HS MATH Set 1-1

Short Answer Simplify the following expression by combining like terms: 12.03A ??? 4.03B ??? 0.03(A ??? 40)

12A ??? 4.03B + 1.2

Short Answer Find the sum of all interior angles, in degrees, in a regular polygon having 100 sides:

17,640

Short Answer Giving your answer in standard form, what is the last term in the binomial expansion of the following: (x + y)6

y6

Short Answer If $10,000 is placed in a savings account that pays 5% interest compounded annually, what is the total amount of money in the account at the end of 2 years, to the nearest dollar?

$11,025

Short Answer Assuming that the natural log of 5 = 1.6, find, to the first decimal place, 1the natural log of 53 :

0.5

Short Answer Giving your answer in centimeters, what is the length of a side of a square whose diagonal measures 12 2 centimeters?

12

Short Answer If the shortest leg of a 30-60-90 right triangle is 6 inches, what is the measure, in inches, of the other 2 sides?

12 AND 6 3

Short Answer What is the area, in square feet, of a triangle whose perpendicular height is 20 feet with a base of 12 feet?

120

Short Answer Simplify the following, giving your answer in proper scientific notation: (6.0 ?? 1012)(2.0 ?? 1010)2

2.4 ?? 1033

Short Answer Multiply the following 4 numbers and give your answer in scientific notation: 30,000 ?? 3,000 ?? 30 ?? 0.1

2.7 ?? 108

Short Answer What is the degree measure of the angle formed by 2 secants intersecting outside a circle if the measures of the intercepted arcs are 80o and 34o?

23

Short Answer Find the area, in square centimeters, of a rhombus with a diagonal of 6 centimeters and a side of 5 centimeters:

24

Short Answer Find the sum of the first 10 terms of the arithmetic sequence whose first three terms are 7, 11, and 15:

250

Short Answer Find the following product, giving your answer in standard form:(4x3 + x)(7x3 + 4x2)

28x6 + 16x5 + 7x4 + 4x3 (ACCEPT: x3(28x3 + 16x2 + 7x + 4))

Short Answer In what quadrant does ?? (read as: theta) terminate if sine ?? is positive and secant ?? is negative?

2nd (ACCEPT: 2)

Short Answer What is the smaller of two integers whose sum is 19 and whose product is 48?

3

Short Answer It takes 20 minutes for Janis to prepare lunch. When Kristen helps, it only takes 12 minutes. How many minutes would it take Kristen to prepare the same lunch if she worked alone?

30

Short Answer Find the numerical value of the geometric mean of the following 4 values: 21; 23; 28; 28

32 (DO NOT ACCEPT: 25) (Solution: 1 + 3 + 8 + 8 = 20/4 = 5; 25 = 32)

Short Answer Evaluate the following expression when a = 13 , b = 4, c = ???1, and d=???5: 2[3a???(b+c)???4d]

36

Short Answer Divide the following and give your answer in scientific notation:8??1071 (4??104)2

4 ?? 105

Short Answer Solve the following equation for x: ???2|3 + ( 2x )| = ???10 (read as: negative 2 times the absolute value of 3 plus, open parenthesis, x divided by 2, close parenthesis, close absolute value, equals negative 10)

4 AND ???16

Short Answer Solve the following equation for all real values of x: 18x2 ???14x???1=0

4 OR ???2

Short Answer A jar of 100 marbles contains only 2 colors of marbles, red and blue. If there are 13 red marbles for every 12 blue marbles, how many blue marbles are in the jar?

48

Short Answer There are 10 people on a bus who, when ranked from youngest to oldest, all differ from those on the bus closest in age to them by the same number of years. If the youngest is 6 and the oldest is 51, what is the common difference in their age?

5

Short Answer Giving your answer in inches and in simplest radical form, if the hypotenuse of a 45-45-90o triangle is 10 inches, find the length of the other sides:

5 2 (ACCEPT: BOTH 5 2 )

Short Answer In a circle with diameter AB, if the radius is 6 centimeters, find the length in centimeters, giving your answer in terms of ??, of the arc AB:

6??

Short Answer If the area of a regular pentagon is 280 square centimeters, what is the length, in centimeters, of each side if the apothem is 16 centimeters?

7

Short Answer A flagpole casts a 100-foot long shadow. If a 6-foot tall person standing at the base of the pole casts an 8-foot shadow, how many feet tall is the flagpole?

75

Short Answer Giving your answer as a proper fraction, what is the cube root of 125 ? 343

75

Short Answer A circle has a diameter of 32 meters. Find the degree measure of the central angle of a sector of the circle if its arc length measures 8?? meters:

90

Short Answer Giving your answer in terms of ?? and in inches, what is the arc-length of a semi-circle whose diameter is 18 inches?

9??

Short Answer What is the determinant of a 2-by-2 square matrix whose rows are 4, 2 and ???3, ???4?

???10

Short Answer Simplify the following without the use of negative exponents: ??? 24x3 y5 10 y 6 z 2

???12x32 5yz

Short Answer Solve the following inequality for x: |3 ??? 2x| ??? 7 (read as: the absolute value of, 3 minus 2x, close absolute value, is less than or equal to 7)

???2 ??? x ??? 5 (ACCEPT: 5 ??? x ??? ???2)

Short Answer What is the slope of a line perpendicular to the line given by the graph of the equation, ???5x = ???6y + 4

???65

Short Answer Simplify the following rational expression by combining like terms, assuming x is not equal to 4: (x2 ???16)(4x ??? x2 )

???x+4 (ACCEPT: x+4 or ???(x+4) or ???x???4)

Short Answer Consider triangle ABC, where the measure of angle A = 20o, B =117o, and C = 43o. Arrange the 3 sides in order of increasing length:

BC; AB; AC

Short Answer Simplify the following rational expression: 5y ??? 3x2 9y2 +5x

CANNOTBEFURTHERSIMPLIFIED (ACCEPT: 5y???3x2 orTHESAME) 9y2 +5x

Short Answer What term BEST describes 2 angles with 90o as the sum of their measurements?

COMPLEMENTARY

Short Answer What is the specific name for a common tangent that intersects the segment joining the centers of 2 circles?

INTERNAL COMMON TANGENT (ACCEPT: INTERNAL or INTERNAL TANGENT)

Short Answer Giving your answer as up, down, left, or right, the graph of the equation x = 5y ??? 8y2 ??? 1 opens in what direction?

LEFT

Short Answer What is the name for the test that can be used to visually determine whether or not a relation defined by a graph represents a function?

VERTICAL LINE TEST (ACCEPT: VERTICAL LINE)

Multiple Choice If triangle ABD is congruent with triangle EFG, which of the following MUST be true:W) side AB is congruent to side EFX) side AD is congruent to side FGY) measure of angle B = measure of angle G Z) measure of angle A = measure of angle G

W) SIDE AB IS CONGRUENT TO SIDE EF

Short Answer Find the x and y intercepts of the line passing through the point (4, 8) that is perpendicular to the line 3x ??? 6y ??? 12 = 0:

X-INTERCEPT = (8, 0) (ACCEPT: 8); Y-INTERCEPT = (0, 16) (ACCEPT: 16)

Multiple Choice Which of the following is NOT a Pythagorean triple:W) 15, 20, 25 X) 10, 24, 26 Y) 16, 24, 30 Z) 33, 44, 55

Y) 16, 24, 30

Multiple Choice If e 5 = 30, which of the following is the value of x, assuming that thenatural log of 2 = 0.7, and the natural log of 15 = 2.7:W) 15 X) 16 Y) 17 Z) 18

Y) 17

Multiple Choice Which of the following numbers is evenly divisible by both 11 and 3:W) 7791 X) 7553 Y) 5181 Z) 8769

Y) 5181

Short Answer Simplify the following expression: x 2 x 59

x10 (ACCEPT: 10 x9 )

Multiple Choice Which of the following is NOT true:W) all central angles in a regular polygon are equalX) irregular polygons are not considered to have centers and have no central anglesY) the circumcircle of a regular polygon is the circle that passes through at least one vertex Z) all regular polygons are convex

Y) THE CIRCUMCIRCLE OF A REGULAR POLYGON IS THE CIRCLE THAT PASSES THROUGH AT LEAST ONE VERTEX

Multiple Choice One-fifth of 0.04% is equal to:W) 8 ?? 10???2 X) 8 ?? 10???3 Y) 8 ?? 10???4 Z) 8 ?? 10???5

Z) 8 ?? 10???5

Short Answer Simplify the following expression, where a is not equal to zero if b = 0 orifb=???1: (ab2 )(ab)

ab2 +b

Short Answer Giving your answer in standard form, give the equation of the circle with center at (0, 0) and diameter of 6:

x2 + y2 = 9