Algebra I Geometry

Algebra I SAMPLE Evaluate: Geometry SAMPLE Find the measure of the supplement of an interior angle of a regular pentagon.

Algebra I QUESTION 1 Simplify: Geometry 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?

Algebra I QUESTION 2 Solve for x: Geometry QUESTION 2 Find the perimeter of a square whose diagonals each have a measure of 36.

Algebra I QUESTION 3 If the sum of 2 numbers is 20 and their product is 96 find the sum of their reciprocals. Geometry QUESTION 3 Assuming that segments that appear to be tangent are tangent, find x. x2 20-x

Algebra I QUESTION 4 Geometry QUESTION 4 If is written in decimal form, what is the 2005th digit after the decimal? Geometry QUESTION 4 If ABCD and PQRS are parallelograms, find m APS. S S S 42° 148° S S 13° S S S

If (a,b) is the solution to the system Algebra I QUESTION 5 If (a,b) is the solution to the system then find ab. Geometry QUESTION 5 If find A C D B O

Algebra I QUESTION 6 Find the units digit of: Geometry 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. A B 8 E D C

Algebra I QUESTION 7 Simplify: Geometry 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.

Find the area of an isosceles triangle with side lengths 5, 5 and 8. Algebra I QUESTION 8 Find the area of an isosceles triangle with side lengths 5, 5 and 8. Geometry 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?

Algebra I QUESTION 9 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? Geometry QUESTION 9 In a plane, given a circle and a spiral with the same center, how many times does the circle cross the spiral?

Find the area of the region enclosed by y=7, y=3, x=2, and y=-x+12. Algebra I QUESTION 10 Find the area of the region enclosed by y=7, y=3, x=2, and y=-x+12. Geometry QUESTION 10 Assuming segments that appear to be tangent are tangent, find the mABC. B 236° A C

Algebra I QUESTION 11 Simplify: Geometry 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.

Algebra I QUESTION 12 Geometry QUESTION 12 If a varies directly with b and a=3 when b=5, find a when b is 25. Geometry QUESTION 12 ∆ABC is circumscribed about circle O. AB=16, AC=12, BC=14. Find AE.

Algebra I QUESTION 13 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? Geometry QUESTION 13 Given: Right ∆DEF, DF=8, EG=12. Find DG.

Algebra I QUESTION 14 One angle in a triangle is 85°. The second angle is 4 times the third. Find the measure of the second angle. Geometry 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)?

Algebra I 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? Geometry 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?

Algebra I QUESTION 16 Simplify: Geometry 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?

Algebra I QUESTION 17 Find the GCF of and Geometry QUESTION 17 Given trapezoid ABCD with AB = CD =13, AD = 22, and BC = 12, find the area of ABCD.

Algebra I 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? Geometry QUESTION 18 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 Geometry QUESTION 19 Evaluate: Geometry QUESTION 19 Given l||m, find l m 1 157° 89°

If find an expression for Algebra I QUESTION 20 If find an expression for in terms of x and y. Geometry QUESTION 20 A square is divided and shaded as shown. If the pattern continued forever, what fraction of the original square would be shaded?

Algebra I Extra QUESTION 1 Geometry Extra QUESTION 1 Find the smallest root of the equation Geometry Extra QUESTION 1 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 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? Geometry 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.