ACT Past Papers with Answers

Paper 82

ACT January 2003

Form 59F · Math Test · 60 questions

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Carmen is playing with blocks. She arranges stacks of blocks so that each successive level of blocks has 1 fewer block than the level below it and the top level has 1 block. Such a stack with 3 levels is shown below. Carmen wants to make such a stack with 12 levels. How many blocks would she use to build this stack?

A66B78C132D144E156

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Paper 82 · ACT January 2003 · Form 59F · Math Test

To keep up with rising expenses, a motel manager needs to raise the $40.00 room rate by 22%. What will be the new rate?

A$40.22B$42.20C$48.00D$48.80E$62.00

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Paper 82 · ACT January 2003 · Form 59F · Math Test

As a salesperson, your commission is directly propor- tional to the dollar amount of sales you make. If your sales are $800, your commission is $112. How much commission would you earn if you had $1,400 in sales? level 1 level 2 level 3

A$210B$196C$175D$128E$ 64

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Paper 82 · ACT January 2003 · Form 59F · Math Test

The word average indicates arithmetic mean. 27 GO ON TO THE NEXT PAGE. ACT-59F-PRACTICE 2 2 2 2 7. What is the least common denominator for adding the fractions , , and ?

A40B120C180D480E1,440

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Paper 82 · ACT January 2003 · Form 59F · Math Test

The total cost of renting a car is $30.00 for each day the car is rented plus 28 ¢ for each mile the car is driven. What is the total cost of renting the car for 5 days and driving 350 miles? (Note: No sales tax is involved.)

A$ 104.75B$ 159.98C$ 249.75D$ 300.00E$1,147.50

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In any parallelogram ABCD, it is always true that the measures of ∠ABC and ∠BCD: 1 _ _ 2 58 __ 3

Aadd up to 180°.Badd up to 90°.Care each greater than 90°.Dare each 90°.Eare each less than 90°.

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Source question 7. Refer to the source image.

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

The product (2x4 y)(3x5 y8 ) is equivalent to: y9 y8 y9 y8 y8

A5x9B6x9C6x9D5x20E6x20

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Paper 82 · ACT January 2003 · Form 59F · Math Test

It costs a dollars for an adult ticket to a reggae concert and s dollars for a student ticket. The difference between the cost of 12 adult tickets and 18 student tickets is $36. Which of the following equations repre- sents this relationship between a and s ?

A= 36B216as = 36C⎪12a – 18s⎪ = 36D⎪12a + 18s⎪ = 36E⎪18a + 12s⎪ = 36

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Paper 82 · ACT January 2003 · Form 59F · Math Test

If x > 1, then which of the following has the LEAST value?

A公僓 xB公僓僓 2xC公僓僓僓僓 x · xDx公僓 xEx · x

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Charles defined a new operation, ♦, on pairs of ordered pairs of integers as follows: (a,b) ♦ (c,d) = . What is the value of (2,1) ♦ (3,4) ? ac + bd ____ ___ ab – cd 12a ___ _ 18s 3 _ _ 8 1 __ 12 4 __ 15

A–2B–1C2D5E10

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In the figure below, ∠BAC measures 30°, ∠ABC mea- sures 110°, and points B, C, and D are collinear. What is the measure of ∠ACD ?

A150°B140°C130°D120°E110°

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In the isosceles right triangle below, AB = 10 feet. What is the length, in feet, of AC ___ ?

A5B10C20D公僓僓 20E10公僓 2

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In a bag of 400 jelly beans, 25% of the jelly beans are red in color. If you randomly pick a jelly bean from the bag, what is the probability that the jelly bean picked is NOT one of the red jelly beans? 16 1 __ 16 3 _ _ 4 1 _ _ 4 1 _ _ 2 A B C 10′ A B C D 2 2 28 GO ON TO THE NEXT PAGE. ACT-59F-PRACTICE 2 2 2 2 15. What polynomial must be added to x2 – 2x + 6 so that the sum is 3x2 + 7x ? + 5x + 6 + 9x + 6 + 9x – 6 + 9x – 6 – 5x + 6

Source page for act-january-2003-form-59f-math-014

AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageE15 __64x273x283x292x2102x2

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Source question 15. Refer to the source image.

Source page for act-january-2003-form-59f-math-015

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

What is the slope of any line parallel to the line 8x + 9y = 3 in the standard (x,y) coordinate plane?

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A–8B–CChoice H — see source imageD3E8

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In the standard (x,y) coordinate plane, a line segment has its endpoints at (3,6) and (9,4). What are the coor- dinates of the midpoint of the line segment?

A( 3,–1)B( 3, 1)C( 6, 2)D( 6, 5)E(12,10)

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Paper 82 · ACT January 2003 · Form 59F · Math Test

When y = x2 , which of the following expressions is equivalent to –y ?

A(–x)2B–x2C–xDx–2Ex

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Paper 82 · ACT January 2003 · Form 59F · Math Test

For the function h(x) = 4x2 – 5x, what is the value of h(–3) ? 8 _ _ 3 8 _ _ 9

A–93B–9C21D51E159

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Paper 82 · ACT January 2003 · Form 59F · Math Test

For all triangles 䉭XYZ where side XZ __ _ is longer than side YZ __ _ , such as the triangle shown below, which of the following statements is true? sure of ∠Y. of ∠Y. sure of ∠Y. measure of ∠Y and sometimes equal to the mea- sure of ∠Y. measure of ∠Y and sometimes equal to the mea- sure of ∠Y.

AThe measure of ∠X is always less than the mea-BThe measure of ∠X is always equal to the measureCThe measure of ∠X is always greater than the mea-DThe measure of ∠X is sometimes less than theEThe measure of ∠X is sometimes greater than the

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Paper 82 · ACT January 2003 · Form 59F · Math Test

⎪7(–3) + 2(4)⎪ = ?

A–28B–13C13D28E29

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Paper 82 · ACT January 2003 · Form 59F · Math Test

If x > ⎪y⎪, which of the following is the solution state- ment for x when y = –4 ?

Ax is any real number.Bx > 4Cx < 4D–4< x < 4Ex > 4 or x < –4

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Paper 82 · ACT January 2003 · Form 59F · Math Test

The perimeter of a parallelogram is 72 inches, and 1 side measures 12 inches. What are the lengths, in inches, of the other 3 sides?

A12, 12, 36B12, 18, 18C12, 24, 24D12, 30, 30ECannot be determined from the given information

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Paper 82 · ACT January 2003 · Form 59F · Math Test

The lengths of the corresponding sides of 2 similar right triangles are in the ratio of 2:5. If the hypotenuse of the smaller triangle is 5 inches long, how many inches long is the hypotenuse of the larger triangle? X Y Z 2 2 29 GO ON TO THE NEXT PAGE. ACT-59F-PRACTICE 2 2 2 2 25. The sides of a square are 3 cm long. One vertex of the square is at (3,0) on a square coordinate grid marked in centimeter units. Which of the following points could also be a vertex of the square?

A2B2.5C7D10E12.56( 6, 0)7冸 4 ,1 冹8( 1, 2)9( 0, –2)10(–3, 0)

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Source question 25. Refer to the source image.

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AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In the circle shown below, M is the center and lies on RU __ _ _ and ST __ _ . Which of the following statements is NOT true? _ __ _ is parallel to RS __ _ ___ _ ≅ TM ___ _ __ _ ≅ SM ___ _

A∠TUM measures 65°BTUCTXU ២ measures 50°DRMERS

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Paper 82 · ACT January 2003 · Form 59F · Math Test

John Jones has decided to go into the business of pro- ducing and selling boats. In order to begin this venture, he must invest $10 million in a boat production plant. The cost to produce each boat will be $7,000, and the selling price will be $20,000. Accounting for the cost of the production plant, which of the following expres- sions represents the profit, in dollars, that John will realize when x boats are produced and sold?

A13,000x – 10,000,000B27,000x – 10,000,000C9,973,000xD20,000xE13,000x

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Paper 82 · ACT January 2003 · Form 59F · Math Test

If 2x2 + 6x = 36, what are the possible values of x ? R S T U X M 50° 1 _ _ 2 1 _ _ 2

A–12 and 3B–6 and 3C–3 and 6D–3 and 12E12 and 15

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Paper 82 · ACT January 2003 · Form 59F · Math Test

As a class experiment, a cart was rolled at a constant rate along a straight line. Shawn recorded in the chart below the cart’s distance (x), in feet, from a reference point at the start of the experiment and for each of 5 times (t), in seconds. t 0 1 2 3 4 5 x 10 14 18 22 26 30 Which of the following equations represents this data?

Ax = t + 10Bx = 4t + 6Cx = 4t + 10Dx = 10t + 4Ex = 14t

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Paper 82 · ACT January 2003 · Form 59F · Math Test

To increase the mean of 4 numbers by 2, by how much would the sum of the 4 numbers have to increase?

A2B4C6D8E16

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Meg pounded a stake into the ground. When she attached a leash to both the stake and her dog’s collar, the dog could reach 9 feet from the stake in any direc- tion. Using 3.14 for π, what is the approximate area of the lawn, in square feet, the dog could reach from the stake?

A28B57C113D254E283

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Television screen sizes are the diagonal length of the rectangular screen. Hector recently changed from watching a television with a 13-inch screen to a televi- sion with a similar 19-inch screen. If a boxcar appeared 8 inches long on the 13-inch screen, how long, to the nearest inch, will it appear on the 19-inch screen? 2 2 30 GO ON TO THE NEXT PAGE. ACT-59F-PRACTICE 2 2 2 2 33. In the figure below, ABCD is a square. Points are chosen on each pair of adjacent sides of ABCD to form 4 congruent right triangles, as shown below. Each of these has one leg that is twice as long as the other leg. What fraction of the area of square ABCD is shaded?

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A10B12C14D16E186Choice A — see source image7Choice B — see source image8Choice C — see source image9Choice D — see source image10Choice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Source question 33. Refer to the source image.

Source page for act-january-2003-form-59f-math-033

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

A surveyor took and recorded the measurements shown in the figure below. If the surveyor wants to use these 3 measurements to calculate the length of the pond, which of the following would be the most directly applicable? triangles triangles length of the side opposite ∠A, b is the length of the side opposite ∠B, and c is the length of the side opposite ∠C, a2 = b2 + c2 – 2bc cos(∠A) length of pond

AThe Pythagorean theoremBA formula for the area of a triangleCThe ratios for the side lengths of 30°-60°-90°DThe ratios for the side lengths of 45°-45°-90°EThe law of cosines: For any 䉭ABC, where a is the

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Which of the following is the graph of the equation 2x + y = 4 in the standard (x,y) coordinate plane?

Source page for act-january-2003-form-59f-math-035

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Which of the following figures in a plane separates it into half-planes?

AA lineBA rayCAn angleDA pointEA line segment

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Paper 82 · ACT January 2003 · Form 59F · Math Test

What is the maximum number of distinct diagonals that can be drawn in the hexagon shown below? x O –4 4 –4 y 4 x O –4 4 –4 y 4 x O –4 4 –4 y 4 x O –4 4 –4 y 4 x O –4 4 –4 y 4 2 2 31 GO ON TO THE NEXT PAGE. ACT-59F-PRACTICE 2 2 2 2 38. In the standard (x,y) coordinate plane, the center of the circle shown below lies on the x-axis at x = 4. If the circle is tangent to the y-axis, which of the following is an equation of the circle? + y2 = 4 + y2 = 16 – y2 = 16 + y2 = 4 + (y – 4)2 = 16

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A4B5C6D9E126Choice A — see source image7Choice B — see source image8Choice C — see source image9Choice D — see source image10Choice E — see source image11(x + 4)212(x – 4)213(x – 4)214(x – 4)215x2

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Source question 38. Refer to the source image.

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AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In what order should , , , and be listed to be arranged by increasing size?

A< < <B< < <C< < <D< < <E< < <

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Mai is putting gold foil around the outside of an ellip- tical picture frame. The perimeter of an ellipse is given by the formula p = , where h is the height and w is the width, as shown in the diagram below. If an elliptical frame has an outside height equal to 4 inches and an outside width equal to 3 inches, what is its outside perimeter, in inches?

Aπ公僓 2Bπ公僓 2C5π公僓 2D(4公僓 2 + 3)E(4π + 3)公僓 2

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Paper 82 · ACT January 2003 · Form 59F · Math Test

If + = and A, B, and x are integers greater than 1, then what must x equal? 7A + 2B _____ ___ x B ___ 105 A __ 30 π _ _ 2 7 _ _ 2 5 _ _ 2 w h 公僓僓僓僓僓僓僓僓 2(h2 + w2 ) π _ _ 2 9 _ _ 8 7 _ _ 4 6 _ _ 5 5 _ _ 3 7 _ _ 4 5 _ _ 3 9 _ _ 8 6 _ _ 5 6 _ _ 5 9 _ _ 8 5 _ _ 3 7 _ _ 4 5 _ _ 3 7 _ _ 4 6 _ _ 5 9 _ _ 8 7 _ _ 4 5 _ _ 3 6 _ _ 5 9 _ _ 8 9 _ _ 8 6 _ _ 5 7 _ _ 4 5 _ _ 3 x y O 4 Kaylee is planning to purchase a car. She will need to borrow some of the money and has a chart, shown below, to use to approximate her monthly payment. The chart gives the approximate monthly payment per $1,000 borrowed. Monthly payment per $1,000 borrowed for various annual rates and various numbers of payments Number of monthly payments Annual interest rate 36 48 60 5% $29.97 $23.03 $18.87 8% $31.34 $24.41 $20.28 10% $32.27 $25.36 $21.24 12% $33.22 $26.34 $22.24

A9B135C210D630E3,150

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Kaylee found a used car she is thinking about pur- chasing. The list price is $8,795. She calculates that she will need to borrow $6,500. Approximately what would her monthly payment be if she borrowed the money for 36 months at an annual interest rate of 10% ?

A$164.84B$171.21C$209.76D$234.72E$283.81

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Paper 82 · ACT January 2003 · Form 59F · Math Test

A local dealership is having an end-of-the-model-year clearance sale and is offering 5% annual interest on new-car loans for 36, 48, or 60 months. The maximum amount Kaylee can budget for her monthly car pay- ment is $300. Of the following loan amounts, which one is the maximum Kaylee can borrow at 5% annual interest and stay within her budget?

A$10,000B$13,000C$14,000D$15,000E$20,000

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Another dealership is offering 5-year loans with a 9% annual interest rate. Kaylee uses her chart to esti- mate the payment per $1,000 borrowed. Of the fol- lowing, which is most likely the monthly payment per $1,000 borrowed? 2 2 Use the following information to answer questions 42–44. 32 GO ON TO THE NEXT PAGE. ACT-59F-PRACTICE 2 2 2 2 45. In 䉭ABC, shown below, the measure of ∠B is 41°, the measure of ∠C is 34°, and AB __ _ is 25 units long. Which of the following is an expression for the length, in units, of BC ___ ? (Note: The law of sines states that, for any triangle, the ratios of the sines of the interior angles to the lengths of the sides opposite those angles are equal.)

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A$20.52B$20.76C$20.85D$21.00E$21.746Choice A — see source image7Choice B — see source image8Choice C — see source image9Choice D — see source image10Choice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Source question 45. Refer to the source image.

Source page for act-january-2003-form-59f-math-045

AChoice A — see source imageBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

For i2 = –1, (4 + i)2 = ?

A15B17C15 + 4iD15 + 8iE16 + 4i

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Paper 82 · ACT January 2003 · Form 59F · Math Test

If r and s can be any integers such that s > 10 and 2r + s = 15, which of the following is the solution set for r ?

Ar ≥ 3Br ≥ 0Cr ≥ 2Dr ≤ 0Er ≤ 2

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Which of the following expressions has a positive value for all x and y such that x > 0 and y < 0 ? y y2 x2 __ y 25 sin34⬚ _ ________ sin75⬚ 25 sin41⬚ _ ________ sin105⬚ 25 sin75⬚ _ ________ sin41⬚ 25 sin105⬚ _ _________ sin34⬚ 25 sin105⬚ _ _________ sin41⬚ A C B ? 34° 41° 25 units

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Ay – xBx + yCx3DChoice J — see source imageEx __

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Paper 82 · ACT January 2003 · Form 59F · Math Test

What is the value of log2 8 ?

A3B4C6D10E16

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In the right triangle below, the measure of ∠C is 90°, AB = 5 units, and CB = 2 units. What is tan B ?

Source page for act-january-2003-form-59f-math-050

AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

A flight instructor charges $50 per lesson, plus an additional fee for the use of his plane. The charge for the use of the plane varies directly with the square root of the time the plane is used. If a lesson plus 16 min- utes of plane usage costs $90, what is the total amount charged for a lesson having 36 minutes of plane usage?

A$185B$150C$135D$110E$ 60

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In 䉭ABD, shown below, C is on BD __ _ , the length of AD ___ is 6 inches, and sin d = 0.8. How many inches long is CD ___ ?

A1.2B1.8C3.6D4.8ECannot be determined from the given information

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Paper 82 · ACT January 2003 · Form 59F · Math Test

For real numbers a and b, when is the equation ⎪a + b⎪ = ⎪a – b⎪ true? 6 ? A B C D d 2 _ _ 5 3 _ _ 5 公僓僓 21 ____ _ 5 3 _ _ 2 公僓僓 21 ____ _ 2 A 5 B C 2 2 2 33 ACT-59F-PRACTICE 2 2 2 2 54. As shown below, rectangle ABCD is divided into 2 large squares (labeled L) each x inches on a side, 15 small squares (labeled S) each y inches on a side, and 13 rectangles (labeled R) each x inches by y inches. What is the total area, in square inches, of ABCD ? + 15y2 + 8xy + 15y2 + 13xy + 15y2

AAlwaysBOnly when a = bCOnly when a = 0 and b = 0DOnly when a = 0 or b = 0ENever62x + 13xy + 15y76x + 16y82x292x2102x2

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Source question 54. Refer to the source image.

Source page for act-january-2003-form-59f-math-054

AChoice F — see source imageBChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

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Paper 82 · ACT January 2003 · Form 59F · Math Test

For some real number A, the graph of the line y = (A + 1)x + 8 in the standard (x,y) coordinate plane passes through (2,6). What is the slope of this line?

A–4B–3C–1D3E7

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Paper 82 · ACT January 2003 · Form 59F · Math Test

The graph of the equation h = –at2 + bt + c, which describes how the height, h, of a hit baseball changes over time, t, is shown below. If you alter only this equation’s c term, which gives the height at time t = 0, the alteration has an effect on which of the following? I. The h-intercept II. The maximum value of h III. The t-intercept h O height time t A C D B L R R R S S S S S S S S S S S S S S S R R R R R R R R R R L

AI onlyBII onlyCIII onlyDI and III onlyEI, II, and III

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Paper 82 · ACT January 2003 · Form 59F · Math Test

When graphed in the standard (x,y) coordinate plane, the lines x = –3 and y = x – 3 intersect at what point?

A( 0, 0)B( 0,–3)C(–3, 0)D(–3,–3)E(–3,–6)

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Paper 82 · ACT January 2003 · Form 59F · Math Test

In pentagon ABCDE, shown below, ∠A measures 50°. What is the total measure of the other 4 interior angles?

A130°B200°C310°D432°E490°

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Paper 82 · ACT January 2003 · Form 59F · Math Test

For all real numbers b and c such that the product of c and 3 is b, which of the following expressions repre- sents the sum of c and 3 in terms of b ?

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Ab + 3B3b + 3C3(b + 3)DChoice D — see source imageE+ 3

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Paper 82 · ACT January 2003 · Form 59F · Math Test

Which of the following expresses the number of meters a contestant must travel in a 3-lap race where the course is a circle of radius R meters? b _ _ 3 b + 3 ___ _ _ 3 A 50° C D E B 2 2 END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST.

A3RB3πRC3πR2D6RE6πR

Form 59F · Math Test · 60 questions

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