ACT Practice Name:. If > 0, 0, each of the following MUST be a real number EXCEPT:. If and are rational, 0, 0, each of the following is a rational number EXCEPT: +. The product of two irrational numbers is alwas: irrational rational positive negative none of the above 4. For the comple number i such that 0 5. In the comple numbers, where i, i i + i i i =, what is the value of i? i i 4 i i? i
6. What is the intercept of the line 5? 5 5 5 5 7. What is the slope of AB? 0 6 6 6 6 B A 8. Which of the lines shown below has a negative slope? I onl II onl I & II onl II & III onl I, II, & III I II III 9. Which of the following is the equation of the line below? 4 4 4 4 4
ACT Practice Name:. Which of the these points lies on the line 5? (, ) (, ) (, 9) (, 9) (, 0). Which of these is parallel to the line 4 and passes through the point ( 4, )? = = = 7 = 7 = 4. Which of the following has a intercept of and passes through the point (, )? = 5 + = 5 + = 6 + 4. What is the equation of the line passing through (,) with a slope of zero? = = = = = 5. If the line, =, is moved units to the left, what is the equation of the new line? = + = = + = + =
6. Which of the following is the graph of = + 9? 7. If k is an real number, the equation, = k, will represent all lines with: a slope of a slope of a intercept of a intercept of all of the above 8. ( ) ( 4 ) =? 8 6 6 4
ACT Practice Name:. 4 9 =? 5 5 6. 6 8 =? 5 5 5 4 5 5. If, 8 6 0 6 4 6 6 6 66 6? 4. 5 5 4 6 4 0 6 0 0 5. 0 45 5 65 5 6 5 5 0
6. 7 48 4 6 7. 5 5 7 47 7 5 47 5 7 5 8. If a 0, a a a a a 6 5 6 a 6 a 9. 4 6 8 4 8 4 6
ACT Practice 4 Name:. For 0, 0 then. There are 8 blocks in a bo. Each one has a different number on it from to 8. If two blocks are drawn from the bo, which of the following CANNOT be the sum? 5 0 5. To have flers printed, costs $50 for the first 00 and $0 for each additional 00. How man can be printed for $00? 500 600 700 800 900 4. If the ruler below is marked in inches, what is the length of the nail to the nearest inch? 7 6 5 4 4 5 6 7 8
5. Two buildings appear to be the same height. One is 50 feet tall. If the other is 5 times as far awa, how tall is it? 0 feet 50 feet 00 feet 50 feet 500 feet 6. If a car gets miles per gallon of gasoline and gasoline costs $.08 per gallon, what would it cost to go 00 miles? $8.7 $9.8 $. $5.64 $06.9 7. Which of the following is equivalent to.000055.00055.0055 55,000,550,000 5.5 0 4? 6 8. Points X, Y, and Z, are on the same line in that order. If the distance from X to Z is 8. 0 and the distance from Y to Z is 5. 0, how far is it from X to Y? 5,790,000 8,067,000 8,94,700 8,45,00 8,57,000 9. The sun is about 50,000,000 km awa. Light travels about 00,000 km per second. About how man seconds does it take for sunlight to reach earth? 5.0 0 0 5.0 0 5.0 0 5.0 0 5.0 0
ACT Practice 5 Name:. What is the total cost of.5 pounds of peaches at 86 cents per pound and 4.5 pounds of pears at 68 cents per pound? $.0 $.06 $6.0 $6.07 $7.60. Bob is buing a car for $ 600. He gets a trade in allowance of $50 for his old car, but has to pa $ 480 for sales ta and license. How much does he need to borrow to cover the balance? $4570 $550 $680 $7070 $800. 6 7.50 0 4 9 0.50.5 0 4 5.0 0.0 0 4.0 0 5 5.0 0 4. If 0, z 0, simplif 5 4 8 z. 6 z 4 6 6 z 4 4 6 z 4 6 z 4 4 z 4 6 z 5. For which nonnegative value of is 9 6 8 9 0 undefined?
6. is defined ecept for which values of? and and 0 and 0 and and 7. 4 6 Which is simplified form of 6 6 6 6 0 8. Which is a simplified version equivalent to 6? 9 6 7 9. For all in its domain, is equivalent to:
ACT Practice 6 Name:. For all positive integers,, and z, is equivalent to: z z z z z z. For all, 6 6 6 8 8 = 8. For all nonzero r, t, and z values, 5 6r tz 4rt z 4z r t 4r z t 4rz t 4 4 7 4r t z 4r t z
0a b 9a b 4. For all nonzero a and b, 5b 5a b 5a b a b 5 5 4 6a b = 5. ABC is a right triangle. If BC = 9 and AB =, then AC =? 9 7 7 5 6 5 A B C 6. ABC is a right triangle. AB = 0, BC = 8, and AD = 5. DC =? 9 0 4 9 A D B C 7. In the right triangle below, find the length of in terms of. + 9 4 9 4 8. In trapezoid ABCD below, ma md 90. If BC = 6, DC = 6, AB = 46, then AD =? 94 4 94 4 A D C B
ACT Practice 7 Name:. In the figure below, the angles are all right angles as marked. AB = 4, BC = 9, CD =, and DE = 4. AE =? C D 7 9 4. In trapezoid RSTU, RS = 8, RU =, ms mt 90, and mu 60. What is the perimeter of the trapezoid? 6 6 54 54 + 6 54 + U R A S T B E. ABC is equilateral. If altitude CD = 9, then AC =? 6 9 4.5 A C D B 4. A 6 foot ladder is leaning against a house. The top of the ladder is about 5 feet above the ground. The base of the ladder is about how far from the house? 4 feet 8 inches 5 feet inches 5 feet 7 inches 6 feet inches 6 feet 9 inches 5. Below is an isosceles right triangle. If AB=8, =? 8 4 4 8 A B C
6. Evaluate 5 when =. 7 8 9 5 7 7. If a = and b =, then a a b ab b? 0 0 8. Find the value of a ab 0 8 4 0 9. For all, ( ) (5 ) =? when a = and b =? 5 0 0 5 0. For all and all N, 4 N? N N N 6 N 6 N 6
ACT Practice 8 Name:. For all <0, > 0, ( +)() 4 =? 6 6 7 6 7 6 4 6 4. For variables a and b, a, a b. Which of the following represents the product of? 4 4a 6a b 4 4a 6a b 4 4a 6a b 4 a 6a b a 6a b. Which of the following is a factor of 4? 6 6 8 4. If >0, 0,? ( )( + ) ( )( + ) ( )( ) ( )( ) 5. What is the greatest common factor of and 8? 4 4 4 4
6. Which is the complete factorization of 6 5 6 5 5 4 4 4 7. For all, L. 0 0 0 0 4 0 8. If 0, z 0, simplif 5 4 8 z 6 z 4 6 6 z 4 4 6 z 4 6 z 4 4 z 4 6 z 9. A rectangle has a length of (4 ) and a width of ( + 5). What is the area? 5 + 4 0 + 8 4 5 4 9 5 4 5