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mathematics
acing the new sat math

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

If sin(5x - 10)° = cos(3x + 16)°, what is the value of x?
In the quadratic equation, p is a constant. What are the solutions for x? (p-1)x² - 2x - (p+1) = 0
In the system of equations, a and b are constants. For which of the following values of a and b does the system of equations have exactly two real solutions? y = bx-3 ly = ax² - 7x
In the figure, the vertex of the graph of the quadratic function is at (3,0). The points Band C lie on the parabola. If ABCD is a rectangle with perimeter 38, which of the following represents the equation of the parabola? B A(-1,0) O (3,0) C D(8,0) X
In the xy-plane, if the parabola with equation passes through (1,3), what is the value of a? y = a (x + 2)² -15
In the quadratic equation, k and r are are constants. What are the solutions for x? 1 A) x = - + r B) x = =+ x= 2 C) x= I+ D) x= ± +²+27-² √k² + 4 /k² +8r² 4 √k² + ² +²² 2 === 2 2 2 √k² +r² 2
If x + y = 10 and x - y = 4, what is the value of x2 - y2?A) 20B) 24C) 36D) 40
If A0 is the initial amount deposited into a savings account that earns at a fixed rate of r percent per year, and a constant amount of 12b is added to he account each year, then amount An of the savings n years after the initial deposit is made is given by the equationWhat is A3, the amount you
Evelyn deposited $3,000 into her bank account, which earns 4 percent interest compounded annually. She uses the expression $3,000(x)t to find the value of the account after t years.What is the value of x in the expression?
Evelyn deposited $3,000 into her bank account, which earns 4 percent interest compounded annually. She uses the expression $3,000(x)t to find the value of the account after t years.Evelyn deposited the same amount into an account that earns 5 percent interest rate compounded annually. How much more
The expression gives the value of an investment, in dollars, that pays an annual interest rate of r% compounded yearly. 5,000 is the initial amount and t is the number of years after the initial amount was deposited. Which of the following expressions shows the difference between the value of a 15
The complete graph of function f is shown on the xy-plane, for −5 ≤ x ≤ 5. Which of the following is/are true?A) I onlyB) II onlyC) III onlyD) I and II only I. II. f(-3)=1 III. f is minimum at x = 5. f is strictly decreasing for -5
If x > 0 and y > 0, which of the following is equivalent to 1 1 y X 1 2 X 1 2 y ?
What is the solution set of the equation above? 4 + x+1 x-4 X 20 2 x²-3x-4
The graph of quadratic functionis shown.Which of the following is an equivalent form of the equation of the graph shown above, from which the coordinates of vertex V can be identified as constants in the equation? y = x² - 6x +5
The xy-plane shows two x-intercepts, a y-intercept and vertex V of a parabola. If the line passes through the points (2,0) and V, which of the following must be the y-intercept of the line? A) 3 B) 2 7|L C) 4 9 2 D)
The graph of quadratic functionis shown.Which of the following is an equivalent form of the equation of the graph shown above, that displays the x-intercepts of the parabola as constants? y = x² - 6x +5
Which of the following is equivalent to the expression? x²-2x-24
Which of the following is equivalent to the expression? 3x² - 48
Which of the following is equivalent to the expression? 91-x/9-x
The graph of the quadratic function shows two x-intercepts and a y-intercept. Which of the following equations represents the graph of the quadratic function? (0,6). (-2,0) O (6,0) X
If x2 - 10x = 75 and x A) -15 B) -10 C) -5 D) 0
In the system of equations, a > 0. If the system of equations has exactly one real solution, what is the value of a? [y=x² + x ly=ax-1
Which of the following is equivalent to the expression? x²-17x+72
The function f and g, defined by andare graphed in the xy-plane. The two graphs intersect at the points (a,b) and (−a,b). What is the value of b?A) 6B) 8C) 10D) 12 f(x) = 2x2 +2
What is the sum of all values of x that satisfy 3x² + 12x 290? A) -4 B) -2 C) 2 D) 4
Which of the following is equivalent to the expression? -1.² -1 +5r+84
Which of the following is an equivalent form of the equation shown, from which the equation could be solved by completing the square? k x² - 4x=5 3
In the xy-plane, the parabola y = a(x - h)2 has one x-intercept at (4,0). If the y-intercept of the parabola is 9, what is the value of a? O y = a(x-h)² (4,0) X
If x2 - kx = 20 and x - k/2 = 6, which of the following is a possible value of x?A) 2B) 4C) 6D) 8
Which of the following is equivalent to the expression? 3x² +7x-6
If the quadratic equation kx2 + 6x + 4 = 0 has exactly one solution, what is the value of k? A) B) D) 74
If (x,y) is a solution to the system of equations, what is the value of x2?A) 2B) 3C) 4D) 5 = 14 [x² + y² = 1. \x² - y = 2
If (x + y)2 = 324 and (x- y)2 =16, what is the value of xy?A) 33B) 55C) 77D) 99
Which of the following is equivalent to the expression? 2x²+x-15
If r and s are two solutions of the equation above and r > s, which of the following is the value of r − s? 6x² +7x-24 0
If x2 + y2 = 10 and xy = -3, what is the value of (x−y)?A) 12B) 16C) 20D) 25
The graph of the equationis a parabola with vertex (h,k). If the minimum value of y is −12, what is the value of a? y = a (x - 1)(x+5)
What are the solutions to x2 + 4 = 6x ? A) -3± √13 B) −3+√5 C) -6± √5 D) -6± √13
If (x - 7)(x - s)=x2 - rx+14 for all values of x, what is the value of r + s?
If (ax + b)(2x−5) = 12x2 + kx − 10 for all values of x, what is the value of k?A) −26B) −10C) 24D) 32
The equation describes the motion of an object thrown upward into the air. In the equation, g is the acceleration due to gravity (9.8m/s2), t is the time elapsed since the object was thrown upward, ν0 is the initial speed of the object, h0 is the initial height from which the object was thrown,
Which of the following is equivalent to the expression? ++2
If r and s are two solutions of the equation, which of the following is the value of r + s? x²-3x = 28
A sequence is recursively defined bywhat is the value of a2? an = √√√(a₁-1)² +2. If a₁ = √ do =√√2,
In the graph, each exponential curve represents the values, in dollars, of two different cars as a function of time in years. At time t = 0, the price of model A was $30,000 and the price of model B was $24,000. At time t = 6, the price of both models were $12,000. Based on the graphs above, which
Which of the following equations has no real solution? A) 5x² - 10x = 6 B) 4x² +8x+4 = 0 C) 3x² -5x = -3 1 D) -x²+2x-2=0 3
The equation describes the motion of an object thrown upward into the air. In the equation, g is the acceleration due to gravity (9.8m/s2), t is the time elapsed since the object was thrown upward, ν0 is the initial speed of the object, h0 is the initial height from which the object was thrown,
The equation describes the motion of an object thrown upward into the air. In the equation, g is the acceleration due to gravity (9.8m/s2), t is the time elapsed since the object was thrown upward, ν0 is the initial speed of the object, h0 is the initial height from which the object was thrown,
The equation describes the motion of an object thrown upward into the air. In the equation, g is the acceleration due to gravity (9.8m/s2), t is the time elapsed since the object was thrown upward, ν0 is the initial speed of the object, h0 is the initial height from which the object was thrown,
The equation describes the height of an object t seconds after it dropped from a height of h0 feet above the ground. If a hiker dropped a water bottle from a cliff 150 feet above the ground, how many seconds will it take to hit the ground? (Round your answer to the nearest second.)A) 2B) 3C) 4D) 5
A sequence is recursively defined byand g(x) = 2x − 3, what is the value of a2? an+1 = an f(an) g(an) If a = 1, f(x)=x²-3x,
During a decade of continuous drought, the water level of a lake has decreased by 10 percent each year. Which of the following graphs could model the water level of the lake as a function of time? A) B) Water Level Water Level 5 Time (years) 10 5 Time (years) 10 x. X
Ifwhat is the value of f ° f ° f °(2)? f(x)=√2x² -1,
The population of a certain town doubles every 25 years. If the population of the town was 51,200 in 1980, in what year was the population 6,400? A) 1855 B) 1880. C) 1905 D) 1930
The number of rabbits in a certain population doubles every 40 days. If the population starts with 12 rabbits, which of the following gives the total number of rabbits in the population after t days? A) 12(2)() 40 B) 12(2)(0) 40 C) 12(2) ¹ D) 12(2) 40
If x2 - 3/2 x + c = (x - k)2, what is the value of c?
A house bought ten years ago for $150,000 was sold for $240,000 this year. Which of the following equations can be used to solve the annual growth rate r of the value of the house? (1+1) A) 240,000=150,000(1+- 10 B) 240,000 150,000(1+107) C) 240,000=150,000(1+7) ¹⁰ D) 240,000=150,000(7-)¹0
The graph shows the size of a certain insect population over 25 days. The population at time t = 0 was 100. A biologist used the equation to model the population.What is the value of din the equation? Population of Insects 500 400 300 200 100 5 Ap 10 15 20 25 Time (days) X
The half-life of a radioactive substance is the amount of time it takes for half of the substance to decay. The table below shows the time (in years) and the amount of substance left for a certain radioactive substance.How much of the original amount of the substance, to the nearest whole gram,
Population P of a town is 80,000 this year. If the population of the town decreases at a rate of 4 percent each year, which of the following expressions gives population P after t years? A) 80,000(0.6) B) 80,000(0.96) C) 80,000(0.96t) D) 80,000(1-0.04t)
The number of gallons, Pn, of a pollutant in a lake at the end of each month is given by the recursively defined formula If the initial amount P0 is 400 gallons, what is P3, the amount of pollutant in the lake at the end of the third month, to the nearest gallon?A) 297B) 285C) 273D) 262
The table gives values of f and g at selected values of x.What is the value of f(g(−2))? -2 0 3 f(x) -5 6 0 g(x) 0 4 -5
If f(x) = √2x and g(x) = 2x2, what is the value of f(g(1))-g(f(1))?A) −4B) −2C) 2D) 4
A radioactive substance decays at a rate of 18% per year. If the initial amount of the substance is 100 grams, which of the following functions models the remaining amount of the substance, in grams, after t years? A) f(t)=100(0.18)* B) f(t)=100(0.82) C) f(t)=100-100(0.18)* D) f(t)=100-100(0.82)*
The table gives values of f and g at selected values of x.What is the value of f(g(3))? -2 0 3 f(x) -5 6 0 g(x) 0 4 -5
The price P, in dollars, of a truck t years after it was purchased is given by the functionTo the nearest dollar, what is the price of the truck 9 years after it was purchased? + P(t) = 24,000(-) 6 2
A function f satisfies f(-1) = 8 and f(1) = -2. A function g satisfies g(2) = 5 and g(-1) = 1. What is the value of f(g(-1)) ?A) −2B) 1C) 5D) 8
The graph shows the size of a certain insect population over 25 days. The population at time t = 0 was 100. A biologist used the equationto model the population.What was the population of the insect after 15 days, to the nearest whole number? Population of Insects 500 400 300 200 100 5 Ap 10 15 20
If f(x) = 12,000(0.9)x and g(x)=14,000(0.85)x, what is the value of g(2)-f(2)?
If f(x) = 1 - 5x/2 and g(x) = 2 - x, what is the value of f(g(3))?A) −7B) −2C) 2D) 3
What is the minimum value of the function graphed on the xy-plane above, for −5 ≤ x ≤ 5? A) -4 B) -3 C) -2 D)
A certain radioactive substance has a half-life of 12 days. This means that every 12 days, half of the original amount of the substance decays. If there are 128 milligrams of the radioactive substance today, how many milligrams will be left after 48 days?A) 4B) 8C) 16D) 32
In the xy-plane, the graph of function ƒ has x-intercepts at −7, −5, and 5. Which of the following could define f? A) f(x)=(x-7)(x² -25) B) f(x)=(x-7)(x² +25) c) f(x) = (x+7)(x²-25) D) f(x) = (x+7)(x² +25)
What is the solution set of the equation?A) 0B) 3C) 6D) 9 11-√2x+3=8
What is the solution set of the equation?A) −15B) −12C) −8D) −6 √-3x+4 = 7
What is the value of a if x + 2 is a factor of ƒ(x) = −(x³ + 3x²) − 4(x-a)?
What is the solution set of the equation? √x+18 = x-2
Which of the following complex numbers is equal to ܕ ܐ–3 3+i
If x - 2 is a factor of polynomial p(x)= a(x3 - 2x) + b(x2 - 5), which of the following must be true? A) a+b=0 B) 2a-b=0 C) 2a+b=0 D) 4a-b=0
For what real value of x is the equation above true? x³8x² + 3x-24=0 3
The graph of f(x) = ax3 + x-18x - 9 intersects the x-axis at (3,0). What is the value of a?A) −1B) 0C) 1D) 2
If -1 and 1 are two real roots of the polynomial function f(x) = ax3 + bx2 + cx + d and (0,3) is the y-intercept of graph of f, what is the value of b ?A) −3B) −1C) 2D) 4
Which of the following complex numbers is equivalent to (1-1)² -? 1+i
A system of three equations and their graphs on the xy-plane are shown. How many solutions does the system have?A) 1B) 2C) 3D) 4 y (0,3) x² + y² = 9 y=-(x-3)² x+y = 3 (3,0) X
The function ƒ is defined by a polynomial. Some values of x and ƒ(x) are shown in the table. Which of the following must be a factor of ƒ(x)? A) x +4 B) x+3 C) x+1 D) x 2
What is the solution set of the equation?A) 2B) 4C) 6D) 8 √√5x-12=3√√2
What is the remainder of polynomial p(x) = 81x5-121x3 - 36 divided by x + 1?A) −76B) −36C) 4D) 6
What is the solution set of the equation? √2x+6=x+3
The function y = f(x) is graphed on the xy-plane above. If k is a constant such that the equation f(x) = k has one real solution, which of the following could be the value of k?A) −3B) −1C) 1D) 3
If function ƒ has four distinct zeros, which of the following could represent the complete graph of ƒ in the xy-plane? A) C) O y B) in aft X X ·x D)
The polynomials p(x) and q(x)are defined. Which of the following polynomials is divisible by x − 1? A) f(x) = p(x)-—-q(x) B) C) h(x)=-p(x)+= q (x) 1 D) k(x) = p(x)+q(x) 2 g(x)=-=p(x)-q(x) 1
Ifwhat is the value of x2? k=8-√√2 and √√x-k= -2,
If a = √3 andwhat is the value of x? 1 √2-3x = -a 3
If (x + 13)= -64, what is the value of x?A) −6B) −5C) −4D) −3
What is the remainder when polynomialA) 4B) 6C) 8D) 10 p(x) = 24x³ -36x² +14 is divided by - ? 2
If (4+i)2 = a +bi, what is the value of a + b?
If x > 0, what is the solution to the equation x4 + -8x2 = 9?
If a ≠ ±1, which of the following is equivalent to 1 a²-1 2 -1 a+1 ?
What is the solution set of the equation? 2 X-3 -2= 4 x-2

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