Name ______

Practice Problems on the PSAT using formulas and definitions from Chapter 1

Distance, Perimeter, and Area

  1. In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

  1. The area of the figure below is . What is the perimeter of the figure?

(A) 6 (B) 6.25 (C) 6.5 (D) 6.75 (E) 7

  1. What is the area of the figure below?

(A) 64 (B) 72 (C) 84 (D) 99 (E) 120

  1. A window company produces a rectangular window that is 12 feet high and 8 feet wide. They also produce a square windowthat has the same area as the rectangular window. How long is each side of the square window? (Picture not drawn)

A)4B) 4 C)8 D)12E)6

  1. A square with sides of length 6 is divided into nine smaller squares of equal size. What is the perimeter of one of the smaller squares? (Picture not drawn)

A)4B) 6C)8D)10E)12

  1. In the figure, PQST and VRSU are rectangles with the same dimensions. If the length of segment is 2 and the area of PQST is 14, what is the length of segment ?

(A) 5 (B) 7 (C) 8 (D) 10 (E) 12

  1. What is the area of the triangle ABC?

A)6 B) 12 C)15 D)17.5 E)20

8. In the two circles shown, the radius of the larger circle is three times the radius of the smaller circle. If the area of the larger circle is 60.84π, what is the area of the smaller circle?

A) 51.84πB) 40.96πC) 31.36πD)20.28πE)6.76π

9. What is the area of the circle shown to the right?

A)4πB) 8πC) 12πD) 16πE) 32π

Angle Relationships

  1. In the figure, angle x is 20 less than angle y. What is the measure of angle y?

A)65B)60C)50D)45E)40

  1. In the figure, lines l and k intersect at point Q. If m=40 and p=25, what is the value of x?

(A) 15 (B) 20 (C) 25 (D) 40 (E) 65

  1. In the figure, point B lies on AC. If x and y are integers, which one of the following is a possible value of x?

(A) 30 (B) 35 (C) 40 (D) 50 (E) 55

  1. In the figure below, point B lies on side AC. If 55 ˂ x ˂ 60, what is one possible value of y?
  1. In the figure, AB, CD, and EF intersect at P. If r=90, s=50, t =60, u =45, and w= 50, what is the value of x? (Note: The three angles of a triangle adds up to 180°)

(A) 45 (B) 50 (C) 65 (D) 75 (E) It cannot be determined.

Coordinate Geometry

Use the distance formula to answer questions 1 and 2.

1. In the figure below, points A, B, C, and D form a square. What is the area of the figure in square units?

A)8 B) 16C)17D)31E)36

2. What is the area of triangle ABC?

A) 6 B)59C)55D)31.5 E)24.5

3. The coordinates of the center of a circle are (5,3). If is a diameter of the circle and the coordinates of B are (8,5) what are the coordinates of A?

(A)(11, 7)(B) (3,1) (C) (3,0) (D) (2,1) (E) (1,2)

Hint: Use the midpoint formula (finding an endpoint when given a midpoint).

4. In the figure, B is the midpoint of and D is the midpoint of If the length of is 9, what is the length of ?

5. In the figure below, point Q lies on . The length of is 6, the length of is twice the length of . What is the length of

(A) 6 (B) 12 (C) 18 (D) 24 (E) 36