900 Practice Questions for the Upper Level SSAT & ISEE

1. A fence in the shape of a regular polygon has a perimeter measuring 130 feet and each side has a length of 13 feet. How many sides does this polygon have?

(A) 7

(B) 9

(C) 10

(D) 11

(E) 13

2. The total of the measures of all the angles of a pentagon is

(A) 180°

(B) 270°

(C) 360°

(D) 540°

(E) 720°

3. An equilateral triangle has the same perimeter as a circle that has the same perimeter as a square. Which of the following lists the shapes in decreasing order of area?

(A) triangle, square, circle

(B) square, triangle, circle

(C) circle, triangle, square

(D) triangle, circle, square

(E) circle, square, triangle

4. Donna’s house is 15 kilometers from the gym and Paul’s house is 8 kilometers from the same gym. In total kilometers, how far does Donna live from Paul?

(A) 7 kilometers

(B) 16 kilometers

(C) 24 kilometers

(D) 30 kilometers

(E) It cannot be determined from the information given.

5. The perimeter of a hexagon is 15 meters. If the length of each side is increased by 3 meters, what is the new perimeter?

(A) 18 meters

(B) 24 meters

(C) 30 meters

(D) 33 meters

(E) 45 meters

6. If the perimeters of triangle ABC and quadrilateral BCDE are each 18, then r + s =

(A) 6

(B) 9

(C) 12

(D) 18

(E) 27

7. Which of the following figures can be drawn without retracing or lifting the pencil?

(A)

(B)

(C)

(D)

(E)

8. Below are three boxes in an L-shape. Which figure in the answers can be covered without any spaces or overlapping boxes by placing several L-shape pieces on it?

(A)

(B)

(C)

(D)

(E)

9. The region in the figure shown is divided by lines A, B, C, and D. The area between A and C is 20 square miles, between B and D is 35 square miles, and between C and D is 30 square miles. What is the area in square miles between A and B?

(A) 5

(B) 10

(C) 15

(D) 25

(E) 85

10. Determine the perimeter of the figure.

(A) 25

(B) 33

(C) 41

(D) 50

(E) It cannot be determined from the information given.

1. The formula for the volume of a pyramid with a square base is Bh, where B represents the area of the square base of the pyramid and h represents the height of the pyramid. The volume of Pyramid A is one half the volume of Pyramid B. Which of the following statements could be true?

(A) The height of Pyramid A is one half the height of Pyramid B, and a side of the base of Pyramid A is the two times a side of the base of Pyramid B.

(B) The height of Pyramid A is one half the height of Pyramid B, and a side of the base of Pyramid A is the same as a side of the base of Pyramid B.

(C) A side of the base of Pyramid A is one half a side of the base of Pyramid B, and the height of Pyramid A is the same as the height of Pyramid B.

(D) Both a side and the height of Pyramid A are one half a side and the height of Pyramid B.

2. The surface area of a right circular cylinder is represented by SA = 2πr² + 2πrh, where r is the radius of the cylinder and h is its height. If the surface area of a right circular cylinder is 36π and its radius is 3, what is its height?

(A) 2

(B) 3

(C) 4

(D) 5

3. Triangle ABC is shown. The length of is 3 inches. The measure of angle ACB is 35°.

Which expression gives the value of ?

(A) 3 tan 35°

(B) 3 cos 35°

(C)

(D)

4. What gives the number of square feet of tiles needed to cover a rectangular floor that is 3 yards long by 4 yards wide?

(A) 12 ft²

(B) 36 ft²

(C) 48 ft²

(D) 108 ft²

5. Use the cube to answer the question.

In the cube above, which corner is farthest from P?

(A) Q

(B) R

(C) S

(D) T

6. A square inscribed in a square is shown.

In terms of x, what is the length of line segment m?

(A) 5x²

(B) 13x²

(C) x

(D) x

7. A Venn diagram is shown.

In the Venn diagram, circle A represents all multiples of 4, and circle B represents all multiples of 7. Which of the following best describes the shaded region?

(A) Multiples of 3

(B) Multiples of 11

(C) Multiples of 28

(D) Multiples of 47

8. Use the cube to answer the question.