ACT Past Papers with Answers

Paper 52

ACT April 2012

Form 70G · Math Test · 60 questions

Back to sections

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

008 x 10

Source page for act-april-2012-form-70g-math-001

A1.008x 10BChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

A bowl contains l 00 jelly beans. of which 42 are red, 36 are blue, and 22 are green. What is the probability that a jelly bean picked at randorn from the bowl will NOT be red? 50 25 21 50 29 50 39 50

Source page for act-april-2012-form-70g-math-002

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

z is a perfect square such that 10 < z < 20 Which of the following integers could be the value yz ACT-70G 25 GO ON TO THE NEXT PAGE.

A32B48C56D72

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

In the figure below, the mea8ure of ZXAB is 150° the Measure of ZYCB is 81° and X, A, C, and Y are collinear. What is the measure of ZB ? DO YOUR FIGURING HERE. 150° 81°

A30"B51°C60°D69°E77°

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Which of the following nurnbcrs is a ,solution to l6=6x? 4+ff6

Source page for act-april-2012-form-70g-math-005

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Source question 6. Refer to the source image.

Source page for act-april-2012-form-70g-math-006

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Dakota bought a pair of shocb that had an original price of $70.00, The store offered a 20% discount on the original price of the shoes, and Dakota paid 6% sales tax on the discounled price of the shoes. How uch did Dakota pay for the shoes, including tax?

A$51.80B$52,64C$59.36D$60.20ES79.80

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

What is the value of x y Xy +xwhenx-_3 and H, 57 63

Source page for act-april-2012-form-70g-math-008

A-63B-57CChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

A toy car travels at a constant rate of I l inche8 every 5 seconds. At this rate, which of the following is clo.sest to the number offeet the caT travels in 2 minuteJ ? ACT-70G 15 GO ON TO THE NEXT PAGE.

A13B22C24D28

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Source question 10. Refer to the source image.

Source page for act-april-2012-form-70g-math-010

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Source question 11. Refer to the source image.

Source page for act-april-2012-form-70g-math-011

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Source question 12. Refer to the source image.

Source page for act-april-2012-form-70g-math-012

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Source question 13. Refer to the source image.

Source page for act-april-2012-form-70g-math-013

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

In the plane shown in the figure below, lines m and are cut by transversal line t. The 8 angles at the intersections of these lines are labeled. Which of the following statements, when it is true, CANNOT always be used to prove that lincs m and n arc parallel? DO YOUR FIGURING HERE.

A£1=£5BZl-Z7CZl=18DZ2-Z7EZ4=£5

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The dimengions of the right trianglc shown below are in feet. What i,g the area, in square feet, of the triangle? x+4 +2 x +5x+4

Source page for act-april-2012-form-70g-math-015

A8xBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

If flx) = x * I, what isf(-3) ? 10 13

Source page for act-april-2012-form-70g-math-016

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

What is the length, in feet, of the side of a square whose area. in square feet, is equal to the area of a 25-fooi-by-16-foot Ie¢tangle? 41 20 400 ACT-70G 17 GO ON TO THE NEXT PAGE.

Source page for act-april-2012-form-70g-math-017

A2fLoBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

One of the following is the value for September 2005 on the model curve. Which one7

Source page for act-april-2012-form-70g-math-018

A24B27C35DChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Whai is the average number of ski boats actually sold per tnonth between and including the months of January 21X)6 and April 2006 ? ACT-70G 18 GO ON TO THE NEXT PAGE

Source page for act-april-2012-form-70g-math-019

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

During the period shown in the grapb. each ski boat sold for exactly $30,000 before sales tax. On January I, 2006, the sales tax was increased froffl 690 to 7%. How much more was the total sales tax on the actual number of ski boats sold in July 2006 than on the actual number sold in July 2005 ? DO YOUR FIGURING HERE.

A$3,600B$5,400C$6.300D$9,000E$9,900

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

For nonzero real numbers a, b, and c, the expression is equivalent to: 5b' 5b' (L7bc) (5abe)' 12

Source page for act-april-2012-form-70g-math-021

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Akiko's average heart rate is 70 beats per minute. In scientific notation, how many times would her heart beat in 24 hours?

Source page for act-april-2012-form-70g-math-022

A1.44 x 10B1.68 x lo,C4.2x10DChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The lengths of the 3 sides of a triangle are in the ratio 5:6:9. The perimeter of the triangle is 100 inches. What is the length, in inches, of the longest side of the triangle? ACT-7¢)G 19 GO ON TO THE NEXT PAGE.

A10B25C30D45E50

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Given that sin A 20 25, which of the following values DO YOUR FIGURING HERE. could tan A equal? 20 15 20 20 15

Source page for act-april-2012-form-70g-math-024

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Which of the following sets of 3 numbers could be Ihe side lengths, in meters, of a right triangle?

AI, 1,1B2,3,5C3,4,7D4,9,13E6,8,10

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

When graphcd in the standard (x.y) coordinate plane. the line IT + 3y- l - O has a slope of:

Source page for act-april-2012-form-70g-math-026

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Which of the following expTessions is equivalent to (2x'+x+3)4(2x+l}+(3x-l)-(2x+2x+2x)? A, 2x +8x+3 ACT-7CG 20 GO ON TO THE NEXT PAGI Use the following information to answer questions 28-30. DO YOUR FIGURING HERE. Jason will have a rectangular concrete patio constructed beside his house, as shown below. The patio will have a length of 18 feet, and the top surface of the patio will have an area of 270 square feet. The patio will be constructed 50 that one side of the patio is against a side of Jason's house, Jason's house patio 18ft

Source page for act-april-2012-form-70g-math-027

A2x +2x+3B8x+3C2T+3DChoice D — see source imageEChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The patio will have a thickncss of 6 inches. The patio will consist of how many cubicfeet of concrete? 45 117

Source page for act-april-2012-form-70g-math-028

A108BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Jason chooses Tully's Concrete Finishing to seal his patio. Tully's Concrete Finishing uses the formula C- 3.5A + 120 to calculate the charge, C dollars, to seal a patio, where A square feet i,£ the area of the top surface of the patio. What will be the charge for sealing Jason's patio?

A$ 483B$ 945C$1,065D$1,128E$1,365

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Jason will plant shrubs along the portion of the perimeter of the patio that is NOT against his house. What is the Icngth, in feet, of that portion? K, 66 ACT.70G 21 GO ON TO THE NEXT PAGE.

A33B43.5C48D51

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

An airplane taking off from an airport climbs at a constant angle of ascent so that it will redch &n altitude of 10,000 fcet whcn the airplane has flown 8 miles, as illustrated in the figure below. Which of the following expressions gives the angle of ascent? (Note: I mile- 5,280 feet) DO YOUR FIGURING HERE. angle of ascent 8 miles 10,o(x> ft airport A, Arcgin 10,000 8(5,280) 10,000 8(5,280) 8(5,280) 8(5,280) 10,0

AArctanBAicsinCArccosDArctan

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Which of the following inequalities orders the 4 numbers Nf3. 1- 1.6, and - from largest to smallest? l->Nf3>->L.6 >1.6>sf3 >l->f3>1.6

Source page for act-april-2012-form-70g-math-032

A15>fvf3>1.6>-BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

What is the 7th term of the geometric sequence I, 10 16 64

Source page for act-april-2012-form-70g-math-033

A-32B56CChoice C — see source imageDChoice D — see source imageEChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The hypotenuse of LXPOM is PM. Which of the followins statements could be truc about LPOM ? The 3 sides of LPOM are congruent. ACT.70G 22 GO ON TO THE NEXT PAGE

AMO-OPBMP=OPCZM is a right angle.DThe 3 interior angles of LPOM are congrueni.

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Let LABC and ADEF be similar triangles such that the scale facior of AABC to LDEF is DO YOUR FIGURING HERE. The perimeter of LkABC is 20 inches. Whal is the petitneter of LDEF, in inches?

A13B25C30D40E45

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Planter's Greenhouse estimates its profit by subtracting its overhead costs from 40% of its net Stiles. Which of the following equations repre.sents this relationship between estimated profit (P), net sales (S), and overhead costs (C) of Planter's Greenhouse? 40 40 100 40 100

Source page for act-april-2012-form-70g-math-036

AP-S-BP-40C-SCP=40S-CDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

In right triangle APQR shown below, QR is 450 fcct long and the Tneasuie of ZR is 35" What is the length, in feel, of PQ ? 450 sin 35° 35° 450 450 450 tan 35°

Source page for act-april-2012-form-70g-math-037

A450 sin 35°B450 tan 35°CChoice C — see source imageDChoice D — see source imageEChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Which of the following is equivalent to 5+3x 3>0? x>0 x>3 ACT.7( 23 GO ON TO THE NEXT PAGE.

Source page for act-april-2012-form-70g-math-038

Ax>6BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Sofia and Lance are contributing a total of $2,500 per year to help their llephew pay foi college. Each yeaI, Lance contributes times the amount Sofia contributeb. What is thc amount, in dollars, Lance will contribute over a period of 4 year8? DO YOUR FIGURING HERE.

A$1.,250B$1,875C$4,000D$5,000E$6.000

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Which of the following is the least common denominator for 4 4x- 2)

A(x-B4(x+2)C(x-2)(x+2)D4(x- 2)(x * 2)E4(x- 2)'(x + 2)

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The circle shown below has a diameter of 6 cm. What is the area, in square centimeters, of the circle? 67r

A37[B97[C127[D36

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Which of thc following is an equation of the line that passes through (10.-2) and (-2.-5) in the standard (x,y) coordinate plane?

Source page for act-april-2012-form-70g-math-042

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

A health club surveyed 175 metnbeis about which types of equipment they had used in the past month. Of the 175 members, 117 had used treadmills, 89 had used staiion&ry bikes, and 53 had used both types of equipment. Some members had used neither type of equipment-. Of the 175 members, how many had used treadmills, stationary bikes, or both? 53 ACT.70G 24 GO ON TO THE NEXT PAGE.

Source page for act-april-2012-form-70g-math-043

A81B122C134D153EChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

What 18 the largest 2-digit integer that is divisible by 7 and is a multiple of 3 ? 21 42 98 DO YOUR FIGURING HERE.

Source page for act-april-2012-form-70g-math-044

A84BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

In the Siandard (x,y) coordinate plane, the line x + 6 is perpendicular to thc linc: -4x+6 4x+6

Source page for act-april-2012-form-70g-math-045

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

An emergency helicopter is located 2 miles north and 4 miles east of City Cenier. There is an emergency 22 miles south and 6 miles west of City Center. Which of the following is the distance, in miles, between the helicopter and the emergency.

A20B22C24D26E34

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The 3 statements given below are all true about certain positive integers x, y, and z. x is an even prime number

Source page for act-april-2012-form-70g-math-047

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The shaded region in the standard (x,y) coordinate plane bclow is bounded by a parabola and a line. The shaded region and its boundary is Ihe solution set of which of the following systems of inequalities? DO YOUR FIGURING HERE. >-2x +3 <-2x +3 <-2x +3 2x-3 2x+3 yg-2 2x+3

Source page for act-april-2012-form-70g-math-048

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

What is the value of y in the soluiion of the system of equations below? x+y= +b ACT-7 26 GO ON TO THE NEXT PAGE.

Source page for act-april-2012-form-70g-math-049

Aa+bBChoice B — see source imageCChoice C — see source imageDChoice D — see source imageEChoice E — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

In the circle shown below, central angle ZAOB measures 45°, and arc AB is X centimeters long. How many centimcters long is the circle's radius? DO YOUR FIGURING HERE. 4xf2

Source page for act-april-2012-form-70g-math-050

A16BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The solution to ax=

Source page for act-april-2012-form-70g-math-051

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

Consider the equation x 6x + k~ O. When solved for x, this equation will have exactly one real solution for which of the following values of k ?

Source page for act-april-2012-form-70g-math-052

A36BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

In the distance that Molly pushed the wheelbarrow shown below, the wheel rotated radians. The distance that Molly pushed the wheelbarrow is what fraclion of the circumference of the wheel? ACT-70G 27 GO ON TO THE NEXT PAGE.

Source page for act-april-2012-form-70g-math-053

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The domain of the function f(x) all Teal values of x EXCEVr: 100- Ixl contains DO YOUR FIGURING HERE. O and 100 Oand 100 and 100 100 and 100

Source page for act-april-2012-form-70g-math-054

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

In the figure below, E lies rectanglc ABCD. The area of LAED is what fraction of the area of rectangle ABCD ? of the way from B to C on io

Source page for act-april-2012-form-70g-math-055

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

A right square pyramid with equilateral triangular faces is shown in the figure below. The slant height of the pyramid is 3<3 inches. What Is the total length, in inches, of all 8 edges of the pyramid? H, 24

Source page for act-april-2012-form-70g-math-056

A12B21C36D48EChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

A circle in the standard (x,y) coordinate plane intersects the i-axis at (-7,0) and (1,0). The radius of the circle is 5 coordinate units. Which of the following could be the center of the circle?

Source page for act-april-2012-form-70g-math-057

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

What percent of the even numbers from 2 to 50, inclusive, have a units digit that is twice the tens digit? 4Yo 5Yo 16% DO YOUR FIGURING HERE.

Source page for act-april-2012-form-70g-math-058

A81.BChoice G — see source imageCChoice H — see source imageDChoice J — see source imageEChoice K — see source image

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

The graphs of f(x) and 8(x) are shown in the standard (x,y) coordinate planes below. One of the following exprestriions represent8 g(x) in term.s of f(x). Which one? -f(x-2)+4 -f(x+2)+4 f(x-2)-4 f(x+2)-4

Source page for act-april-2012-form-70g-math-059

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

Tools:

Paper 52 · ACT April 2012 · Form 70G · Math Test

A news anchor made the true statemcnt below. If il is rainlng, then the parade is cancelcd. Which of the following statements is logically equivalent to the news anchor's statement? END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT.7(M3 29

AIf it is not raining, then the parade is noi canceled.BThe parade is canccled if and only if it is raining.CIf it is not raining, then the parade is canceled.DIf the parade is canceled, then it is raining.EIf the parade is not canccled, then it is not raining.

Form 70G · Math Test · 60 questions

1 / 60