SAT Pastpaper with Solutions

The function h is defined by ,where b and c are constants. In the xy-plane, the graph of y = h(x) contains the points (2,0) and (0,-) . If h(m)= 0 , what is the greatest possible value of m ?

The functions f and g are defined by the equations shown, where a and b are integer constants , a <b and b <0 .If y = f(x) and y = g(x) are graphed in the xy-plane, which of the following equations displays, as a constant or coefficient, the y-coordinate of the y-intercept of the graph of the corresponding function?
Ⅰ. f(x)=a(2.1)^x+b
Ⅱ. g(x)=a(2.1)^x+b

A square map has a side length of 30 inches, and l inch on the map represents an actual distance of 17 miles. A smaller version of the same map is printed as a square with the side length 65% shorter than the side length of the previous map. On the smaller map, which of the following is closest to the actual distance, in miles, represented by 1 inch ?

In a set of four consecutive odd integers, where the integers are ordered from least to greatest, the first integer is represented by x . The product of 28 and the third odd integer in the set is at most the value of 50 less than the sum of the first and fourth odd integers in the set.What is the greatest possible value of x ?

The table shows three values of x and their corresponding values of y , where s is a constant.There is a linear relationship between x and y . which of the following equations represents this relationship?

The figure shows a rectangular pool surrounded by a concrete path that is a feet (ft ) wide on all sides. The pool is 21 ft long and 13 ft wide. The area of the concrete path is 240 ft² .what is the value of x ?

A model estimates that at the end of each year from 2015 to 2020 , the number of rabbits in a population was 170% more than the number of rabbits in the population at the end of the previous year. The model estimates that at the end of 2016, there were 216 rabbits in the population. Which of the following equations represents this model, where n is the estimated number of rabbits in the population t years after the end of 2015 and t ≤5 ?

One of the factors of 2x³+44x²+234x is x +b , where b is a positive constant. What is the smallest possible value of b ?

In a collection of items, 10% are red , 25% are green , 35% are blue , and 30% are yellow. If there are 40 green items, how many blue items are in the collection?

In the given equation, c is a constant. A solution to the equation is . what is the value of c ?
x(13x+27)+c=5

In the given equation, r is a positive integer. If the given equation has exactly one solution ,what CANNOT be the value of r ?
x(r-7)+3=19x+25

In triangle ABC , point D is the midpoint of segment AB and point E is the midpoint of segment BC , If BD = 8 and DE = 14, what is the length of segment AC?

A right circular cone has a base diameter of 28 inches and a height of 6 inches. The volume of this cone is kπ cubic inches. what is the value of k ?

The table shows the distribution of people in a certain city by age group.If a person in this city is selected at random, which of the following is closest to the probability of selecting a person who is greater than 65 years old ,given that the person is at least 18 years old?

A sample of a certain isotope takes 29 years to decay to half its original mass. The function s(t)= 128 gives the approximate mass of this isotope, in grams, that remains t years after a 128-gram sample starts to decay. which statement is the best interpretation of s(58)= 32 in this context ?

For the linear function f , the table shows three values of x and their corresponding values of f(x) . Which equation defines f ?

In the linear function f , f(0)= 5 and f(7)=5 . Which equation defines f ?

The scatterplot shows the relationship between two variables, x andy , for data set A. A line of best fit for the data is also shown.Data set B is created by subtracting 9 units from the value of g for each data point from data set A . Which of the following is closest to the y-coordinate of the y-intercept of the line of best fit for data set B?

The potential difference across a capacitor in an electric circuit is initially 16 volts and decreases with time, as shown in the graph. Which of the following is closest to the time, in seconds, from the initial measurement at which the potential difference across the capacitor is 15% of its initial value?

For the function f defined by the equation shown, what is the value of f(-6) ?
F(x) = (x+9)/3