SAT Pastpaper with Solutions

Which expression is a factor of x ⁴+14ax ²+49a ²-64, where a is a positive constant?

In triangle ABC, is parallel to , BD=AD, BE=9, and AC=17. What is the length of ?

In the given figure, points M and N divide the side AB of △ABC into three equal parts. Line segments MP and NQ are both parallel to BC and meet AC at P and Q respectively. What is the length of AC equal to?

A sum of 9,000 dollars was invested in a certificate of deposit (CD) that earns interest, and no other deposits or withdrawals were made after that. The function f(x)=9,000(1+0.03)² gives the value of the CD, in dollars, x years after the investment was initially made, where x≤5. Which of the following is the best interpretation of the statement "f(2) is approximately equal to 9,474.08" in this context?

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

The table shows three values of x and their corresponding values of y. There is a quadratic relationship between x and y. Which equation represents this relationship?

The figure shows a rectangular pool surrounded by a concrete path that is x feet (ft) wide on all sides. The pool is 21 ft long and 11 ft wide. The area of the concrete path is 144ft ². What is the value of x?

At a nature preserve, a wildlife biologist counted bald eagles from an observation deck at the same time each day for 21 days. The table summarizes the resulting data set, data set A.

The data value 19 was recorded in error and is removed from data set A to create data set B, which consists of the remaining 20 data values. Which statement best compares the median of data set A and the median of data set B?

The table shows the volume of two similar solids, right circular cylinder A and right circular cylinder B. The radius of right circular cylinder A is 7 units. The surface area of right circular cylinder A is kπ square units, and the surface area of right circular cylinder B is nπ square units, where k and n are constants. What is the value of n-k? (The surface area of a right circular cylinder with radius r and height h is 2πr ²+2πrh.)

In the xy-plane, a right triangle has vertices at points A(2,3), B(2,7), and C(6,3). A semicircle is drawn with the hypotenuse of this right triangle as its diameter. What is the area of this semicircle?

What is an equation of the graph shown?

A circle in the xy-plane has its center at (-5,2) and the point (-9,5) lies on the circle. Which equation represents this circle?

Which of the following are solutions to the given equation, where a is a constant and a>25?

I. a

II. 24

III. 25

For what value of x is the given expression equivalent to (117n) ^12x, where n>1?

The shaded region shown represents the solutions to which inequality?

Which of the following equivalent forms of the given function f displays, as the base or the coefficient, the y-coordinate of the y-intercept of the graph of y=f(x) in the xy-plane?

The length of a rectangle's diagonal is , and the length of one of the rectangle's sides is 4. What is the perimeter of the rectangle?

For two acute angles X and Y, the measure of angle Y is 24° and . What is the measure, in degrees, of angle X?

The positive number a is 270% of the number b, and a is 80% of the number c. If c is p% of b, which of the following is closest to the value of p?

The function h is defined by h(x)=7∣x∣. What is the value of h(-4)?