Algebra I

Geometry

Algebra I SAMPLE

Find the measure of the supplement of an interior angle of a regular pentagon.

Geometry SAMPLE

22486

Evaluate:

Simplify:

11664

Algebra I QUESTION 1

A six-pointed regular star consists of two interlocking equilateral triangles. What is the ratio of the area of the entire star to the area of one of the equilateral triangles?

Geometry QUESTION 1

Solve for x:

632 279 xx

Algebra I QUESTION 2

Find the perimeter of a square whose diagonals each have a measure of 36.

Geometry QUESTION 2

If the sum of 2 numbers is 20 and their product is 96 find the sum of their

reciprocals.

Algebra I QUESTION 3

Assuming that segments that appear to be tangent are tangent, find x.

Geometry QUESTION 3

x2

20-x

If is written in decimal form, what is the 2005th digit after the decimal?

27

1

Algebra I QUESTION 4

If ABCD and PQRS are parallelograms, find m APS.

Geometry QUESTION 4

42°S

S

SS

S

S

S S148°

13°

If (a,b) is the solution to the system

Algebra I QUESTION 5

If

find

Geometry QUESTION 5

2725 yx036 yx

then find ab.

.m COB m AOD

90;m AOB m COD

C

A

D

BO

Find the units digit of:

200520052005 735

Algebra I QUESTION 6

Find the area of the overlapping

region of the congruent squares

if E is the intersection

of the diagonals of

the square ABCD.

Geometry QUESTION 6

A B

CD

E8

Simplify:

52

36

75

53

3

2

3

2

y

x

y

x

Algebra I QUESTION 7

Suppose a semicircular tunnel has a diameter of 40 ft. A sign stating “Entering Tunnel – Do Not Pass” must be hung 16 ft above the roadway inside the entrance of the tunnel. Find the length of the horizontal crossbeam

that will support the bottom of the sign.

Geometry QUESTION 7

Find the area of an isosceles triangle with side lengths 5, 5 and 8.

Algebra I QUESTION 8

A square floor is tiled with congruent square tiles. The tiles on the two diagonals of the

floor are black, the rest of the tiles are white. If 101 black tiles are used, then what is the

total number of tiles?

Geometry QUESTION 8

Ryan can build a shed in ten days, while Adam can build one in 15 days. How many days will it take them to build 6

sheds if they work together?

Algebra I QUESTION 9

In a plane, given a circle and a spiral with the same center, how many times does the circle

cross the spiral?

Geometry QUESTION 9

Find the area of the region enclosed by y=7, y=3, x=2, and y=-x+12.

Algebra I QUESTION 10

Assuming segments that appear to be tangent are tangent, find the mABC.

Geometry QUESTION 10

B

236°

A

C

Simplify:

644235 2 xxxxxx

Algebra I QUESTION 11

Four times the measure of the complement of an angle is 12 more than twice the difference

of the measures of its supplement and its complement. Find the sum of the three

angles.

Geometry QUESTION 11

Algebra I QUESTION 12

∆ABC is circumscribed about circle O. AB=16, AC=12, BC=14. Find AE.

Geometry QUESTION 12

If a varies directly with b and a=3 when b=5, find a when b is 25.

During a baseball season, Bo had 500 hits. Among his hits were 13 homeruns, 16 triples,

and 21 doubles. The rest of his hits were singles. What percent of his hits were

singles?

Algebra I QUESTION 13

Given: Right ∆DEF, DF=8, EG=12. Find DG.

Geometry QUESTION 13

Algebra I QUESTION 14

Each line segment of this figure is 10 cm long, and each interior angle is either 45, 135, 90,

or 270. What is its area (in square centimeters)?

Geometry QUESTION 14

One angle in a triangle is 85°. The second angle is 4 times the third. Find the

measure of the second angle.

Algebra I QUESTION 15

Three views of the same block are shown below. What letter is on the side parallel to the

side with the letter A?

Geometry QUESTION 15

The digit sum of any number is the sum of its digits. For example, the digit sum of 247 is 13. How many numbers between 10 and

200 have a digit sum of 7?

2

3

23

662

x

x

xx

x

Algebra I QUESTION 16

If the side of one square is the diagonal of a second square, what is the ratio of

the area of the first square to the second?

Geometry QUESTION 16

Simplify:

2534 ba

Algebra I QUESTION 17

Given trapezoid ABCD with AB = CD =13, AD = 22, and BC = 12,

find the area of ABCD.

Geometry QUESTION 17

Find the GCF of

andba351

Algebra I QUESTION 18

Geometry QUESTION 18

This school year, Grissom’s enrollment is 1775. In May, 20% of those students will graduate. Assuming no one transfers or drops out, how many Freshmen must register to have a 5%

increase in enrollment for the next school year?

The centers of two circles of radii 3 and 8 are 13 units apart. Find the length of a common

external tangent segment.

Algebra I QUESTION 19

Given l||m, find

Geometry QUESTION 19

Evaluate:2005...15105

1m

l m

1

89°

157°

Algebra I QUESTION 20

A square is divided and shaded as shown.

If the pattern continued forever,

what fraction of

the original square

would be shaded?

52 yx

Geometry QUESTION 20

If find an expression for

in terms of x and y.22 yx

Algebra I Extra QUESTION 1

Geometry Extra QUESTION 1

Find the smallest root of the equation

068132 xx

The degree measure of one angle is 15 less than 4 times its complement. Find the measure of the smaller

of the two angles.

Algebra I Extra QUESTION 2

The measures of the angles in a triangle are :

x+5, 2x-15, and 6x+10.

Name the triangle according to its sides.

Geometry Extra QUESTION 2

A collection of dimes and quarters has a total value of $5.00 and contains 32

coins. How many quarters are in this collection?