ACT Past Papers with Answers

Givenr=6,b=4,andg-_9. (r+b-g)(b+g)-? -95 13

What is the length, in inches, of the hypotenuse of a right triangle with a leg that is 9 inches long and a leg that is 2 inches long. 22 DO YOUR FIGURING HERE. 11

A bau contains exacily 18 solid-colored buttons: 3 red, 5 blue, and 10 whitc. What is the piobabÈlity of randomIy selecting I button that is NOT white? 18

What is the sum of 3 consecutive odd integers whose mean is 27 ? . 39 D, 87

Two dials are shown below. When the arrow on each dial is spun: it is equally likely lo point at atty of the numbered sectors on its dial after it has Stopped spinning. After the arrows are next spun, the numbers in the sectors the arrows point at after they stop spinning will be added togethei. Which of the folIowing values is NOT a possible sum of those 2 numbers? ACT-B02 15 GO ON TO THE NEXT PAGE.

Givcnthat3x+2=4and2y+6-5.whatisx+y 15

For all x such that x * O, which of the following expressions is equivalent to 151+ 25x 3x+5 ACT-B02 16 GO ON TO THE NEXT PAGE.

What is the value of the expression DO YOUR FIGURING HERE. 16- 4x2-5 26

The graph below shows the amount of water in a pond over a period of 7 hours. One of the following values is the number of hours the amount of waler in the pond remained constant. Which one? 0 1 2 3 4 5 6 7 time (hours)

If it rains ill Franklin City on a particular day, the PTobability that it will rain there the following day is

In the standard (x,y) coordinate plane, what is the slope of the line given by the equation 5x - 9y + 18 ? DO YOUR FIGURING HERE.

One of the following equations represents the line graphed in the standard (x.y) coordinate plane below. Which one? -2x+2 -2x+4 4x+2

In the figure below, line m is perpendicular to line n, and line p is parallel to line q. Lines m. n. and p intersect at a single point. Some angle measures are given. What is the value of x ? IL 122 IL 158

A bag contains 10 solid-colored marbles of the same size: 3 red, 2 green, l yellow, and 4 blue. Which of the following expressions gives the probability of drawing, at random and without replacement. a blue marble on the 1st draw, a green marble Oll th¢ 2nd draw, and a blue marble on the 3rd draw? 10 io 10 10 10 10 10 10 10 Acf-B02 18 GO ON TO THE NEXT PAGE.

A physical education teacher recorded the distances, in inches, Ihat her students jumped durÉng a long jump lesson.-The distances of l jump by each of the students are represented in the stem-and-leaf plot beIow. DO YOUR FIGURING HERE. Stem Leaf 3567 24589 01236 012 Key: 5 2= 52 inches What is the probability that a student chosen at random from the class will have jumped ai leas't 60 inches? 24 19 19 19

Given that the function f defined as f(x)= 5 - 3x has domain {-1, 0, 2 }, what is the range of f ?

To the nearest I foot, what is the height of a rectangular PTlSIll Wlth a base length of 15 feet, a base width of l- feet. and a volume of l 00 cubic feet? ACT-B02 19 GO ON TO THE NEXT PAGE.

Tables of values for the 2 functions f and g are shown below. What is the value of g(f(5)) f(x) DO YOUR FIGURING HERE. g(x)

In the figure shown below, a ladder 15 feet long forms an angle of 56° with the level ground as it leans against the vertical side of a building. The distance along the building. in feet, between the ground and the top of the ladder is equal to which of the following expressions? 15 15xf3 15 56° 15 cos 56°

The isotope iodine-131 has a half-life of 8 days. which means that the amount of iodine-131 remaining after Idays ISN where N is the number of grams of iodine-131 at i- O. How many grams of iodine-13 1 will Tell￿1￿ after 16 days if there were 32 grams of iodine-131 at t- O ?

Which of the following expressions is equivalent to 16 12 64x 12 ACT-802 20 GO ON TO THE NEXT PAGE.

Two concentric circles have radii of 5 centimeters and 6 centitneters. respectively. How many celltimeters longer is the circumference of the larger circle than that of the smaller circle? DO YOUR FIGURING HERE.

Squares with sides of length x cm have been removed from each corner of a rectangle measuring 8 cm by 18 cm, resulting in the figure shown below. In terms of x, what is the area, in square cenlimeters, of the figure? 18 52-4x' 144-8x

In the standard {x,y) coordinate plane below. LABC will be translaied 10 units down and then the resulting Rmage will be reflected over the y-axis. What will be the coordinates of the final image of A resulting from both tranSfQrn￿ti0￿s9 B(-3,4) c(-I,i) A{_5.1)

Olivia. Ashton, and Jane are standing on a soccer field such that Olivia is 20 meters due west of Ashton and Jane is 40 meters due north of Ashton. Their positions are at the vertices of a triangle. Which of the following expressions gives the degree mcasure of the angle of the triangle at the v¢rtex where Olivia is standing. cos 20 sin 20 20 40 40 20 20 40 sin AGT.B02 21 GO ON TO THE NEXT PAGE. DO YOUR FIGURING HERE. Use the following information to answer questions 33-35. In the standard (x,y) coordinate plane below, ￿AOB is fonned by AB, the x-axis. and the y-axis. A(0,6) B(6,0)

What is the area of AAOB in square coordinate units? 6fvf2

What is the Icngth of AB in coordinate units? 2fvf6 6(2

Which of the following is an equation of AB ? -x+6 x+6

Which of the following aiianges the numbers

Which of the following operations will produce the largest result when substituted for the blank in the expression 14 Divided by

The equation t~_0.0066a + 15 models the noon temperature, t degrees Celsius, a meters above sea level. on a certain day on Laurel Mountain. According to this equation, what would be the noon temperature for that certain day on L&urel Mountain at sea levcl?

What is the smallest positive integer having exactly 5 different positive integer divisoTS?

If49°_7 and3 a+b 81,thenb=?

The difference lies in which of (he following iniervals graphed on the real number line? DO YOUR FIGURING HERE.

The recursive forniula for a sequence is given below, where a. is the value of the nth tern]. 10 Which of the following equations is an explicit forn]ula foi this sequence? -5ll+lO 5n+ 5 5n+lO Ion- Ion+ 5

The probabilities that each of 2 independent events will occur are given in the table below. Event Probability

Source question 50. Refer to the source image.

Source question 51. Refer to the source image.

Jarrod went on Tour A, and his trip covered a distance of 6 miles. Bhumi went on Tour C, and her trip covered a distance of 9 miles. Which of the following values is the diffeience. in miles per hour, of the average speeds of their balloons during their tours? DO YOUR FIGURING HERE.

A foresi fire is contained within a triangular region, which is shown below. The supervising firefighter plans to fight the fire by positioning a firefighter about evcry 4 meters alon(y the perimeter of the trianole. Among the following, which expression best estimates the planned number of firefighters along the peIimeter? (Note: The law of sines states that in every triangle, the 3 ratios of length of a side to the sine of the angle opposite that side are eqllal.) 91° 47° 130 meters 130+ 130 sin 42° sin91° 130 sin 47° sin 91" 130+ 130 sin91° sin 42° 130 sin91° sin 47" 130 sin 42" sin91° 130 sin 47° gin91° 130 sin 47° 5in91° (130)

How many integers between, but not including. 20 and 30 have a prime factorization with exactly 3 factors that are NOT necessarily unique? (Note: l is N(Yr a prime number.) AGT.B02 27 GO ON TO THE NEKf PAGE.

Thegraphs of y=_.x*l,y=x-3, and/+y-_9are shown in the standard (x.y) coordinate plane below. The shaded region is the solution set to one of the following systems of inequalities. Which system is it? DO YOUR FIGURING HERE. +f-9 x'+(>9

The function f(x) is shown below with several points labeled. Another function, g(x), is defined such that g(x) = _If(x) - 3]. What is g(4) ? f(x) {-1,2) (1.2) (5,1) {4,-1)

The ratio of a to b is 6 to I, and the ratio of b to c is 12 to l. What is the value of 2d+3b 4b+3c 17 16 17 60 17 48 ACT402 28 GO ON TO THE NEXT PAGE.

In the standard (x.y) coordinate pltine, what is the y-intercept A)f the graph of the function y -f(x) defined b¢low? I for x<-3 5 for-3<x.<2 31for x>2

What is the matrix product 2a4b 6c5d (2a + 4b) (6c + Sd) [(2a + 6c) (4b + 5d)] (2a 4 6b) {4a + 5b) (2c + 6d) (4c + Sd) (?a + 4c) (2b + 4d) (6a + sc) (6b + Sd) END OF TEST 2 STOP! DO NOT TURN THE PAGE UNTIL TOLD TO DO SO. DO NOT RETURN TO THE PREVIOUS TEST. A¢T-B02 29