance between two points (3,x) and (13,−12) is 26. What is the value of x?
When 17 is divided by k, where k is a positive integer less than 17, the remainder is 3. What is the remainder when the sum of the possible values of k is divided by 17?A. 2B. 3C. 4D. 5E. 6
At a wallpaper store 30 square feet of wallpaper costs $18. At this price, how much does 90 square feet of wallpaper cost?A. $24B. $36C. $48D. $54E. $72
A jar contains 4 blue marbles, 2 red marbles, and 6 green marbles. What is the probability that a marble chosen at random is red?A. 1/2B. 1/3C. 1/4D. 1/5E. 1/6
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 + 0.5z.C. 25x + 10y + 5z.D. 0.25x + 0.10y + 0.5z.E. 25x + 10y + 50z.
x/y =5, 2 · x2/y2 =A. 10B. 25C. 50D. 100E. 125
If x − 4 = 10, then 3x − 12 =A. 10B. 20C. 30D. 40E. 50
If x + y > 8, which of the following statements is true?A. x2 + 2xy + y2 = 64.B. x2 + 2xy + y2 > 64.C. x2 + 2xy + y2 < 64.D. x2 + 2xy + y2 > 16.E. x2 + 2xy + y2 < 16
20 is 40% of x. x is 25% of what number?A. 200B. 50C. 20D. 8E. 2
What is the perimeter of a triangle in the xy-coordinate plane whose vertices are the points (5,8), (5,2), and (9,8)?A. 6B. 10C. 2√13D. 2 + 2√13E. 10 + 2√13
The height of triangle ABC is twice the height of parallelogram ADEC. If the area of triangle ABC is 14, what is the area of parallelogram ADEC?A. 1/2B. 2C. 7D. 14E. 28 D A B E C
The graph of f (x) is shown below. Which of the following choices is the graph of |f (x)|? Graph of f(x) A. →
The perimeter of the rectangle below is 50. What is the value of x? 2x + 2 4x1
The length of each side of the square below is 6. P, Q, R, and S are each midpoints. What is the area of the shaded region (middle region)?A. 36B. 27C. 18D. 9E. 4 S P R
If the perimeter of the rectangle below is 56, what is the value of the base?A. 18B. 20C. 36D. 40E. 56 10
All rectangles below are congruent. Which choice lists all those figures with the largest shaded region?A. I onlyB. II onlyC. III onlyD. I and IIE. I, II, and III I. II. III.
What is the perimeter of a square with area 49?A. 4B. 7C. 14D. 28E. 35
What is the area of the rectangle below? 60° A. 10√3 B. 20√3 C. 40√3 D. 50 √3 E. 100 √3 20
What is the perimeter of the square seen below? 5√2
What is the value of x in the parallelogram below?A. 40B. 80C. 140D. 260E. 320 ot 40°
What is the value of x in the parallelogram below?A. 6B. 8C. 10D. 12E. 14 (15x-7)⁰ (13x +9)/
The area of the rectangle below is 40. What is the perimeter? x + 3 9+x
What is the area of the square below? 4x - 3 2x+5
If the area of the rectangle is 120, what is the area of triangle CPD?A. 60B. 100C. 120D. 200E. 240 A C P B D
In the parallelogram below, if x is 4 times as big as y, then x − y =A. 36B. 108C. 144D. 180E. 220 to 你
What is the area of the parallelogram below?A. 80B. 120C. 10√3D. 100√3E. 400√3 20 60⁰ 40
The base of a rectangle is three times as long as the height. If the perimeter is 64, what is the area of the rectangle?A. 24B. 64C. 96D. 192E. 216
What is the value of x in the figure seen below?A. 4B. 4√2C. 8D. 8√2E. 16 10 6 10 x 6
What is the area of a regular hexagon with perimeter 24?A. 4√3B. 8√3C. 12√3D. 16√3E. 24√3
The angles of a pentagon are in ratio 9 : 10 : 12 :14 : 15. What is the sum of measures of the smallest and largest angles?A. 54°B. 81°C. 135°D. 216°E. 270°
What is the area of the figure seen below? 12 4 in 5 3 برا 15
Which of the following expressions represents the area of the shaded region below?A. x2 + y2.B. 2(x2 + y2).C. 2xyD. x2 + 2xy + y2.E. x + y. y x y y x
What is the value of x?A. 60B. 70C. 80D. 90E. 100 130°, 口 70°
What is the area of the figure below? 12 20
m∠ABC =A. 35°B. 45°C. 55°D. 65°E. 75° A /(4x)° B ((5x)° (3x)° C
A triangle has a base of 12 in and an area 72 in2. What is the height of the triangle?
What are the possible values of x? 27 x 42
List the sides from longest to shortest. R 40° T 60° S
What is the area of the triangle below?A. 4 in2B. 5 in2C. 6 in2D. 7 in2E. 8 in2 4 in 45°
What is the value of x? (6x)⁰ (8x) (4x)°
What is the value of x? 130° † 35°
The area of the triangle below is 56 cm2. What is the height of the triangle? 7
What is the value of x? X 15 11
Which of the following could be the lengths of the sides of a triangle?I. 3,3,6II. 3,4,8III. 4,5,8A. IB. IIC. IIID. I and IIE. II and III
What is the value of x? 25 60 x
What are the values of x and y? X 60° 24 y
If the angles of a triangle have a ratio of 1 : 2 : 3 which of the following statements are true?I. The triangle is a right triangle.II. The ratio of the sides are 1 : √3 : 2.III. The angle measures are 30°, 60°, 90°.A. IB. IIC. I and IID. II and IIIE. I, II, and III
m∠CBA =A. 125B. 105C. 75D. 50E. 25 (5x) A B (3x)\ 50° C
What is the perimeter of an equilateral triangle with a height of 6 feet? A. 2√3 B. 4√3 C. 6√3 D. 10√3 E. 12√3
Two sides of a triangle are 7 and 16. Which of the following is not the length of the third side?A. 22B. 17C. 12D. 10E. 9
Which of the following is the longest side?A. B̄D̄B. B̄C̄C. ĀB̄D. D̄C̄E. ĀD̄ A 80° B 55° 70° 45° 60° D 50% C
a + b + c + x + y =A. 360B. 310C. 270D. 180E. 90 Z rº o [ Po 50°
The area of an equilateral triangle is 36√3 cm2 What is the height of the triangle?A. 6 cmB. 12 cmC. 6 √3 cmD. 12√3 cmE. 36 cm
In the figure below, if BC = 5 then AB =A. 5B. 10C. 25D. 5√2E. 10 √2 A 135° 90° C B
m∠BCA = 45°, m∠BAC = 60°m∠CBA = 75°, and m∠BDC = 90°. If DC = 5 then AD = B A D C
What is the value of x?A. 40B. 50C. 60D. 70E. 80 60° 50° 如 140°
What is the length of the base of the right triangle below if the area is 20 in2? x + 6 x + 3

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