ACT Past Papers with Answers

Paper 61 · ACT June 2009 · Form 67C · Math Test

If r = 9, b = 5, and g = −6, what does (r + b − g)(b + g) equal?

Paper 61 · ACT June 2009 · Form 67C · Math Test

A copy machine makes 60 copies per minute. A second copy machine makes 80 copies per minute. The second machine starts making copies 2 minutes after the first machine starts. Both machines stop making copies 8 minutes after the first machine started. Together, the 2 machines made how many copies?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Marlon is bowling in a tournament and has the highest average after 5 games, with scores of 210, 225, 254, 231, and 280. In order to maintain this exact average, what must be Marlon’s score for his 6th game?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Joelle earns her regular pay of $7.50 per hour for up to 40 hours of work in a week. For each hour over 40 hours of work in a week, Joelle is paid 1 times her regular pay. How much does Joelle earn for a week in which she works 42 hours?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Which of the following mathematical expressions is equivalent to the verbal expression “A number, x, squared is 39 more than the product of 10 and x” ? = 390 − 10x = 390 + 00x10 = 390 + 10x

Paper 61 · ACT June 2009 · Form 67C · Math Test

If 9(x − 9) = −11, then x = ? 9 2 _ _ 9 11 _ __ 9 20 _ __ 9 92 _ __ 9 1 _ _ 2 GO ON TO THE NEXT PAGE.

Paper 61 · ACT June 2009 · Form 67C · Math Test

Discount tickets to a basketball tournament sell for $4.00 each. Enrico spent $60.00 on discount tickets, $37.50 less than if he had bought the tickets at the regular price. What was the regular ticket price?

Paper 61 · ACT June 2009 · Form 67C · Math Test

The expression (3x − 4y2 )(3x + 4y2 ) is equivalent to: − 16y4 − 08y4 + 16y4 − 16y4 − 08y4

Paper 61 · ACT June 2009 · Form 67C · Math Test

A rectangle has an area of 32 square feet and a perimeter of 24 feet. What is the shortest of the side lengths, in feet, of the rectangle?

Paper 61 · ACT June 2009 · Form 67C · Math Test

In 䉭ABC, the sum of the measures of ∠A and ∠B is 47°. What is the measure of ∠C ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

In the school cafeteria, students choose their lunch from 3 sandwiches, 3 soups, 4 salads, and 2 drinks. How many different lunches are possible for a student who chooses exactly 1 sandwich, 1 soup, 1 salad, and 1 drink?

Paper 61 · ACT June 2009 · Form 67C · Math Test

For 2 consecutive integers, the result of adding the smaller integer and triple the larger integer is 79. What are the 2 integers?

Paper 61 · ACT June 2009 · Form 67C · Math Test

A function f(x) is defined as f(x) = −8x2 . What is f(−3) ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

If 3x = 54, then which of the following must be true?

Paper 61 · ACT June 2009 · Form 67C · Math Test

What is the least common multiple of 70, 60, and 50 ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Hot Shot Electronics is designing a packing box for its new line of Acoustical Odyssey speakers. The box is a rectangular prism of length 45 centimeters, width 30 centimeters, and volume 81,000 cubic centimeters. What is the height, in centimeters, of the box?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Four points, A, B, C, and D, lie on a circle having a circumference of 15 units. B is 2 units counterclockwise from A. C is 5 units clockwise from A. D is 7 units clockwise from A and 8 units counterclockwise from A. What is the order of the points, starting with A and going clockwise around the circle?

Paper 61 · ACT June 2009 · Form 67C · Math Test

A group of cells grows in number as described by the equation y = 16(2)t , where t represents the number of days and y represents the number of cells. According to this formula, how many cells will be in the group at the end of the first 5 days? GO ON TO THE NEXT PAGE. ACT-67C-PRACTICE 2 2 18263 Preparing ACT 2012-13_5003 AAP Prep for ACT 6/8/12 9:34 AM Page 27

Paper 61 · ACT June 2009 · Form 67C · Math Test

The length of a rectangle is 3 times the length of a smaller rectangle. The 2 rectangles have the same width. The area of the smaller rectangle is A square units. The area of the larger rectangle is kA square units. Which of the following is the value of k ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

(a + 2b + 3c) − (4a + 6b − 5c) is equivalent to:

Paper 61 · ACT June 2009 · Form 67C · Math Test

The dimensions of the right triangle shown below are given in feet. What is sin,θ ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

In a basketball passing drill, 5 basketball players stand evenly spaced around a circle. The player with the ball (the passer) passes it to another player (the receiver). The receiver cannot be the player to the passer’s immediate right or left and cannot be the player who last passed the ball. A designated player begins the drill as the first passer. This player will be the receiver for the first time on which pass of the ball? c _ _ a b _ _ a b _ _ c a _ _ c a _ _ b b c a θ 1 _ _ 3 1 _ _ 9

Paper 61 · ACT June 2009 · Form 67C · Math Test

Lines p and n lie in the standard (x,y) coordinate plane. An equation for line p is y = 0.12x + 3,000. The slope of line n is 0.1 greater than the slope of line p. What is the slope of line n ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

The expression −8x3 (7x6 − 3x5 ) is equivalent to: + 24x8 − 24x8 + 24x15 − 24x15

Paper 61 · ACT June 2009 · Form 67C · Math Test

−3⏐−6 + 8⏐ = ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

In right triangle 䉭ACE below, BD ___ is parallel to AE ___ , and BD ___ is perpendicular to EC ___ at D. The length of AC ___ is 20 feet, the length of BD ___ is 3 feet, and the length of CD ___ is 4 feet. What is the length, in feet, of AE ___ ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

As part of a lesson on motion, students observed a cart rolling at a constant rate along a straight line. As shown in the chart below, they recorded the distance, y feet, of the cart from a reference point at 1-second intervals from t = 0 seconds to t = 5 seconds. Which of the following equations represents this data? t 0 1 2 3 4 5 y 14 19 24 29 34 39 A E B D C ? 3 4 20 GO ON TO THE NEXT PAGE. ACT-67C-PRACTICE 2 2 28 18263 Preparing ACT 2012-13_5003 AAP Prep for ACT 6/8/12 9:34 AM Page 28 29

Paper 61 · ACT June 2009 · Form 67C · Math Test

The inequality 6(x + 2) > 7(x − 5) is equivalent to which of the following inequalities?

Paper 61 · ACT June 2009 · Form 67C · Math Test

The sides of a square are 3 cm long. One vertex of the square is at (2,0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square?

Paper 61 · ACT June 2009 · Form 67C · Math Test

For 䉭FGH, shown below, which of the following is an expression for y in terms of x ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

A bag contains 12 red marbles, 5 yellow marbles, and 15 green marbles. How many additional red marbles must be added to the 32 marbles already in the bag so that the probability of randomly drawing a red marble is ? 3 _ _ 5 公僓僓僓僓僓 僓 x2 + 16 公僓僓僓僓僓 僓 x2 − 16 公僓僓僓僓 僓 x2 + 8 公僓僓僓僓 僓 x2 + 4 x meters y meters 4 meters H F G

Paper 61 · ACT June 2009 · Form 67C · Math Test

What are the quadrants of the standard (x,y) coordinate plane below that contain points on the graph of the equation 4x − 2y = 8 ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

The graph of y = −5x2 + 9 passes through (1,2a) in the standard (x,y) coordinate plane. What is the value of a ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Jerome, Kevin, and Seth shared a submarine sandwich. Jerome ate of the sandwich, Kevin ate of the sandwich, and Seth ate the rest. What is the ratio of Jerome’s share to Kevin’s share to Seth’s share?

Paper 61 · ACT June 2009 · Form 67C · Math Test

A particular circle in the standard (x,y) coordinate plane has an equation of (x − 5)2 + y2 = 38. What are the radius of the circle, in coordinate units, and the coordinates of the center of the circle? radius center 1 _ _ 2 1 _ _ 3 y x II I III IV O quadrants of the standard (x,y) coordinate plane GO ON TO THE NEXT PAGE. ACT-67C-PRACTICE 2 2 18263 Preparing ACT 2012-13_5003 AAP Prep for ACT 6/8/12 9:34 AM Page 29

Paper 61 · ACT June 2009 · Form 67C · Math Test

The figure below consists of a square and 2 semicircles, with dimensions as shown. What is the outside perimeter, in centimeters, of the figure?

Paper 61 · ACT June 2009 · Form 67C · Math Test

In the figure below, points E and F are the midpoints of sides AD ___ and BC ___ of rectangle ABCD, point G is the intersection of AF ___ and BE ___ , and point H is the intersection of CE ___ and DF ___ . The interior of ABCD except for the interior of EGFH is shaded. What is the ratio of the area of EGFH to the area of the shaded region?

Paper 61 · ACT June 2009 · Form 67C · Math Test

The coordinates of the endpoints of CD ___ , in the standard (x,y) coordinate plane, are (−4,−2) and (14,2). What is the x-coordinate of the midpoint of CD ___ ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

What is the surface area, in square inches, of an 8-inch cube? A E D B F C H G 8 cm 8 cm

Paper 61 · ACT June 2009 · Form 67C · Math Test

The equations below are linear equations of a system where a, b, and c are positive integers. ay + bx = c ay − bx = c Which of the following describes the graph of at least 1 such system of equations in the standard (x,y) coordinate plane? I. 2 parallel lines II. 2 intersecting lines III. A single line

Paper 61 · ACT June 2009 · Form 67C · Math Test

According to the measurements given in the figure below, which of the following expressions gives the distance, in miles, from the boat to the dock?

Paper 61 · ACT June 2009 · Form 67C · Math Test

The circle graph below shows the distribution of registered voters, by age, for a community. Registered voters are randomly selected from this distribution to be called for jury duty. What are the odds (in the age range:not in the age range) that the first person called for jury duty is in the age range of 25−35 years? 18–24 25–35 36–44 45–55 56 and up Distribution of Registered Voters byAge 8% 42% 14% 25% 11% 30 _ ______ sin52° 30 _ ______ cos52° lighthouse dock 52° boat 30 miles GO ON TO THE NEXT PAGE. ACT-67C-PRACTICE 2 2 30 18263 Preparing ACT 2012-13_5003 AAP Prep for ACT 6/8/12 9:34 AM Page 30 31 The figure below shows the design of a circular stained- glass panel on display at Hopewell’s Antique Shop. Seams separate the pieces of the panel. All red triangular pieces shown are congruent and have a common vertex with each adjoining triangular piece. The 2 squares shown are inscribed in the circle. The diameter of the panel is 2 feet.

Paper 61 · ACT June 2009 · Form 67C · Math Test

The design of the stained-glass panel has how many lines of symmetry in the plane of the panel?

Paper 61 · ACT June 2009 · Form 67C · Math Test

What is the area of the stained-glass panel, to the nearest 0.1 square foot?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Kaya wants to install a new circular stained-glass window in her living room. The design of the window will be identical to that of the panel. The diameter of the new window will be 75% longer than the diameter of the panel. The new window will be how many feet in diameter? red piece orange piece seam 2 feet yellow piece

Paper 61 · ACT June 2009 · Form 67C · Math Test

In the figure below, AB ___ 储 CD ___ , AE ___ bisects ∠BAC, and CE ___ bisects ∠ACD. If the measure of ∠BAC is 82°, what is the measure of ∠AEC ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

In the circle shown below, chords TR ___ and QS ___ intersect at P, which is the center of the circle, and the measure of ∠PST is 30°. What is the degree measure of minor arc RS ២ ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

For what value of a would the following system of equations have an infinite number of solutions? 2x – 0y = 80 6x – 3y = 4a 30° T Q P R S ? A B D C E GO ON TO THE NEXT PAGE. ACT-67C-PRACTICE 2 2 Use the following information to answer questions 44–46. 18263 Preparing ACT 2012-13_5003 AAP Prep for ACT 6/8/12 9:34 AM Page 31 Marcia makes and sells handcrafted picture frames in 2 sizes: small and large. It takes her 2 hours to make a small frame and 3 hours to make a large frame. The shaded triangular region shown below is the graph of a system of inequalities representing weekly constraints Marcia has in making the frames. For making and selling s small frames and l large frames, Marcia makes a profit of 30s + 70l dollars. Marcia sells all the frames she makes.

Paper 61 · ACT June 2009 · Form 67C · Math Test

The weekly constraint represented by the horizontal line segment containing (9,2) means that each week Marcia makes a minimum of:

Paper 61 · ACT June 2009 · Form 67C · Math Test

For every hour that Marcia spends making frames in the second week of December each year, she donates $3 from that week’s profit to a local charity. This year, Marcia made 4 large frames and 2 small frames in that week. Which of the following is closest to the percent of that week’s profit Marcia donated to the charity?

Paper 61 · ACT June 2009 · Form 67C · Math Test

What is the maximum profit Marcia can earn from the picture frames she makes in 1 week? l s 0 2 4 6 8 10 8 6 4 2 0 number of small frames number of large frames (0,8) (9,2)

Paper 61 · ACT June 2009 · Form 67C · Math Test

The determinant of a matrix 冤 冥 equals ad − cb. What must be the value of x for the matrix 冤 冥 to have a determinant of −16 ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

A formula for finding the value, A dollars, of P dollars invested at i% interest compounded annually for n years is A = P(1 + 0.01i)n . Which of the following is an expression for P in terms of i, n, and A ? n

Paper 61 · ACT June 2009 · Form 67C · Math Test

If x and y are real numbers such that x > 1 and y < −1, then which of the following inequalities must be true? 2 > ⏐y⏐ + 1 > y2 + 1 > y−2 x _ _ 3 y _ _ 3 x _ _ y A _________ _ (1 + 0.01i)n A _________ _ (1 − 0.01i)n A _ _______ _ 1 + 0.01i 8 _ _ 3 8 _ _ 5 x x 8 x a c b d GO ON TO THE NEXT PAGE. ACT-67C-PRACTICE 2 2 Use the following information to answer questions 50–52. 32 18263 Preparing ACT 2012-13_5003 AAP Prep for ACT 6/8/12 9:34 AM Page 32 33

Paper 61 · ACT June 2009 · Form 67C · Math Test

Triangles 䉭ABC and 䉭PQR are shown below. The given side lengths are in centimeters. The area of 䉭ABC is 30 square centimeters. What is the area of 䉭PQR, in square centimeters?

Paper 61 · ACT June 2009 · Form 67C · Math Test

Triangle 䉭ABC is shown in the figure below. The measure of ∠A is 40°, AB = 18 cm, and AC = 12 cm. Which of the following is the length, in centimeters, of BC ___ ? (Note: For a triangle with sides of length a, b, and c opposite angles ∠A, ∠B, and ∠C, respectively, the law of sines states = = and the law of cosines states c2 = a2 + b2 − 2ab cos,∠C.) + 182 − 2(12)(18) cos 40° 公僓僓僓僓僓僓僓 僓 122 + 182 公僓僓僓僓僓僓僓 僓 182 − 122 C B 40° A 18 cm 12 cm sin ∠A ___ ___ a sin ∠B ___ ___ b sin ∠C ___ ___ c 70° A B C x y 110° Q R P x y

Paper 61 · ACT June 2009 · Form 67C · Math Test

What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13 ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

In the equation x2 + mx + n = 0, m and n are integers. The only possible value for x is –3. What is the value of m ?

Paper 61 · ACT June 2009 · Form 67C · Math Test

The solution set of which of the following equations is the set of real numbers that are 5 units from −3 ? ACT-67C-PRACTICE 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. 18263 Preparing ACT 2012-13_5003 AAP Prep for ACT 6/8/12 9:34 AM Page 33