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acing the new sat math

Acing The New SAT Math 1st Edition Thomas Hyun - Solutions

What is the value of 9 - n if n - 9= - n + 16 - 3n?
Ifwhat is the value of m + n? (3ab²)(2a²b)³ 8a²b² = 3ab"
If (x,y) is solution to the system of equations, what is the value of x + y? 3x +2y = 24 -2x+3y=10
The table gives values of f and g at selected values of x.What is the value of g(f(2))? X -1 2 3 f(x) -3 3 5 g(x) -2 1 6
If the linear equation has no solution, which of the following could be the value of k?A) −1B) 2C) 5D) 8 11+5x = kx-3(x-4)
A skier starts a downhill race course that is 1,800 meters long, and the finish line is 360 meters below the start line. During the race, the skier averaged a speed of 9 meters per second.Which of the following expressions gives the skier’s elevation above the finish line t seconds after she
The expressions in the table show the distance from Burbank to a helicopter and a plane t hours after 10:00 AM. At what time will the helicopter and the plane be equidistant from Burbank?A) 11:00 AMB) 11:15 AMC) 11:30 AMD) 11:45 AM Helicopter Plane Distance from Burbank (miles) -150t +260 -270t +
How many ordered pairs (x, y) satisfy the system of equations shown?A) 0B) 1C) 2D) Infinitely many x=y=5 y = (3x+1)(x-2)
In the figure, segments ST and QR are parallel. What is the length of P̅T̅?A) 2.6B) 3.0C) 3.4D) 3.8 S P 2.4 3.6 T 1.3 R
The line of a graph in the xy-plane has slope 13 and contains the point (6,−1). The graph of a second line passes through the points (0,1) and (1,0). If the two lines intersect at the point (p,q), what is the value of p ⋅ q?A) −6B) −3C) 3D) 6
In the xy-plane, the graph of function f has x-intercepts at −3, 0, and 6. Which of the following could define f? A) f(x) = 2x³ +8x² - 24x B) f(x)=2x³8x² - 24x C) f(x) = 2x³ +6x² -36x D) f(x)=2x³-6x² -36x
If f(2 − x) = 3x − 5 for all values of x, what is the value of f (−3)?A) −14B) −2C) 10D) 14
During a basketball game, the Lancers scored 15 points in the first quarter, 2/7 of their total score in the second quarter, 1/4 of their total score in the third quarter, and the remaining 11 points in the fourth quarter. What is the total number of points the Lancers scored in the game?A) 48B)
A skier starts a downhill race course that is 1,800 meters long, and the finish line is 360 meters below the start line. During the race, the skier averaged a speed of 9 meters per second.How far is the skier from the finish line one minute after she started the race?A) 540 metersB) 780 metersC)
At a certain concert, all tickets are equally priced. A survey showed that decreasing the price of these tickets by 10 percent would increase the number of tickets sold by 20 percent. If each concert ticket is discounted by 10 percent, what is the percent increase in the amount of money received
The chart shows approximations of the density of metals, d, in grams per cubic centimetersfor six metals. The mass of an object can be found by using the formula m = d ⋅ V, in which m is the mass of a metal measured in grams and V is the volume of a metal measured in cm3.Which of the following
A weather balloon was launched for weather forecast. At an elevation of 1,000 meters above the sea level, the outside temperature recorded 12°C.As the balloon went up, the outside temperature decreased linearly. At an elevation of 1,500 meters above the sea level, outside temperature recorded
In a right triangle, one angle measures x°, for which COS.X° √√7 4 What is cos(90° - x°) ?
If (x,y) is a solution to the equation and y ≠ 0, what is the ratio x/y? 1 x=y=-y 2
List A and List B each contains 30 numbers. Frequency distributions for each list are recorded in the histograms below.The average (arithmetic mean) of the numbers in list A is 3.7, and the average of the numbers in list B is 10.1. List C contains 60 numbers: the 30 numbers of list A and the 30
The chart shows approximations of the density of metals, d, in grams per cubic centimetersfor six metals. The mass of an object can be found by using the formula m = d ⋅ V, in which m is the mass of a metal measured in grams and V is the volume of a metal measured in cm3.What is the volume, in
If an event can succeed in S ways and fail in F ways, the probability of success P is given asWhich of the following expresses S in terms of the other variables? P= S S + F
The xy-plane shows two x-intercepts, a y-intercept, and vertex V of a parabola. Which of the following must be the coordinates of the vertex of the parabola? (0,16 O (2.0) V(h.k) (8,0) X
In the quadratic equation, a and b are positive constants, with a > b. If the graph of the equation in the xy-plane is a parabola with vertex (6,−18), what is the value of a?A) 3B) 6C) 9D) 12 y=2(x-a)(x-b)
In the figure, lines k, ℓ, and n intersect at point P. If ℓ ∥ m and ℓ ⊥ n, which of the following is true? xº n 2.0 P k l m
Printer A, working alone at a constant rate, prints 100 pages of documents in m minutes. Printer,B working alone at a constant rate, prints 100 pages of documents in n minutes. If printers A and ,B working together at their respective constant rates, printed p pages of documents in 1 hour, which of
List A and List B each contains 30 numbers. Frequency distributions for each list are recorded in the histograms below.The average (arithmetic mean) of the numbers in list A is 3.7, and the average of the numbers in list B is 10.1. List C contains 60 numbers: the 30 numbers of list A and the 30
In the xy-plane above, O is the center of the circle, and the measure of ∠POQ is θ. If sin θ = a/r, what is sin(2π - θ)? P AY Ө Q X
The table shows the number of people in two groups who rated a bestseller on a scale of 1 to 3.If a person is chosen at random from those who gave a rating of at least 2, what is the probability that the person belongs to Group B? Group A Group
A system of inequalities and a graph are shown. Which section or sections of the graph could represent all of the solutions to the system?A) Section AB) Section BC) Section CD) Section D section C [2x+y 2-1 2x-3y
Grape juice makes up 12% of brand A fruit punch and 20% of brand B fruit punch. If 10 ounces of brand A fruit punch are mixed with 15 ounces of brand B fruit punch, what percent of the mixed punch is the grape juice?A) 14.2%B) 15.4%C) 16.8%D) 20.6%
In the system of equations, a and b are constants and x and y are variables. If the system of equations above has no solution, what is the value of a/b? ax-9y=7 bx - 4y = 5
A grain silo of a barn consists of a right circular cylinder capped by a right circular cone. The heights of the cylinder and cone are represented by the figure. If the volume of the grain silo is 224π cubic meters, what is the diameter of the silo, in meters? 6 m 12 m
In a book store, hardcover copies of a certain book are priced at $24 each and paperback copies of the same book are priced at $13.50 each. Last week, the total amount collected in the sales of the hardcover and paperback copies was the same as if every book sold had cost $15.60 each. If 300 hard
What is the value of r if the line that passes through (−5,4) and (3,)r has a slope of −1/5?
At a farmers market, n pounds of avocados cost $4.50. If Gloria paid 4n dollars for 8 pounds of avocados, what is the value of n?
If (ax - 1)(bx + 2) = cx2 - x - 2 for all values of x, and a + b = 10, what is the value of c?
The purchase price of a car is $24,000, and the value of the car decreases by 15 percent per year. The value V, in dollars, t years after the car is purchased is given by the function V= 24,000(x)t. What is the value, in dollars, of the car 10 years after it is purchased? (Round your answer to the
In the figure, point O is the center of the circle, and line segments PQ and PR are tangent to the circle at points Q and R, respectively. If the radius of the circle is 9/π, what is the length of the minor arc Q̑Ȓ? R 50° P
Half the difference of 18 and a number n is equal to the sum of n and three. What is the value of n? A) 5 2 B) 4 11 2 D) 6 C)
If 0.14x = 2.8, what is the value of 1/x?A) 0.2B) 0.5C) 0.02D) 0.05
The equation of a circle in the xy-plane is shown. Which of the following is true about the circle? x² +12x+y²-4y+15= 0
In the figure, the circle is tangent to the x-axis and has center (−4,−3). Which of the following equations represents the equation of the circle shown in the xy-plane? (-4,-3) ·x
In the figure, the radius of the circle is 8 and m∠AOB = 120°. What is the length of ĀB̄? A 0 8 B
The equation of a circle in the xy-plane is shown above. If the area of the circle is ,kπ what is the value of k? x²+2x+y²-4y-9=0
In the figure, ΘO is inscribed in ΔPQR. If 12 = PA, 6 = QA, and 9.5 = RB, what is the perimeter of ΔPQR?A) 46B) 49C) 52D) 55 R 6 0. 9.5 A B 12 P
In the figure, rectangle OPQR is inscribed in a quarter circle that has a radius of 9. If PQ = 7, what is the area of rectangle OPQR? P R
What is the area of the circle in the xy-plane above?A) 20πB) 24πC) 26πD) 30π 2 x² - 4x + y² - 6x-17 = 0
In the figure, OP is a radius and PQ is tangent to circle O. If the radius of circle O is 10 and 16 = QR, what is the length of PQ?A) 16B) 20C) 24D) 28 O 10 P R 16 Q
Which of the following is the equation of a circle that has a diameter of 8 units and is tangent to the graph of y = 2? A) (x+1)² + (y + 2)² = 1 B) (x-1)²+(y-2)² = 16 C) (x+2)² + (y+1)² = 16 D) (x-2)² + (y-1)² = 16
In the figure, OP = OQ and P̄Q̄ is tangent to circle O. If the radius of circle O is 8, what is the length of Q̄R̄? P O R 30° Q
In a circle with center O, the central angle has a measure of 2π/3 radians. The area of the sector formed by central angle AOB is what fraction of the area of the circle?
In the figure, the length of arc ȂB̑ is π. What is the area of sector OAB? 36° A В
In the figure, a quadrilateral is inscribed in a circle.What is the value of x?A) 70B) 80C) 90D) 100 70° P 80° x R 75° S
In the figure, BD is a diameter, and PA and PD are tangents to circle O. m∠CDE = 52, m∠APD = 45, and AP = 9.What is the length of PD? 52° E D O B A 45° P
The figure shows a semicircle with the lengths of the adjacent arcs a, a + 1, a + 2, a + 3, and a + 4. If the value of x is 42, what is the value of a?A) 7B) 8C) 9D) 10 a +4, a +3 a+2 O a +1 a
Which of the following represents an equation of a circle whose diameter has endpoints (−8,4) and (2,−6)? A) (x-3)² + (y−1)² = 50 B) (x+3)² + (y+1)² = 50 C) (x-3)²+(y-1)² = 25 D) (x+3)² + (y+1)² = 2
In the figure, the radius of the circle is 12. If the length of chord A̅B̅ is 18, what is the distance between the chord and the diameter? A 0 в
In the figure, a double cone is inscribed in a cylinder whose radius is x and height is 2x. What is the volume of the space inside the cylinder but outside the double cone, in terms of x? 2x
A square pyramid and a cube have equal volumes. The cube has an edge length of 4 inches and the pyramid has a base side length of 6 inches. What is the height of the pyramid in inches?
The figure shows two cylinders that are rolled up from a poster 36 centimeter (cm) wide and 50 cm long without overlap. For cylinder I, the height is 36 cm and the circumference of the base is 50 cm. For cylinder II, the height is 50 cm and the circumference of the base is 36 cm. Which of the
The surface area of a cube is 54 square centimeters (cm2). What is the volume of the cube in cubic centimeters?
A cone with a height of 10 cm and radius of 3 cm is 90 percent filled with shaved ice. What is the volume of the shaved ice, to the nearest cubic centimeter?
In the figure shown, if all the water in the rectangular container is poured into the cylinder, the water level rises from h inches to (h + x) inches. Which of the following is the best approximation of the value of x?A) 3B) 3.4C) 3.8D) 4.2 + N OOD
If the circumference of the base part of cone is 10 centimeters (cm) and the height of the cone is 8 cm, what is the volume of the cone, to the nearest cubic centimeter?A) 18B) 21C) 24D) 32
In the cylindrical tube shown, the height of the tube is 30 and the circumference of the circular base is 32. If the tube is cut along A̅B̅ and laid out flat to make a rectangle, what is the length of A̅C̅ to the nearest whole number?A) 24B) 30C) 34D) 38 A D 30 B C
An aquarium tank in the shape of a rectangular prism is 20 inches (in) long by 16 in wide by 12 in high. If 2,400 cubic inches of water is added into the empty tank, how far is the surface of the water from the top of the tank?
A manufacturing company produces cardboard boxes by cutting out square corners 3 inches (in) by 3 in. from rectangular pieces of cardboard 3x in. by 2x + 2 in. The cardboard is then folded along the dashed lines to form a box without a top. If the volume of the box is 162 in3, what is the dimension
A regular hexagonal prism with edge lengths of 2 inches is created by cutting out a metal cylinder whose radius is 2 inches and height is 4 inches. What is the volume of the waste generated by creating the hexagonal prism from the cylinder, rounded to the nearest cubic inch?A) 7B) 9C) 11D) 14 2
A plane parallel to the base of a cone divides the cone into two pieces, and removes the top part. The radius of the cone is 6 inches (in), the height of the cone is 16 in, and the distance from the base to the parallel plane is 8 in. What is the volume of the remaining bottom part, in cubic
The figure shows two cylinders. The height of cylinder I is twice the height of cylinder II and the radius of cylinder II is twice the radius of cylinder I. If the volume of cylinder I is 45 inπ3, what is the volume of cylinder II in cubic inches?A) 22.5πB) 45πC) 67.5πD) 90π I 1 2h II 2r h
In the figure, a sphere is inscribed in a cylinder, so that the diameter of the sphere is the same as the diameter of the cylinder and the height of the cylinder. What is the value of Volume of the sphere Volume of the cylinder ?
The figure shows a pyramid with regular hexagonal base. The length of each side of the hexagonal face is 4 units and the height of the pyramid is 7 units. What is the volume of the pyramid? 4 4 7
The figure shows the mechanical part in the shape of a steel cylinder 8 inches high and 6 inches long in diameter. A hole with a diameter of 3 inches is drilled through the mechanical part. The density of steel is 490 lb/ft3. What is the mass of the mechanical part, to the nearest pound? (1 foot =
Water is pouring into a conical reservoir at the rate of 2.43 m per minute. If the radius of the base of the conical reservoir is 9 meters (m) and the length of the lateral edge is 15 m, to the nearest minute, how long will it take to fill up the empty reservoir?A) 212B) 318C) 424D) 530 9 m 15 m
The figure shows an aluminum block of 10 in * 8 in * 12 in with an 8 in * 6 in * 12 in opening. What is the weight of the aluminum block to the nearest pound? (The density of aluminum is 0.098 lb/in3)A) 32B) 38C) 42D) 48 12 in 6 in 10 in 8 in 8 in
The figure shows a cube and a rectangular prism. If the volume of the rectangular prism is 30 times the volume of the cube, what is the value of x?A) 1.5B) 2C) 2.5D) 3 X X X Jangan 4x + 3 2x 4x-3
The figure shows a cement block of 36 cm * 20 cm * 9 cm with two 10 cm * 8 cm openings. What is the weight of the cement block to the nearest gram? (The density of cement is 1.7 gram /cm3)A) 5,040B) 6,048C) 7,560D) 8,568 8 10 36 cm 10 9 cm 20 cm
A wheel with a radius of 2.2 feet is turning at a constant rate of 400 revolutions per minute on a road. If the wheel traveled kπ miles in one hour what is the value of k? (1 mile = 5,280 feet)
In the xy-plane, O is the center of the circle, and the measure of ∠POQ is kπ radians. What is the value of k? AY O P(1.1) Q X
In the xy-plane, O is the center of the circle, and the measure of ∠POQ is a°.What is the cosine of a°? P(-1.√√3) O AY Q X
In the xy-plane, O is the center of the circle, and the measure of ∠POQ is kπ radians.In the right triangle shown, if tan θ = 3/4, what is sinθ? P(-1-15) y kл Q X
In the xy-plane, O is the center of the circle, and the measure of ∠POQ is kπ radians.In the isosceles right triangle shown above, what is tan∠A? P(-1-15) y kл Q X
In the triangle shown below AB = BC = 10 and AC = 12.What is the value of tanθ? 10 10 в 12 10 # Ө C
Which of the following is equal to cos(π/8)? 3π COS (³7) A) cos(- 77 8 B) cos(- C) sin( sin (377) in(77) D) sin(- 8
In the triangle shown below AB = BC = 10 and AC = 12.What is the value of cosθ?A) 0.4B) 0.6C) 0.8D) 1.2 10 10 в 12 10 # Ө C
In the triangle shown below AB = BC = 10 and AC = 12.What is the value of sinθ?A) 0.4B) 0.6C) 0.8D) 1.2 10 10 в 12 10 # Ө C
In the xy-plane, O is the center of the circle, and the measure of ∠POQ is a°.What is the cosine of (a + 180)°? P(-1.√√3) O AY Q X
What is the value of k? A) B) C) D) 5/3
What is the value of k? A) B) D)
In the figure, what is the value of cos ∠AOD? O y A(3,4) D B x
In the xy-plane, O is the center of the circle and the measure of ∠AOD is π/3. If the radius of circle O is 6 what is the length of AD? A) 3 B) 3√2 C) 4.5 D) 3√3
In triangle ABC, AC ⊥ BD. Which of the following does not represent the area of triangle ABC? A B D C
In the xy-plane, O is the center of the circle, and the measure of the angle shown is kπ radians.What is the value of tan(kπ)? P(-3,-1) кл У 0 o X
In the figures y A) 16B) 21C) 24D) 27 xº yº Note: Figures not drawn to scale.
Given the right triangle ABC, which of the following is equal to a/c?I. sinAII. cosBIII. tanAA) I onlyB) II onlyC) I and II onlyD) II and III only В a с b с A
What is cos(k + 1)π? D B) 6 D) √√3
In the isosceles triangle, what is the value of sin x°? 20 в 24 н xº C
In the right triangle ABC, the cosine of x° is 3/5. If BC = 12, what is the length of AC? B A
In triangle ABC, the measure of ∠C is 90°, AC = 24, and BC = 10. What is the value of sin A?

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