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.

the-area-of-trapezoid

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 ?

(1) -8x2 - x + 5

(2) -8x4 - x + 5

(3) -8x2 - 13x + 13

(4) -8x4 - 13x2 + 13

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

length-of-the-missing-side-of-the-triangle-q4

Solution

Problem 5 :

Approximate the length of the perimeter of the quadrilateral below.

length-of-the-perimeter-of-the-quadrilateral-q5

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.

length-of-the-missing-side-of-the-triangle-q6
6

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)

coordinates-of-q

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

Answer Key

1)  A = 4x + 8

2)   -8x2 - x + 5

3)  3x5 + 17x3 - 7

4)  x2 + 20 cm

5)  11.3

6)  133%

7)  y = -x +10

8)  14.2

9)   rectangle that is not a square 

10)  (11, -2).

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

12)  v = 508.68

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