ACT Past Papers with Answers

Source question 3. Refer to the source image.

The largest square in the figure below is.partitioned into 36 congruent smaller squares. What fraction of the interior of the largest square is black7 12

WheJLx-. l alld y- 3, what is the value of 4I- 3zy ?

Syhich of the tollowing 18 a value for x that solves the K25

Ms. Juarez annourAced the grade distribution for the last book report. .Of tbe 24 students in the class, 8 earned A's. 10 carlled B's. and 6 earncd C's. Wbcn a student is p.icked at random to bc the fwst to present his or ber book rtsport to the class. wbat is the probabil- ity that the student picked had earned an A OEL the book report? DO YOUR FIGURING HERE. 12

A man started a 280-Jnile drive with a'full tank of gas .in his car. At the end of the.trip he spent $23.40 to refill hig car's taDk with 18 gallons of gasoline selling for $1.30 per gallon. Which of thc following is an expression for the number of miles per gallon the car. averaged? 280 18 280 30 280 18-

For whatyalue of kisx= 2 a solution of £_ &t + k= O ? -12

One side of square ABCD is 12 meters long. A. rectan- gle with tlie same area as square ABCD has a length of 9 metcrs. What is the rectangle's width, in meters? 21 144 AGf-01F 16 GO ON TO THE NErf PAGE.

The figure below shows 3.circles in the standard (X*y) coordillate plane. Which of the .following shows the reflection of the 3 circles across the x-axis? 00 00 oo OO 00 00 AGT41F. 17 . GO ON TO THE NEXT PAGE.

What is the slope of any line parallel to tbe line 6x+5y=77 DO YOUR FIGURING HERE.

of the following is a possible deflljition forf(x) if f(2) - 5 ? f(x)= z +4 L f(x)-5x +2

A forniula for the volume, V, of & right circular cyJin- dcr in ternis of its radius. r. and its height. h, is TPh. What is the heigh( in centimetttrs, of a.right circular cylinder that has a volume of 2707t cubic cen- tiincters and a radius of 3 centimete13? 30 90 279 810

Gerry is building a dollbouse that ig to be a scale model of a house that is 36 feet high, 84 feet long, and 48 "feet wide. What should be the dimensions. i)) feeL of the dollhouse Ge￿ is building if th& scale of the model to the house is 1:12 7 Height Length Width 12 12 12 36 432 48 1,008 576 ACT41F 18 GO ON TO THE NEXT PAGE.

One pair of correspondjng sides of 2 similar triangles arc 3 and 8 inches long, respectively. If the perimeter of the smaller triangle is 12 inches. what is the perime- ter, in inches, of the larger. ttiangle? 36 32

The equation sh(>wn bclow is trne for what value of x ? 3(x-5)-2(x-4)=8x 23

Bach of the 4 sides of the "W, tray in an office has the shape of a tratLzoid, as shown below. inchcs The Isngth of the bottoLn of each side is 13- inches and the length of the top of each side is 11 inches. Whit is the lengtlL ill inches. of tbc median of each trdpezoid? A￿[￿lF 19 GO ON TO THE NEXT PAGE.

What is tbe sllm of the 2 solutions of the equatioll l+x-6-0?

The ratio of a to b is 3 to I, and the ratio of b to C IS I to 5. what.is the va]ue of 2a+3b 4b+3c 16 19 18 19

The probability that a. specific evenL E, happens is ' dsnoted P(E). The probability that this event does nol happen is denoted P(DOt Ej. Syhich of the following statements is always true? L P(E) + P(Dot E)= I DO YOUR FIGURING HERE.

.Which of the following exprèssions is 'equivalent to a , where a is a real llUmb￿?

Which Df the following is cquivalent to (y + 5)3 ? /+ IOy+25 <+. 15y +75y+L25

In tbe right triangle shown below. a leg is 2 meters long and its adjacent acllte angle mca5ur¢s 53°. About how many meters long is the hypotenuse? (Note: sin 53° . 0.80 cos 53° _ 0.60 tall 53° _ 1.33) il J 53°

Boaters use 5 sm&ll flags of different colors to send messages to eople in o.ther boats. All 5 fligs are flosyn Oll I. po e, and the message5 are conyeycd by the order of the flags from tbc top of the pole downward. "lry how many different orders can tho 5 flags be flown? 25 AGf4iF 21 GO ON TO THE NEXT PAGE.

As sbown bclow..gears p and q mesh smoothly so that they turn simultaneously with each otber. Each gear. rotates about its fixed center. tf gear p bas 17 teéth and gear q. has 51 teeth, bow llLany revolutions will gear q if gear p makes 15 revolutions?

Source question 38. Refer to the source image.

To prepare 8 boxes of books for sbipping. LaRonda will put 2 strips of strapping tape around each box, as ' shown below. Each Strip of tape goes all tbe way around the.bo4 and the strips of tape meet at right angles on the top and bottom of the box. Each box is 24 incbes long. 18 inches wide. and 20 inche$ high. What is the minimum. number of inches of strapping tape LaRonda will need to prepare all 8 boxes for shipping. 20 24 18 . 164 496 656 992 ACT41F 23 GO ON TO THE NEXT PAGE.

The interior anglc measures of & triangle are in th tatio 3:8:9. What is thG rneasure of this triangle's largest interior angle? DO YOUR FIGURING HERE.

What is th& value off(x) at x = 4 7

How many horizontal andlor v¢rtical asymptotes are therc for the grapb.of f(x) ? DO YOUR FIGURING HERE.

The area of a rectallgular piece of poster boaTd is 220 square inches. A rectangular photograph that is twice as tall as it is wide is glued to the postsr board so that tbe poster board extends 3 inches beyond the pbotograph on the top and bottom aDd 2 inches beyond the photograph on the left and right silks. as sbown below. How many inches wide is the pbotograph?

A circle with a diameter of 8 incbes is inscribed in square ABCD. as shown below. What is the are4 in square inches, of the shaded region? - 167[ 4%-16 ACT-BIF 25 GO ON TO THE NEXT PAGE.

Th6 side leDgths of ￿X￿z, shown in tlke figure below, are in centimeters. One of tbe 5 points A-E is the center of the circle that goes through points X. Y, and Z. Svbich poiiit is the center? DO YOUR FIGURING HERE. •C 2

Svcn obtained the weighL y pounds. alld shoe size, x, of 25 randomly selected male students at his school. He det¢rniined that the line best fitting his data was givell by the equation y = 110 . H¢ iised this line fo predict the weight of a Dew male student who wears size 9- shoes. Comparcd to this stud¢nt's a¢tuaL weight of 165 pounds, the prediction of his weight from Sven's jine was= ' G. too high by more than I pounLL too low by exactly I poun(L li too low by more thall I pound.

Shown in thc standard (x,y) coordinate plane below, the graph of I" + y l is rcstsicted by one of trie fol- ,lowing conditions. Ivhich one7 x20 x>OaDdy>O

The triangle shown in the standard (x,y) coordinate plane below has vertices as marked. If each coordinate of each vertex is multiplied by 4, what will be the are in square coordinate units. of the triangle with the reslllting points as its vertices7 (1,2) (0.0) (2,0) AOT-61F 26 GO ON TO THE NExf PAGE.

A circle with ccntcr (-1,4) is shown in the standard (z,y) coordinate plane beloiy. IVI)ich of the following is an equation of th¢ line that is tangent to the circle at the point (0.-2) ? DO YOUR FIGURING HERE. (0,-2) Ir+2

The right rectangular prism shovin below has a base that 15 4 meters by 6 meters and a volume of 240 cubic meters. What is the total surface area, in square me*rs, of all 6 faces of the prisrn?

In the fig1￿e below, AC is ttie longer diagonal of rhorn- blls ABCD and E is on AD. The mcasllre of 2BAC is . What is the rneasure of ZCDE, iu terms of m ?

Nvhich of the following is a solution of tbe equatson ACT41F 27 GO ON TO T.HE NEXT PAGE.

Consider the functions f (x) = I. | and g(x) - _} + a. OD& of the following graphs is the graph of y - f(g(x)) in the standard (x,y) coordinatc plarLe. for some a > O. Which graph is It? DO YOUR FIGURING HERE.

Whicb of the following hag a greater Yalue "t1￿1 all the others for all va]ucs Df x in thc interyal O < x < l ?

For positive rèal nllRnbers a. b, and c such that b<2_ ,. which of tile following is true? 25 a>b>c c>b>a ACT-61F 28 GO ON TO THE NErf PAGE. "58. The r￿U[c below shows the path of a certain Fsrojectile launched from the grollnd at. an angle.of e. The bon- zont&l range. r, of this projectile when launcbed from the ground at a speed of 20 meters pet second. is mod- eled by r = 40 sin(28). DO YOUR FIGURING HERE. For this model. the angle measure e that reS￿ts in the greatcst horizontal rang¢, T. is 45° because: . sin 90° is as large as sine can get. sin 45° is as latge as sine caA gcL sin 45° is about 0.707. sin 20 is greater than sin e.

Source question 58. Refer to the source image.