ACT Past Papers with Answers

Tbe top surface of a rectangular table has an area of 144 square feet and a width of 4 feet. What is the length, in feet, of the surface? 12 140

+x 36 DO YOUR FIGURING HERE.

The first question on a 2-question quiz offers 2 answers, and exactly l answer must be chosen. The second question offers 5 answers, and exactly l answer musi be chosen. Thc quiz has how many possible combinations of answers?. 10 25 ACT-70C GO ON TO THE NEXT PAGE. For what value of x is the equation 2(x true?

Source question 8. Refer to the source image.

What value of a will make the equation true? 4+a 9+a 19 30

The I st term in the oeometric sequence below is -6. If it can be detern]ined, what ks the 6th term? -6, 12, -24, 48, -96, 192 144 144 192

In the standard (x,),) coordinate plane, A has coordinates (-4,-9), Point A is translatcd 4 units to the right and 9 units up and labeled A,. What are the coordinates of A, ?

A formula used to compute the volume, V, of a rectangular prism is V - livh, where l is the length of the base, w is the ￿,]dth of the base, and h is the height of the prism. What is the height, in centimeters. of a rectangular prism that has a volume of 510 cubic centimeters and a base that measures 5 centimeters by 12 centimeters?

Solar panels that produce 150 amps of electric current each are needed for a proposed space station. If the solar panels are manufactured to produce 0.75 amps per square meter of surface area, the surface area of cach solai panel needs to be how many square meters? 20 75 DO YOUR FIGURING HERE.

Which of the following expressions is equivalent to

In the standard (x,y) coordinate plane, the coordinates of the endpoints of DM are (11,3) and (17,15). What is the y-coordinate of the midpoint of DM ?

The expression 5 - 3(2x- l) is equivalent to: -2+4x 2-6x 8-5x 9-6x

Which of the following anLTle measures CANNOT be the measure of any angle in an obiuse triantsle? (Note: An obtuse triangle is a triangle that has l anole WLth a measure greater than 90° but less than 180°.) 30° 90°

What is the value of f(-5) when f(x) -3(x' + 3x + 2) 151+15 19 10 12 25 19 io ACT-70C 18 GO ON TO THE NEXT PAGE.

In the standard (x,y) coordinate plane, what LS the slope of the line with equation 3.¥ + 2y- 6 ? DO YOUR FIGURING HERE.

Which of the following is a simplified form of 45 ? 5<5

A formuIa for simple interest is l = Prt, where l is the interest in dollars, P is the principal in dollars, r is the annual interest rate expressed as a decimal, and t is the time in years the money is invested. Which of the following expressions gives t when the annual interest rate is 5(Yo

What is the lenoth, in meters, of BC ? 10 20 52

Which of the following statements about the measures of the interior angles in AABC is true? (Note: MZA represents the degree measure of ZA.) niZA = InZB mZB= nizc FnZA - MZB + MZC ntZB + mZC= 180° MZA + 171ZB + mZC= 360°

Which of the following expressions iepresents cos B ? AC AB BC AC BC AC AB BC AB

Given the functions f and g defined by f(x) = x + 3 and g(x) x + I, what is the value of flg(l)) ? 20 GO ON TO THE NEXT PAGE. ACT-7(

Which of the following expressions is equivalent to DO YOUR FIGURING HERE.

Mar.%ha is making a sail for a model boat. In the figure below, the sail is represented by LABC. Base BC is 18 inches long, and legs AB and AC are each 15 inches long. The mast, represented by AD, is perpendicular to the base and extends 4 inches below tbe bottom of the sail. How many inches long 18 the mast? 15 15 18

Which of the following inequalities orders the nuTnbers below fiom least to greaiest? (-3.5) < 3- < 3- ACT-70C 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information lo answer questions 33-35. The table below gives the prices for dog orooming at Pretty Pooches. Size of dog Shampoo Haircut Small Large $20 $35 $30 $55

Hoakoa brouoht 10 dogs to Pretty Poochcs and paid $260 to have all 10 shampooed. How many large dogs did Hoakoa have shampooed?

When the owner of Pretty Pooches increases the price to have a small dog shampooed, the number of small dogs shampooed per day decreases. The expiession ax + b represents the number of small dogs shampooed in I day whenever the price is x dollars per dog. The number of small doos shampooed per day was 12 when the price in the table was in effect. The niimber of small dogs shampooed per day decreases by 2 for every $5 increase in price. What are the values of a andb? 62 20 200 ACT-70C 22 GO ON TO THE NEXT PAGE. 36. DO YOUR FIGURING HERE.

Source question 36. Refer to the source image.

In the standard (x,y) coordinate plane, what is the x-intercept of the line represented by y = _2x + 8 ?

A toy rocket is launched from the ground. Its height, h feet above the ground, t seconds after it is launched, is given by h 161 + 48t. During the rocket's ascent, at what value of t is the rocket 32 feet above the ground?

Which of the following graphs illustrates the solution set for the system of inequalities 3x 2>9 and -2x>-10? empty set ACT-70C 23 GO ON TO THE NEXT PAGE.

During a competition, a swimmer will be swimming the width of a river. from X io Y in the figure below. The swimmer wants to know how wide the river is. The right triangle shows the measurements the swimmer obtained by walking 100 feet from X to Z, sighting to Y from both points. From this siuhting, it is determined that the measure of ZZ is 40° How wide, in feet, is the liver? 40° 100 loo sin 40° 100 tan 40°

The figure below shows a support wire for a television transmission tower. The wire, which is fastened to the tower at a point 125 feet above the level ground: has an angle of elevation of 65° Which of the following expressions gives the length, in feet, of the wire? 125 sin 65° 125 cos 65° 125 tan 65° 125 feet 125 sin 65° 65° ACT-70C 24 GO ON TO THE NEXT PAGE.

A circle is inside a rectangle 6 inches wide and 8 inches long and is tangent to 3 sides of the rectanole. What is the area, in square inches, of the circle? 67[ DO YOUR FIGURING HERE.

In trapezoid KLMN shown below, ZM measures 45° and ZK and ZN are both right angles. The given side lengths are in feet. Wbich of the followinu values is closest to the area, in square feet, of KLMN ? 18 10 45°

For tbe 2 O'clock hour on Milena's grandfather clock (Shown below), the bell is struck 2 times. For the o'clock hour, the bell is struck 3 times. For every hour, 2 seconds elapse between consecutive strikes of the bell. For the 9 O'clock hour, how many seconds elapse between the 1st strike of the bell and the 9th strike of the bell?

For positive real numbers a, b, and r such that 2a and c, which of the following inequalities is 3b true? c<b<a c<a<b a<b<c ACT-70G 26 GO ON TO THE NEXT PAGE.

For all pairs of nonzero real numbers a and b, the product of the complex number a + bi and which of the followinLT complex numbers is a real number? abi a+bi

Four congruent semicircles touch only at their corners, as shown in the figure below. If the paih from A to B along tbe diaTncters of the semicircles is l 00 centimeters long, how many centimeters long is the path from B back to A along the arcs of these semicircles? 25 507[ 150

A magnet attracts a nail with a force that varies inversely with the square of the distance between them. The nail is 12 inches from the magnet. How many inches from the magnet would the nail need to be to have twkce as much attractive force on it as it currently has? DO YOUR FIGURING HERE. 6<2

What is the area, in square meters, of a rhombus (a parallelogram having 4 congruent sides) with side length 4 meters and 2 angles that each measure 600 ? 8%f3

The right triangle shown below with hypotenuse 13 inches long and vertical leg 5 inches long is rotated 360° around the vertical leo to form a right circular cone. What is the volume of this cone, in cubic inches? (Note: V I ￿Ph, where V is the volume, r is the radius, and IT is the heigbt.) 80 13 407C 320 240

Which of the following fractions is equal to 20 22 11 10 li 10 li, 21 ACT.7CC 28 GO ON TO THE NEXT PAGE.

Which of the following is equal to tan 8 cos g when sin0= andO<O< DO YOUR FIGURING HERE. 2if5 2<5

An equilateral triangle is partitioned into 4 smaller congruent equilateral triangles. What is tbe ratio of the perimeter of l of the smaller trianoles to the perimeter of the original triangle?

If Ixl -x, which of the following statements must be true? x<0 x#0 x is not a real nurnber. END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. ACT-70C 29