8TH GRADE GEOMETRY REVIEW PACKET

Problem 1 :

The area of a trapezoid is found using the formula A = 1/2 h(b₁ + b₂), where A is the area, h is the height, and b₁ and b₂ are the lengths of the bases.

What is the area of the above trapezoid ?

A)  A = 4x + 2               B) A = 4x + 8

C) A = 2x² + 4x - 21      D) A = 2x² + 8x  - 42

Solution

Problem 2 :

What is the sum of -3x² - 7x + 9 and -5x² + 6x - 4 ?

Solution

Problem 3 :

Which expression is equivalent to (3x⁵ + 17x³ - 1) + (-2x⁵ - 6) ?

A) x⁵ + 17x³ - 7         B) x⁵  - 11x³ - 1

C) 5x³ + 17x³ + 7      D) 6x⁵ + 17x³ + 6

Solution

Problem 4 :

Find the length of the missing side of the triangle below.

Perimeter = x² + 5x + 11 cm

Solution

Problem 5 :

Approximate the length of the perimeter of the quadrilateral below.

Solution

Problem 6 :

Silvia worked in a store that sold cylinder - shaped children's pools. She made a sign relating the volumes of these two pools.

The volume of the Paddler Pool is 108π cubic feet.

The Splasher Pool holds which percent of the water the Paddler Pool holds ?

A. 33%         B 75%          C 133%              D 300%

Problem 7 :

A line segment has endpoints J(2, 4) and L(6, 8). The point K is the midpoint of JL What is an equation of a line perpendicular to JL and passing through K ?

A) y = -x + 10           B) y = -x - 10

C) y = x + 2              D) y = x - 2

Solution

Problem 8 :

A triangle has vertices at (1, 3), (2, -3), and (-1, -1). What is the approximate perimeter of the triangle ?

A) 10     B 14       C 15           D 16

Solution

Problem 9 :

The vertices of quadrilateral EFGH are E(-7, 3), F(-4, 6), G(5, -3), and H(2, -6), What kind of quadrilateral is EFGH ? 

A) trapezoid       B) square   C) rectangle that is not a square     D) rhombus that is not a square

Solution

Problem 10 :

R is the midpoint of segment PS, Q is the midpoint of segment RS.

P is located at (8, 10),and S is located at (12, -6). What are the coordinates of Q ?

A) (4, 2)         B (2, -8)        C (11, -2)            D (10, 2)

Solution

Problem 11 :

County X has a population density of 250 people per square mile. The total population of the county is 150,000. Which geometric model could be the shape of county X?

A)  a parallelogram with a base of 25 miles and a height of 25 miles.

B) a rectangle that is 15 miles long and 45 miles wide

C) a right triangle with a leg that is 30 miles long and a hypotenuse that is 50 miles long 

D) a trapezoid with base lengths of 10 miles and 30 miles and a height of 25 miles.

Solution

Problem 12 :

A company is designing a cylinder to hold marbles for a new game it is inventing. The cylinder has a height of 18 inches and a diameter of 6 inches. Find the volume of the cylinder to the nearest of a cubic inch.

[1] 108.0      [2] 508.9      [3] 678.6     [4] 1065.92

Solution