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mathematics
acing the new sat math

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

Which of the following is equivalent to the expression shown? A) 4mn² B) 4m²n C) -2m²n+2mn² D) 2m²n+2mn²
How many different four-letter patterns can be formed from the word MATH if the letters cannot be used more than once?
Which of the following is equivalent to the expression shown? 4x² -12xy +9y²
In a box of 12 headlamps 3 are defective. If you choose two headlamps without replacement, what is the probability that both headlamps are defective?
Which of the following is equivalent to the expression shown? A) 5b(a - b)² B) 5c(a-b)² C) 5a(b-c)² D) 5b(a-c)²
If the expression is written in the form ax2 + bx + c, in which a,b, c are constants, what is the value of a + b + c?A) 2B) 3C) 4D) 5 (2x²-3x+1)-(-2x² − 3x+2) -
If ((2/3)a2b)2 ((4/3ab)-3 = kambn, what is the value of k?
If (-a2b3)(2ab2)(-3b) = kambn, what is the value of m + n?
The average (arithmetic mean) of five numbers n, n - 3, 2n + 1, 3n -4, and 5n + 10 is 8. Which of the following is true? A) median = 5, range = 18 B) median = 5, range = 25 C) median = 7, range = 18 D) median = 7, range = 25
The figure shows a normal distribution with mean m and standard deviation d, including approximate percentages of the distribution corresponding to the regions shown. Suppose the SAT math scores of 1,200 students entering a certain university are normally distributed with a mean score of 600 and
The line graph shows the enrollment for College R between 1950 and 2000.What is the average rate of increase in enrollment per decade between 1950 and 2000?A) 500B) 600C) 750D) 875 Enrollment (in Thousands) 4 5 M 1950 Enrollment for College R 1960 1970 1980 1990 2000 Year
The scatter plot shows the average scores of 10 golfers and their weekly practice times. The line of best fit is also shown.There are two golfers whose average practice time is the same. What is the difference between their average scores?A) 4B) 6C) 8D) 10 Average Scores 100- 90+ 80+ y 0 2 4 6
The scatter plot shows the average scores of 10 golfers and their weekly practice times. The line of best fit is also shown.What is the median score of the 10 golfers?A) 96B) 97C) 98D) 99 Average Scores 100- 90+ 80+ y 0 2 4 6 8 6 8 10 12 14 Average Practice Time per Week (in hours) X
According to the line of best fit in the scatter plot, which of the following best approximate the year in which the number of cars repaired by Jay’s Motor was estimated to be 4,500?A) 1996B) 1998C) 2000D) 2002 Average Scores 5,000- 4,000- 3,000- 2,000- 1,000- 1970 Number of cars Repaired
Based on the histogram, what is the average number of hours worked by the 20 salespersons in Company G?A) 36B) 37C) 38D) 39 Number of Sales Persons Number of Hours Worked by the 20 Salespersons in Company G 7- 3- 30 34 40 45 50 Hours Worked
The table shows the frequency distribution of the number of children in each of 8 families.Let d be the standard deviation of the data set above. What is the value of d? (Round your answer to the nearest hundredth.) Number of Children Frequency 0 1 1 2 2 4 3 4 0 1
The table shows the frequency distribution of two lists. List A and list B each contain 40 numbers.What is the difference between the average of the numbers in list Band the average of the numbers in list A?A) 6.5B) 7C) 7.5D) 8 Frequency Distribution for List A Number 0 4 5 6 Frequency 8 10 12
The average (arithmetic mean) test score for all the students in a class is 84. The average score of m boys in the class was 79, while that of n girls was 87. What is the ratio of m to n?
The table shows the frequency distribution of the number of children in each of 8 families.Add 2 to each entry on the original list. Let ma and da be the new mean and the new standard deviation of the data set. Which of the following is true? Number of Children Frequency 0 1 1 2 2 4 3 4 0 1
The table shows the frequency distribution of two lists. List A and list B each contain 40 numbers.List C contains 80 numbers: the 40 numbers in list Aand the 40 numbers in list B. Let m be the average of 80 numbers in list C and M be the median of 80 numbers in list C. What is the value of
A student has an average (arithmetic mean) score of 86 points for 4 tests. What total score does this student need in the next two tests in order to have an average of 90 for all 6 tests?
Multiply each entry by 2 on the original list. Let mp and dp be the new mean and the new standard deviation of the data set. Which of the following is true? A) m₂ = 2m and dp = 2d B) mp = m and dp = d C) mp = 2m and dp = d D) mp = m and d₁ = 2d
The tables below give the distribution of ratings of two different laptops by 100 people each.Which of the following is true about the data shown for the ratings of the two laptops?A) The standard deviation of the ratings of laptop Ais larger.B) The standard deviation of the ratings of laptop Bis
Which of the following is equivalent to the expression shown above? A) (7y-3)(y-2x) B) (7y-2)(2y-3x) C) (7y-2)(y-3x) D) (7y+2)(2y-3x)
Ifwhat is the value of m? ∞ 771 انا حداد .8 00 أنبا 1
In the equation above, a is a constant and ax − 1 ≠ 0. What is the value of a? -12 ax-1 (14x² +9x-20)÷(ax-1)= 7x+8+₁
Which of the following is equivalent to the expression shown above? (3+3+3*).3*
Which of the following is equivalent to the expression shown above? A) (1+2w)(x+2y-3z) B) (1-2w)(x-2y+3z) C) (1+2w)(x-2y-3z) D) (1-2w)(x-y-3z)
If xy ≠ 0, then 3 (-2.xy²)³ 4x giờ 4
Ifwhat is the value of A? 6x² -5x+4 -3x+1 = −2x+1+ A -3x+1 9
If the expression above is written in the form axmyn, what is the value of m + n? (6xy²)(2xy)² 8x²y²
Ifis equal towhat is the value of n? 240 6,000 80,000 900,000 ·X.
Which of the following is equivalent to the expression shown above? (3x³ 2x²-7)-(-2x² +6x+2)
If 2x = 5, what is the value of 2x + 22x + 23x?
Which of the following is equivalent to the expression shown above? A) 36-18x-x² B) 36+12x-x² C) (6-x)(6+x) D) (6-x)²
If x12 = 32n4 and x9 = 4n, then x = A) 2n 1 B) 2n2 C) 4n² D) 4n
If x is not equal to zero, what is the value of (2x)³ (3x) ? (6x²)²
If 2 × 59 - k 58 = 2 × 58, what is the value of k?
In the equation above, what is the value of a? +² -x-a x-2 8 x-2 =x+1-.
Ifwhat is the value of n? (2.1×10-³)(2×105) = 6×10", 7x104
If 1299 - 1297 = 1297 × n, what is the value of n?
If a3/4 = 8, what is the value of a-1/2?
If 8,200 × 300,000 is equal to 2.46 × 10n, what is the value of n?
Which of the following is equivalent to the expression shown above? 2ax-6a - 3x+9
Ifwhat is the value of m + n + p? -2 (x)³(-y)²z=² (x)¯²y³z xm y" zp
Which of the following is the quotient of the expression shown above? (x²-x² + 3x-3)÷(x-1)
Which of the following is equivalent to the expression shown above? (x+y)(x−y)(x² + y²)
Which of the following is equivalent to the expression shown above? A) (m-5)(n-1) B) (m-1)(n-5) C) (m+5)(n+1) D) (m-5)(5n-1)
IfthenA) 3B) 5C) 7D) 9 (x + ¹² ) ² = 9.
Which of the following inequalities is equivalent to 0.6(k-7)-0.3k > 1.8+0.9k ?
Which of the following numbers is NOT a solution to the inequalityA) 0B) 2C) 4D) 6 1 2 x-1≤1?
The product of 7 and number n is no less than 91. Which of the following inequalities represents the statement? A) 7n≤91 B) 7n 91
If the system of inequalities 2 - y < 2x and -x ≤ 4 - y is graphed on the xy-plane above, which quadrant contains no solutions to the system?A) Quadrant IIB) Quadrant IIIC) Quadrant IVD) There are solutions in all four quadrants.
Which of the following numbers is a solution to the compound inequality?A) 2B) 3C) 4D) 5 4m-3 ≤2(m+1) or 7m+23
Which of the following inequalities represents the graph? A) n≤-5 B) n-5
Which of the following inequalities represents the graph? A) 2y-3x ≥ 6 B) 2y-3x≤6 C) 3y-2x ≥6 D) 3y-2x≤6
Which of the following is the graph of 1 -x≤5 and 7-x>x+1? 2 A) B) C) D) -5 -5 -5 4 4 4
Which of the following ordered pairs (x,y) is a solution to the system of inequalities y > x - 4 and x + y <5? A) (4,-2) B) (0,2) C) (5,3) D) (0,-5)
If -3a + 7 ≥ 5a - 17, what is the greatest possible value of 3a +7?A) 16B) 14C) 12D) 10
Which ordered pair (x, y) satisfies the system of equations shown? y = 2x+4 x=y=-1
What is the rate of change shown in the graph of the line? [(-3,3) (0.-1) O X
What is the domain of the function that contains points at (−5,2), (−2,1), (0,2), and (4,−3)? A) {-3, 1, 2} B) {-2, 1, 0} C) {-5, -2, 1, 2} D) {-5, -2, 0, 4}
In the table, if f(x) is a linear function, what is the value of k?A) 2.5B) 3C) 3.5D) 4 X f(x) -4 -4 0 -1 6 K
Which of the following equations represents a line that is parallel to the line with equation y = -1/2x+ 5 and contains the point (-2,1/2)? A) x-2y = -3 B) x+2y=-1 C) 2x - y = -5 D) 2x+y=-3
If (x, y) is a solution to the system of equations above, what is the value of x + y? A) -2 B) -1 C) 1 D) 2
Which of the following relation is a correct representation of the mapping shown? X -5 -2 2 5 y 7 -1 4 8
What is the average rate of change for the relation shown in the table? X y -3 -1 0 1 3 3 6 5
Which of the following expressions is equal to −1 for some values of x? A) 1-x+6 B) 1-x+4 C) 1-x+2 D) 1-x-2
Which of the following equations represents a line that passes through (7, 6) and is parallel to the x-axis? A) x = 6 B) y = 7 C) y = 7 D) y = 6
If |2x + 7| = 5, which of the following could be the value of x? A) -6 B) -4 C) -2 D) 0
The graph of the linear function f passes through the points (a,1) and (1,b) in the -xyplane. If the slope of the graph of f is 1, which of the following is true? A) a-b=1 B) a+b=1 C) a b=2 D) a+b=2
In the system of equations, k is a constant and x and y are variables. For what values of k will the system of equations have no solution? 2x-ky = 14 5x-2y = 5
Which of the following equations represents a line that passes through (−5,1) and is parallel to the -yaxis? A) y = -5 B) y = 1 C) x = -5 D) x = 1
Which of the following expressions is equal to 0 for some value of x? A) 5+x+5 B) 5+x-5 C) −5+x+5 D) -5-x-5
For the function g defined, k is a constant and g(-1) = 5. What is the value of (1)g? E + xy = (x) 8
For what value of x is |x - 1| -1 equal to 1? A) -1 B) 0 C) 1 D) 2
The graph of a line in the xy-plane has slope 1/3 and contains the point (9,1). The graph of a second line passes through the points (-2, 4) and (5,−3). If the two lines intersect at (a,b), what is the value of a + b?A) −2B) 2C) 4D) 6
If point (7,b) is in Quadrant I and point (a, − 3) is in Quadrant III, in which Quadrant is the point (a,b)?A) Quadrant IB) Quadrant IIC) Quadrant IIID) Quadrant IV
Which of the following systems of equations has infinitely many solutions? A) x+y=1 x=y=1 B) -2x + y = 1 -2x + y = 5 1 =y=1 3 3x-2y = 6 D) 2x+3y = 1 3x-2y = 1 1 C) 2 X -
For what value of x is |3x− 5| = −1? A) -2 B) -1 C) 0 D) There is no such value of x.
Which of the following is the equation of the line that passes through point (4,−1) and has slope −2? A) x + 2y = 2 B) x-2y = 6 C) 2x−y=9 D) 2x+y = 7
The table shows some values of the linear function f. Which of the following defines f? X f(x) -3 -1 5 9 1 1 5 -7
In the xy-plane, line ℓ is parallel to line m. What is the value of b? (-4,b) O (-1,-3) (0,3) m (2,0) l X
In 2005, 120 students at Lincoln High School had smart phones. By 2010, 345 students in the same school had smart phones. Which of the following best describes the annual rate of change in the number of smart phones students had from 2005 to 2010 at Lincoln High School?A) The average increase in
What is the slope of the line that passes through (3,2) and (−1,−8)?
In the system of equations, a and b are constants and x and y are variables. If the system of equations has no solution, what is the value of a ⋅ b? ax - y = 0 x-by=1
In the system of equations, a is a constant and x and y are variables. For what values of a will the system of equations have infinitely many solution? 2x- ax- 1 2 1 3 = 15 y = 10
The graph shows the relationship between the height of paraglider H, in feet, and time m, in minutes.Which of the following represents the relationship between H and m? Height (feet) 3,000 H 2,000- 1,000- 0 Height of a Paraglider 5 10 Time (minutes) 15 m
Line ℓ in the xy-plane contains points from each of the Quadrants I, III, and IV, but no points from Quadrant II. Which of the following must be true?A) The slope of line ℓ is zero.B) The slope of line ℓ is undefined.C) The slope of line ℓ is positive.D) The slope of line ℓ is negative.
In the xy-plane, if line ℓ is perpendicular to line t, what is the value of a? (-1,4) (-4,-3) O (2,1) (a,-2) l X
The graph of the function f is shown in the xy-plane above. For what value of x is the value of f(x) at its maximum? A) -3 B) -1 C) 1 D) 3
In the function, b is a constant. If f(−2) = 7, what is the value of f(b)? f(x)=x²-b
What is the value of r if the line that passes through (4,3) and (−5,r) has a slope of −1?
Ifequal to?A) −3x + 7B) −3x − 5C) −3x + 1D) −3x − 1 f(x) = −6x +1, what is f(x-1) f(x-1)
What is the slope of the line in the equation? -x+4y=6
The graph shows the relationship between the height of paraglider H, in feet, and time m, in minutes.If the height of the paraglider is 1,350 feet, which of the following best approximates the time the paraglider has been flying?A) 10 minutesB) 10 minutes and 30 secondsC) 11 minutesD) 11 minutes
What is the value of a if the line that passes through (a,7) and (1,a) has a slope of -5/9?
For what value of n is 3−|3 − n| equal to 3?
A line in the xy-plane passes through the point (1,−2) and has a slope of 1/3. Which of the following points lies on the line? A) (3,-2) B) (2,- C) (0, -2) D) (-1,-) 3
In the function, a is a constant. If f(-1) = 4, what is the value of f(-1/2)? f(x) = ax + 2

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