SAT Pastpaper with Solutions

In the figure shown, the length of is 66;
Which statement provides sufficient information to prove that triangle is isosceles?

If of is 62, what is the value of  ?

For the linear function , the graph of in the-plane has a slope of 0 and passes through the point. Which equation defines ?

The amount of money owed on a certain type of loan has two components: the principal balance of the loan and the amount of interest accrued on the loan. For a loan of this type, each payment was and there were 60 payments total. Part of each payment was applied to the principal balance of the loan, and the rest was applied to the amount of interest accrued on the loan. The amount of the 1st payment that was applied to the principal balance was . For each additional payment, the amount that was applied to the principal balance was approximately greater than the amount that was applied to the principal balance for the previous payment. Which function best approximates the amount of the th payment, in dollars, that was applied to the amount of interest accrued, where ?

If and , which expression is equivalent to ?

In the given equation, is a constant. The equation has infinitely many solutions. What is the value of ?

What is the -intercept of the graph of in the-plane?

During an experiment, the temperature, in degrees Celsius, of a mixture was recorded to the nearest integer at certain times. The scatterplot shows the recorded temperature , in of the mixture hours after the start of the experiment.

What was the average rate of change of the recorded temperature of the mixture over time, in per hour, from to ?

Data set A:
Data set , which consists of the 5 values shown, has a mean of 44 and a standard deviation of approximately 14.10; Data set B consists of the 5 values from data set A and one additional value, . For which of the following values of will the standard deviation of data set be less than the standard deviation of data set ?

A right square pyramid has a surface area of 75,264 square inches, which includes a base area of 36,864 square inches. What is the slant height, in inches, of this pyramid?

A company developed a plan to set the selling price of a product. The company determined that for a selling price of , zero products would be sold. For each decrease in the selling price, the number of products sold would increase by one. For a revenue of exactly , which of the following could be the number of products sold? (revenue price number of products sold)

How many distinct real solutions does the given equation have?

As the size of a firework's shell increases, the height above the ground when the firework bursts increases. For a firework to burst 1,075 feet above the ground, a firework's shell in the shape of a sphere with a volume of 514.23 cubic inches could be used. To the nearest whole number, what is the volume of this firework's shell in cubic centimeters? (1 inch = 2.54 centimeters)

One solution to the given equation can be written as , where and are positive integers. What is the value of ?

Right rectangular prism is similar to right rectangular prism . The surface area of right rectangular prism  is 52 square centimeters, and the surface area of right rectangular prism is . The volume of right rectangular prism is 10.5 cubic centimeters. What is the volume, in , of right rectangular prism ?

(This question is highly debatable, as there are multiple possible answers, However, considering that it's an actual digital SAT question, we have kept it for student reference. Even the SAT isn't always rigorous in its question formulation): In the given expression, is a positive integer. If is a factor of the expression, where and are positive integers, what is the greatest possible value of ?

The cost of renting a piece of equipment is for the first day and for each additional day, where is a positive integer.
Which of the following functions gives the cost , in dollars, of renting this equipment for days, where is a positive integer?