ACT Practice test. Hamilton Qtr

Transcription

1 ACT Practice test Hamilton Qtr 3 011

2 WARM UP ACT PRACTIC 1. Find the value of x so that the distance between points P(3, 5) and Q(x, 11) is Find the standard form of the equation of the parabola. Which equations represent the locus of all points in a coordinate plane that are equidistant from the points (1, -) and (, -5)?

3 1. What is 4% of 1,100 A.4 B.4.4 C.40 D.44 E.440. For all x, (x + 4)(x 5) F. x -0 G. x - x 0 H. x 1 J. x - 1 K. x x If x + y = 1 and x y = 1, then y =? A.-1 B.0 C.½ D.1 E.

4 1. What is 4% of 1,100 1,100 x If you answered B or E, you may have used rules about moving decimal points and moved the wrong number of places.. For all x, (x + 4)(x 5) (x + 4)(x 5) x + 4x - 5x - 0 x x - 0 Should have used the distributive property (FOIL) If you got F, you probably just multiplied the first and the last terms. 3. If x + y = 1 and x y = 1, then y =? x - y = 1 x = y + 1 x +y = 1 (y+1)+y=1 y + 1 = 1 y = 0 y = 0 If you chose D, you probably found x instead of y.

5 4. What is the slope of the line containing? the points (-, 7) and (3, - 3) F. 4 G. ¼ H. 0 J. ½ K If the measure of an angle is 37 ½, what is the measure of its supplement, shown in the figure below? 37 ½,? A.5 ½ B.6 ½ C.17 ½ D.14 ½ E.Cannot be determined from the given information. 6. What is the sine of A in the triangle below? 6 B C 10 8 F G H.0.60 J K A

6 4. What is the slope of the line containing? the points (-, 7) and (3, - 3) y x 1 1 y x If you answered J, you probably got the expression for slope upside down. 5. If the measure of an angle is 37 ½, what is the measure of its supplement, shown in the figure below? 37 ½,? ½ = 14.5 If you answered A, you found the complementary angle. 6. What is the sine of A in the triangle below? C 6 10 B 8 opp sin A hyp A If you answered something other than H, you either did not know the trig functions or which ones to use.

7 7. What is the total cost of.5 pounds of bananas at $0.34 per pound and.5 pounds of tomatoes at $0.66 per pound? A.$1.00 B.$.40 C.$.50 D.$3.50 E.$ The relationship between temperature expressed in Degrees Fahrenheit (F) and degrees Celsius (C) is given by the formula 9 F C 3 5 If the temperature is 14 degrees Fahrenheit, what is it in degrees Celsius? F. -10 G. -1 H. -14 I K Amy drove the 00 miles to New Orleans at an average speed of 10 miles per hour faster than her usual average speed. If she completed the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour? A.0 B.30 C.40 D.50 E.60

8 7. What is the total cost of.5 pounds of bananas at $0.34 per pound and.5 pounds of tomatoes at $0.66 per pound?.5(0.34) +.5(0.66) or.5( ) = $ The relationship between temperature expressed in Degrees Fahrenheit (F) and degrees Celsius (C) is given by the formula 9 F C 3 5 If the temperature is 14 degrees Fahrenheit, what is it in degrees Celsius? C C 3 C 9. Amy drove the 00 miles to New Orleans at an average speed of 10 miles per hour faster than her usual average speed. If she completed the trip in 1 hour less than usual, what is her usual driving speed, in miles per hour? r 10 r r r 10 r 00r r 190r 000 r 10r ( r 50)( r 40) 0 r 40

9 10. A map is laid out in standard (x, y) coordinate plane. How long, in units, is an airplane flies along a straight line from City A located at (0, 14) to City B located at (5, 10)? F. G. H. J. 7 K A person meters tall casts a shadow 3 meters long. At the same time, a telephone pole cast a shadow 1 meters long. How many meters tall is the pole? A.4 B.6 C.8 D.11 E The hiking path to the top of a mountain makes, at the steepest place, an angle of 0, with the horizontal, and it maintains this constant slope of 500 meters, as illustrated below. Which of the following is the closest approximation to the change in elevation in meters, over this 500-meter section? F. 0 G. 170 H. 180 J. 50 K. 470? 0 You may use the follow cos 0 =.94, sin 0 =.34, tan 0 =.36

10 10. A map is laid out in standard (x, y) coordinate plane. How long, in units, is an airplane flies along a straight line from City A located at (0, 14) to City B located at (5, 10)? AB ( x 1 (0 5) x ) ( y 1 y (14 10) 3 1 3h ) 11. A person meters tall casts a shadow 3 meters long. At the same time, a telephone pole cast a shadow 1 meters long. How many meters tall is the pole? h h 4 h The hiking path to the top of a mountain makes, at the steepest place, an angle of 0, with the horizontal, and it maintains this constant slope of 500 meters, as illustrated below. Which of the following is the closest approximation to the change in elevation in meters, over this 500-meter section?? 0 h sin h h

11 13. IF were calculated it would have 79 digits. What would the digit farthest to the right be (the ones digit)? A.1 B.3 C.4 D.7 E If a < -1, which of the following best describes a general relationship between a 3 and a F. a 3 > a G. a 3 < a H. a 3 = a J. a 3 = -a K. a 3 1 a 15. If n 4 5 Then n =? A.- 3/ B.-1 C.-/3 D./3 E.3/ 5 4 3

12 13. IF were calculated it would have 79 digits. What would the digit farthest to the right be (the ones digit)? 7 0 = 1, 7 1 = 7, 7 = 49, 7 3 = 743, 7 4 =401, 7 5 = 16807, 7 6 = 117,649, 1 s digit Power If a < -1, which of the following best describes a general relationship between. a 3 and a If a is a negative number, when squared it will be positive, when its cubed, it will be negative. Therefore a 3 < a. 15. If n Then n =? The fraction is flipped so n will have to be negative. To put the exponents into a rational number put he power on top and the root on the bottom. n = - 3 / 3

13 16. In the standard (x,y) coordinate plane, the triangle with vertices at (0,0), (0,k) and (, m), where m is a constant. Changes shape as k changes. What happens to the triangle s area, expressed in square coordinate units, as k increases starting from? F. The area increases as k increases G. The area decreases as k increases H. The area always equals J. The area always equals m. K. The area always equals m. 17. In the figures below, AB =AC and BC is 10 units long. What is the area, in square inches of ABC? A B A.1.5 B.5 D C C. 5 D.50 E.Cannot be determined from the given information. 18. A bag of pennies could be evenly divided among 6 children, 7 children, or 8 children with each getting the same number, and with 1 penny left over in each case. What is the smallest number of pennies that could be in the bag? F. G. 43 H. 57 J. 169 K. 337

14 16. In the standard (x,y) coordinate plane, the triangle with vertices at (0,0), (0,k) and (, m), where m is a constant. Changes shape as k changes. What happens to the triangle s area, expressed in square coordinate units, as k increases starting from? (0,k)hb (0,0) A = ½ bh As k increase, the base gets larger, therefore the area increases 17. In the figures below, AB =AC and BC is 10 units long. What is the area, in square inches of ABC? A B D C Not enough information. 5 The drawing may throw you off. It could also look like this. B A D C 18. A bag of pennies could be evenly divided among 6 children, 7 children, or 8 children with each getting the same number, and with 1 penny left over in each case. What is the smallest number of pennies that could be in the bag? F. G. 43 H. 57 J. 169 K. 337

15 19. There are n students in a class. If, among those students, p% play at least 1 musical instrument, which of the following general expressions represent the number of student who play NO musical instruments? A. Np B..01np C. D. ( 100 p) n 100 ( 1 p) n Starting at her doorstep, Ramona walked down the sidewalk at 1.5 feet per second for 4 seconds. Then she stopped for 4 seconds, realizing that she had forgotten something. Next she returned to her doorstep along the same route at 1.5 feet per second. Which graph of Ramona s distance (d) from her doorstep as a function of time (t) would resemble which of the following? F. J. G. K. H. d d d t t d d t t 1.An object on radar is 5 miles to the east, 4 miles to the north, and 1 mile above the tracking station. Among the following, which is the closest approximation to the distance in miles, that the object is from the tracking station? A. 6.5 B. 7. C. 9.0 D E. 100(1 p)n t

16 19. There are n students in a class. If, among those students, p% play at least 1 musical instrument, which of the following general expressions represent the number of student who play NO musical instruments? 100 p = % none players 100 p = % none players 100 (in decimal form) 0. Starting at her doorstep, Ramona walked down the sidewalk at 1.5 feet per second for 4 seconds. Then she stopped for 4 seconds, realizing that she had forgotten something. Next she returned to her doorstep along the same route at 1.5 feet per second. The graph of Ramona s distance (d) from her doorstep as a function of time (t) would resemble which of the following? d Walking away from home Stopped for 4 seconds Tracking station Walking back home 1.An object on radar is 5 miles to the east, 4 miles to the north, and 1 mile above the tracking station. Among the following, which is the closest approximation to the distance in miles, that the object is from the tracking station? 5 mi object 1 mi ( 100 p) n 100 Answer C # of none players Answer J t ( 41) 1 4 Answer A 65.

17 Same graph for 4 At both Quick Car rental and speedy Car Rental, the cost in dollars, of renting a full size car depends on a fixed daily rental fee and a fixed charge per mile that the car is driven. However, the daily rental fee and the charge per mile are not the same for the companies. In the graph to the right, line Q represents the total cost for Quick Car Rental and line S represents the total cost for Speedy Car Rental. 60 Q 50 S CMiles driven

18 . Robert plans to rent a full-size car for 1 day and drive only 50 miles. If his only consideration is to incur the least cost, which company should he choose? F. Quick Car Rental, because the cost is $5 less. G. Quick Car Rental, because the cost is $15 less H. Either company, because the costs are equal. J. Speedy Car Rental, because the cost is $5 less K. Speedy Car Rental, because the cost is $15 less 3. If you rent a fullsize car from Quick Car Rental for 1 day, how much more would the total rental cost be if you drove the car 78 miles than if you drove it 77 miles? A. $0.10 B. $0.15 C. $0.0 D. $0.40 E. $ What would be the total cost of renting a full-size car from Speedy Car Rental for 1 day and driving the car 150 miles. F. $60 G. $75 H. $85 J. $90 K. $10

19 . Robert plans to rent a full-size car for 1 day and drive only 50 miles. If his only consideration is to incur the least cost, which company should he choose? Answer F The lower line is for Q and is saves about $ CMiles driven Q S 3. If you rent a fullsize car from Quick Car Rental for 1 day, how much more would the total rental cost be if you drove the car 78 miles than if you drove it 77 miles? The slope of the Q line gives you the cost per mile. Pick two points, (100, 55) and (0, 15) Then find the slope $0. Answer D 4. What would be the total cost of renting a full-size car from Speedy Car Rental for 1 day and driving the car 150 miles. C = $ (.) = $60 Answer F