ACT Past Papers with Answers

Which of the following is a simplified form of tbe expression 4(2 + 5x) + 9 - 2x g 3x+17 7x+15

A point at (-2,8) in the standard (x,y) coordinate plane is shifted right 8 units and down 2 units. What are the new coordinates of the point? 14 GO ON TO THE NEXT PAGE. ACT.68G

In AABC, IA and ZC are congruent, and the measure of ZB is l14°. What is the ￿eaSllre of ZA ? 33° 60° 66°

ero. a positive value, but the value varies. a negative value, but the value varies.

What is an automobile's aveTage speed, in miles per hour, if it travels 60 miles in l- hours7 30 DO YOUR FIGURING HERE. 90

For the Equation sy + n m, which of the following expresslons gives y in terms of m and n ? m+n

The perimcter of & square is 24 feet. What is the area of. the square, in square feet? 72

What is 70/0 of 4.58 x Lo6 ? 3,206,000 320,600 16 GO ON TO THE NEXT PAGE. ACT.68G

Which of the following expressions is a factor of the expression x &¥+8? DO YOUR FIGURING HERE.

Given real nllmbers a, b, c, d, and e such that c < d, e < c, e > b, and b > a, which of these numbers is the gr¢ate81?

A llew operation, +, is defined on pairs of ordered pairs of integers as follows: (a,b) + (c,d) ac+bd 7b-cd" What is the value of (2,1) + (4,6) ? li

0 1,680 DO YOUR FIGURING HERE.

The figure below shows Mark's, Cal's, and Lakecia's houses at the 3 vertices of the right triangle fornied by 3 roads, The distances given in the figure ale in miles. Mark and Lakecia each make a trip frorri Mark's house to Lakecia's house. Mark takes Grapcvine Road. Lakecia takes Harbor Road to pick up Cal, and then takes Lott Road. How many miles shorter is Mark, trip than Lakecia's trip. Lakecia's house Grapevine Road Lott Road Mark's house 12 Harbor Road Cal's house

Which of the following is equivalent to (a ) 32a 24 32

For the function h(x) 4x h(-3) ? 15 45 . 153 3x, what is the value of

The Carousel Clothes Shop is advcrtising a sale featuring 3090 off the Marked price on any item. Which of the following gives the sale price, in dollars, of an item with a marked price of p dollars? F, 0.3p p-30p p+ 0.3p

Johnny is Sellkng lemonade. He paid $5.00 for his suppLies and charges $0,50 per glass of lemonade. Johnny's profit is found by subtracting his expenses from hks income. Which of the folLowing graphs represents his profit as a function of the number of glasses of lemonade he sells? 15 15 2 6 10 14 glasses of lemonade 2 6 10 14 glasses of lemonade 15 15 2 6 10 14 glasses of Lemonade .2..'6' 10 14 glasses of lemonade 15 2 6 10 14 glasses of lemonade

The positive integer n! is defined as the produci of all Ihe posktive integers less than or equal to n. For example, 31 1(2)(3) - 6. What is the value of the expression 3121 ACT-68G 19 GO ON TO THE NEXT PAGE.

Ms. Johnson. urchased 1,000 prizes for the school carnival for

A circle with a radius of l inch is inscribed in a square as shown below. What Es the area of the shaded region, in square inches?

For the polygon below, which of the following represents the length, in meters, of AE ? 20m 50° 50m 20 tan 50° 30 ian 50° 20 GO ON TO THE EXT PAGE. ACT-68G

Which of the following is a solution statement for the inequaliLy 3x - 7 < 5 + 9x ? -2<x -2>x l >x 2>x

The pep squad plans to make a circular sign in che shape of a basketball to hang on a wall for the game. The circle will have a radius of 4 feet, Which of the following is closest to the perimeter, in feet, of the circle? 50 -85 . 85

Source question 33. Refer to the source image.

In a laTge high school, some teachers teach only I subject, and some teachers teach more than I subject. Using the information given in the table below about the math, science, and gyin teachers in the school, how many teachers tsach math only. Nutnber of teachers Subject(s) taught at least I class of math at least I class of gym at least I class of science both gym and science but not math both math and science but not gy gyrn only math, gym, and sci¢nce 12 10 20 ACT-e8G 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questlons 35-37. The Environmental Club at Forrest Hills High School grows plants in the school's greenhouse. The members of the club sell the plants to raise nlouey for the school, and Sami and Jacque are taking an inventory of the plants. The table below gives the nllmbers of packs of plants. For example, theie are 60 packs of sunflowers with I plant per pack, 25 packs of petunias with 4 plants per pack, and 15 packs of tomatoes with 6 plants per pack. All of the packs have been counted except for the 6-plant packs of ruarigolds. Nutnber of l-plant packs 30 60 Number of 4-plant packs Number of 6-plant packs 15 Plants Tomatoes Marigolds Petunias Sunflowers 40 25 100 60

Helen takes all of the tornato plants in l-plant packs and puts them together to make as many 4-plant packs as she can. How many whole 4-plant packs of tomato plants can Helen make? 22 GO ON TO THE NEXT PAGE. ACT.t18G DO YOUR FIGURING HERE. Use the following information to answer questions 38-40. Parallelogram IVXYZ is shown in the standard (x,y) coordinate plane below. The coordinates for 3 of its vertices are W(O,O), X(a,b), and Z(c,O). X(a,b) w(o,o} Z(c,O)

Parallelogram WXYZ is rotated clockwise (c ) by 90° about the origin. At what ordered pair is the image of Z located? GO ON TO THE NEXT PAGE. ACT.68G 23

A liter is 1,000 cubic centimeters. Which of the following is closest to the height, in centimeters, of a cylindrical container, shown below, with diameter 10 cm and capacity I liter? (Note: The volume of'a cylinder with radius r and height h 18 K/h.) DO YOUR FIGURING HERE. 10

For World Litcrature clas3, Lenka must read Anna Karenina in 8 days. She reads 12 of the book each of the first 3 days. For the remaining 5 days, what fraction of the book, on average, must Lenka read per 12 20 20 25

Which of the following equations shows a correct use of the quadratic fonnula to solve x 5x+3-0? 25 - 4(1)(3) 2(1) 25 + 4(1)(3) 2(1) 25 - 4(1)(-3) 2(1) 25 - 4(1)(3) 2(1) 25 + 4(1)(3) 2(1) 24 GO ON TO THE NEXT PAGE. ACT.68G

A straight l O-foot-tall ladder is leaning against a house at an angle of 75° as shown in the figure below. Which of the following ¢xpre88ions gives the distance, in feet, the base of the ladder is from the house along the level ground? ladder 10 cos 75° 10 10 Lan 75° 75°

One of the following equations its graphed in the standard (x,y) coordknate plane below. Whxch one? -x+l -3x+2 A¢T.68G 25 GO ON TO THE NEXT PAGE.

Mr. Cleary's algebra class is discussing slopes of lines. The class is to graph the total cost, C, of buying h hamburgers that cost 99¢ each. Mr. Cleary asks the class to describe the slope between any 2 points (h,C) on the graph. Devon giv¢s a correct response that the sLope between any 2 points on Ihis graph is always: zero. a positive value, but the value varies. a negative value, but the value varies.

The volume of a cube is 64 cubic centimeters. What is the total surface area, in square centimeters, of the cube? 16 96 ACT.68G 26 GO ON TO THE NEXT P

In ￿ABC, the measure of ZA is 47° the measure of ZB is 76° and the length of BC is 18 centimeters. Which of the following is an expression for the length, kn centimeters, of AC ? (Note: The law of sines states that for any triangle, the ratios of the lengths of the Skdes to the sines of the angles opposite those sides are equal.) sin 47° 18 sin76° sin76° L8 sin47° 18 &in47° sin 76° 18 sin76° sin 47° (sin 47°)(sin 76°) 18 27 GO ON TO THE NEXT PAGE. AGT-68Q

The side of a square is I meters longer than the side of a Second square. How tnany meters lontrer is the diagonal of the first square than the diagonal of the second square? DO YOUR FIGURING HERE.

If x < 2, then x+2 -x+2 56, There are 25 buildings on Elm Street. Of ihese 25 buildings, 10 have fewer than 6 rooms, 10 have more than 7 rooms, and 4 have more than 8 rooms. What is the total number of buildings on Elm Street that have 6, 7, or 8 rooms? K, 15

Source question 56. Refer to the source image.

Ifcosx- what is the value of cos 2x ? Note: (cos x) i+cos2x

Letf(x) - fvfx and g(x) - lox + b. In the standard (x,y) coordinate plane, y -f(g(x)) passes through (4,6). What is the value of b ? -37 28 GO ON TO THE NEXT PAGE. ACT-68G

Source question 60. Refer to the source image.