! Practice!Math!ACT!Test!2" " Notes on the Practice Exam

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PracticeMathACT Test2 Notes on the Practice Exam This practice exam has three major sections to it: test, answer key with hints, and scoring guide.

1 PracticeMathACT Test2 Notes on the Practice Exam This practice exam has three major sections to it: test, answer key with hints, and scoring guide. You ll get the most out of this practice if you make the experience as authentic as possible so carefully follow the directions below. Good luck. Directions Find a quiet place to spend the next hour or two. Clear away all distractions and set a timer for 60 minutes. Once you start the timer resist the urge to pause for any reason or to peek ahead at the answers and hints. Once the timer goes off stop all work on test. Use the answer key to correct your test and the scoring guide to estimate your score on this practice exam. Lastly, go back through the exam using the hints to brush up on the ones you missed. Practice Exam 2. Which of the following numbers is the smallest? A. 8.5% B. 85/00 C (0.00) 8.5 x Find the value of x in the following equation: 4x 7 = 6x + 3 A. x = -0 B. x = -5 C. x = -2 x = - x = Which of the following is NOT a rational number? A. 6 B. 2 C. 2%

2 PracticeMathACT Test2 4. Amanda scored 87%, 97%, 88%, and 94% on the first four out of six tests in her math class. If she needs an average of 93% on all of the tests to get an A in the class, what must her average score be for the last two tests in order to get an A? A. 9.8% B. 93% C. 94.5% 96% 99% 5. A car s tank holds gallons of gasoline when full. After driving 76 miles, the tank is 79% full. How many miles can the car go on a full tank of gas, to the nearest tenth of a mile? A B C A bag contains 6 blue candies, 8 yellow candies, and 2 red candies. What is the probability that a candy randomly drawn from the bag is NOT blue? A. B. C Jennifer found a jacket at the store that originally cost $9.95 on sale for 30% off. If there was a 7.5% sales tax applied after the discount, how much did Jennifer pay for the jacket to the nearest cent? A. $35.99 B. $38.68 C. $83.97 $90.26 $ In the senior class, the ratio of female to male students is 5:3. If there are 95 male students, what is the total number of students in the senior class? A. 7 B. 32 C

3 9. If 60% of z is 90, what is 40% of z? A. 54 B C PracticeMathACT Test2 0. At the school cafeteria, students can get a lunch combo with an entrée, side, drink, and dessert. The options are listed in the table below. How many different lunch combos are possible? Entrée Side Drink Dessert Hamburger Salad Milk Cookie Pizza Soup Juice Brownie Turkey Sandwich Fruit Lemonade Grilled Cheese Chips A. 3 B. 48 C ,024. What is the greatest common factor of 32, 48, and 20? A. 4 B. 8 C Ryan is driving to his grandparents house for his grandmother s 80 th birthday and is running late. Their house is 20 miles away, and the party starts at 3:00 pm. If he leaves at :00 pm and drives at a rate of 65 miles per hour, how many minutes late will he be to the party (choose the closest answer)? A. 3 B. 4 C What is the product of (8.5 x 0 7 )(6.3 x 0-5 )? A x 0-35 B C x x x 0 2

4 4. Which of the following is a prime number? A. B. 2 C None of these PracticeMathACT Test2 5. What is the simplest expanded form of (4x 2-3y) 2? A. 6x 4 + 9y 2 B. 6x 4-9y 2 C. 6x 4-2x 2 y + 9y 2 6x 4-24x 2 y + 3y 2 6x 4-24x 2 y + 9y 2 6. What is the product of the roots of the equation 2x 2 + 9x 8 = 0? A. -9 B. 9 C /2 7. What is the simplified form of the expression 3x 2 y 4 z 3 y 2 z 2 A. 2x 2 y 2 B. 2x 2 z 4 C. 2x 2 y 2 z 4 y 2 z 4 2x 2 y 2 2x 2 z 2 6y 2 z, written without negative exponents? 8. Graham and John both have summer jobs mowing lawns for a yard service. Graham gets paid a base rate of $0 per week, plus $8 for each lawn that he mows. John gets paid a base rate of $8 per week, plus $6 for each lawn that he mows. If in one week, Graham and John mow the same number of lawns and make the same amount of money, how many lawns do they each mow? A. /4 B. 2 C

5 PracticeMathACT Test2 9. The length of a fenced-in garden is 4 feet more than the square of its width. Which equation gives the length, l, of the garden in terms of its width, w? A. l = w B. l = w 2-4 C. l = 2w + 4 l = 2w - 4 l = (/2)w To convert a temperature from degrees Fahrenheit to degrees Celsius, you can use the formula C = (5/9)(F-32), where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius. How can this formula be written in terms of degrees Celsius? A. F = (5/9)C + 32 B. F = (9/5)C - 32 C. F = (9/5)(C + 32) F = (9/5)C + 32 F = (5/9)(C + 32) 2. What is the value of a if a = -4? A. -5 B. C In a set of numbers, the second number is 3 more than twice the first, and the third number is 7 less than 5 times the second. Which of the following is an expression that represents the sum of the three numbers in terms of the first number, x? A. 2x + 3 B. 0x + 3 C. 3x + 8x - 4 5x If a is an even integer and b is an odd integer, which of the following must be an even integer? A. a + b B. C. (a + b)2 4(a + b) (a b) 2 a b

6 24. Solve for x: 3(x+6) = 7(2x-) A. B. C PracticeMathACT Test2 25. What is the simplified form of the expression 3x 2 y 4 z 3 y 2 z 2 A. 2x 2 y 2 B. 2x 2 z 4 C. 2x 2 y 2 z 4 y 2 z 4 2x 2 y 2 2x 2 z 2 6y 2 z 26. If 2x + 3y = 3 and 2x - 4y = -, then what is the value of x + y? A. 2 2, written without negative exponents? B. 5 2 C What is the value of i 2 i? A. i B. -i C.

7 - 0 PracticeMathACT Test2 28. If f(x) = 4x 2 + 2, what is f(x - )? A. 4x B. 4x 2 2x + 6 C. 4x 2 8x + 4 4x 2 8x + 6 4x Which of the following represents the solution to -3 x ? A. 3 x 5 B. x -3 C. x 5 x -3 or x 5 - x 30. Which of the following is not in the domain of the function f(x) = A. 2 B. -3 C. 4-4 All of these are in the domain of f(x) x 2 + x 6 x 2 9x + 20? 3. What is the simplest form of A. (8x 5 y 4 z 3 ) B. 3x2 y 2 z (2xz) C. 9x 4 y 4 z (2xz) 3x2 y 2 z (xz) 3x2 y 2 z (2x 3 y 2 z 2 ) (xy 3 z) (3xy) (6x 3 z 2 )? 32. Find the next term in the following geometric sequence: 3x, 6x 2 y, 2x 3 y 2, A. 24x 3 y 2 z B. 24x 4 y 3 z 2 C. 8x 4 y 3 z 2 8x 4 y 3 24x 4 y 3

8 PracticeMathACT Test2 33. What is the solution set for the equation (4 x) = 5? A. {-2} B. {-3} C. {7} {29} Ø 34. What is the slope of the line represented by the equation 3x 4y = 7? A. 3 B C Find the equation of a line perpendicular to 6x 4y = 3 that goes through the point (-3,4) A. y = 3 2 x 3 4 y = 2 B. 3 x + 6 y = 2 C. 3 x + 2 y = 2 3 x 3 y = 3 2 x A map of a state park can be represented by placing it on a standard x-y coordinate plane. On this map, there is a ranger station located at the point (7, -2) and a trailhead located at the point (-3, 4). If each unit on the coordinate plane represents a quarter of a mile, about how many miles is the ranger station from the trailhead? A. 6 B C A circle on the standard x-y coordinate plane has a diameter with endpoints at (-4, 3) and (6, -5). What is the length of the radius of the circle?

9 A. 2 4 B. 4 C PracticeMathACT Test2 38. Which of the following equations represents the line in the given graph? y = 4 A. 3 x + 4 y = 4 B. 3 x + 4 y = 4 C. 3 x + 3 y = 3 4 x + 4 y = 3 4 x Which of the following number line graphs shows the solution to the inequality 3(x + 2) + < 4?

10 PracticeMathACT Test2 40. Megan s house is located at the point (5, 6) on the x-y coordinate plane. If Diana s house is located at (-3, -8), what are the coordinates of the point halfway between their two houses if a straight line is drawn between them? A. (4, 7) B. (-8, -4) C. (2, -2) (-4, -7) (, -) 4. A circle in the coordinate plane has the equation (x 2) 2 + (y + 3) 2 = 6. What is the circumference of the circle? A. 2π B. 4π C. 8π 9π 6π 42. What is the slope of the line between the points (3, 9) and (-2, 5) in the x-y coordinate plane? 5 4 A. B. 4 4 C Two similar triangles have a ratio of side lengths of 5:3. If the sides of the smaller triangle are 4 in, 7 in, and 0 in, what is the perimeter of the larger triangle?

11 A. 2.6 B. 2 C What is the area of the given figure? PracticeMathACT Test2 A. 48 ft 2 B. 56 ft 2 C. 2 ft 2 20 ft 3 68 ft Linel is tangent to circle C at A. If the radius of circle C is 5 and BC = 5, what is the length of segment AB?

12 PracticeMathACT Test2 A. 5 3 B. 5 2 C A circle has an area of 64π. What is the diameter of the circle? A. 4 B. 8 C The given pie chart shows students participation in after school sports. What is the measure of the central angle for the section representing the number of students that play golf?

13 A. 8 B C PracticeMathACT Test2 48. A sphere is inscribed in a cube whose faces each have an area of 36 ft 2. What is the volume of the sphere? V sphere = 4 3 πr3 A. 27π B. 36π C. 26π 288π 972π 49. In quadrilateral CDEF, CD FE. If CFE measures 50, what is the measure of CDE? A. 40 B. 50

14 C PracticeMathACT Test2 50. In rhombus FGKH, diagonal FK measures 6 cm and GK measures 5 cm. What is the length of diagonal HG, in cm? A. 4 B. 6 C A cylindrical well is no longer in use and is being filled with concrete. The well is 250 ft deep and has a radius of 4 ft. If the concrete is poured into the well at a rate of 75 cubic yards per hour, about how many hours will it take to fill the well? V cylinder = πr 2 h A B. 7.95

15 C PracticeMathACT Test2 52. A circular swimming pool is being built in a fenced in yard. If the dimensions of the yard are 0 yd by 5 yd and there must be at least one yard between the edge of the swimming pool and the fence, what is the radius of the largest swimming pool that can be built, in yards? A. 4 B. 4.5 C In the given figure, JM, the diameter of the circle, is 5 2, and JL LM. What is the area of JLM? A B. 25 2

16 C PracticeMathACT Test2 54. In the given diagram, QR measures ft, the radius of circle D is 3 ft, and QR and ST are both tangent to circle What is the area of the shaded region? A. 66 3π B. 33 6π C. 66 9π 66-6π 33 9π 55. In order for l and m to be parallel, which of the following must be true?

17 PracticeMathACT Test2 A. 2 and 3 are congruent B. 4 and 6 are supplementary C. 6 and 8 are supplementary and 7 are congruent 3 and 6 are supplementary 56. The measure of ZWX is 80. What is the measure of ZYX? A. 40 B. 80 C The sine of an angle θ between 90 and 80 is 8 7. What is tan(θ)?

18 8 A. 5 B C PracticeMathACT Test If 80 < θ < 270 and 4sin 2 θ = 3, what is the value of θ? A. 20 B. 50 C Which of the following is equivalent to (csc(θ)tan(θ))? cos( θ) A. B. C. cos 2 (θ) cos 2 (θ)

19 cos 3 (θ) sin 2 (θ) PracticeMathACT Test2 60. Jamie is sitting on a cliff looking down at a campsite. As she looks down, her line of vision makes an 8.5 angle with the horizon. If the campsite is 00 feet away from the base of the cliff, how tall is the cliff? A ft B ft C ft 0. ft ft ANSWER KEY IS ON THE NEXT PAGE Answer Key Question #: Correct Answer Hint E These numbers will be easier to compare if they re all in the same form. Try converting all of them to decimals. 2 B Start by moving all the variable terms to one side and all the constants to the other. 3 B Remember, a rational number is any number that can be written in the form a/b, where A and B are both integers. 4 D Be careful There are SIX tests total. Make sure to take that into account when computing the average 5 B Think about what percent of gas the car USED to go the first 76 miles. 6 D To find the probability that the candy is NOT blue, you need to find the

4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3

4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3 SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want