ACT --Sample Mathematics Questions: Set 2

DIRECTIONS: Solve each problem, choose the correct answer, and then fill in the corresponding oval on your answer document.

Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.

You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.

Note: Unless otherwise stated, all of the following should be assumed.

1. Illustrative figures are NOT necessarily drawn to scale.
2. Geometric figures lie in a plane.
3. The word line indicates a straight line.
4. The word average indicates arithmetic mean.

1. The lead of a screw is the distance that the screw advances in a straight line when the screw is turned 1 complete turn. If a screw is 2 inches long and has a lead of  inch, how many complete turns would get it all the way into a piece of wood?
   1. A.   5
   2. B. 10
   3. C. 15
   4. D. 20
   5. E. 25
2. If xy = 144, x + y = 30, and x > y, what is the value of x – y ?
   1. F.   4
   2. G.   6
   3. H. 18
   4. J. 22
   5. K. 24
3. Which of the following is the sine of A in the right triangle below?
   
   1. A. 
   2. B. 
   3. C. 
   4. D.
   5. E. 
4. Ding’s Diner advertised this daily lunch special: “Choose 1 item from each column—only $4.95!” Thus, each daily lunch special consists of a salad, a soup, a sandwich, and a drink.

   Salads	Soups	Sandwiches	Drinks
   cole slaw lettuce potato	onion tomato	meat loaf chicken hamburger ham tenderloin	milk cola coffee tea

   How many different daily lunch specials are possible?
   1. F.     4
   2. G.   14
   3. H.   30
   4. J. 120
   5. K. 180
5. The volume, V, of the right circular cone with radius r and height h, shown below, can be found using the formula V =  r2h. A cone-shaped paper cup has a volume of 142 cubic centimeters and a height of 8.5 centimeters. What is the radius, to the nearest centimeter, of the paper cup?
   
   1. A.   2
   2. B.   4
   3. C.   8
   4. D. 12
   5. E. 16
6. A boat departs Port Isabelle, Texas, traveling to an oil rig. The oil rig is located 9 miles east and 12 miles north of the boat’s departure point. About how many miles is the oil rig from the departure point?
   1. F.     3
   2. G.  
   3. H.   15
   4. J.   21
   5. K. 225
7. In the figure below, ABC  DFE, BAC  FDE, D and Fare on AB, AD  FB, and distances in centimeters are as shown. What is the length of AD, in centimeters?
   
   1. A. 5
   2. B. 4
   3. C. 3
   4. D. 2
   5. E. 1
8. Which of the following is a factor of the polynomial 2x2 – 3x – 5 ?
   1. F.   x – 1
   2. G. 2x – 3
   3. H. 2x – 5
   4. J. 2x + 5
   5. K. 3x + 5
9. What is x, the second term in the geometric series  + x +  +  + … ?
   (Note: In a geometric series the ratio of any term to the following term is constant.)
   1. A. 
   2. B. 
   3. C. 
   4. D.
   5. E. 
10. What is the slope of any line parallel to the line 9x + 4y = 7 ?
    1. F.   –9
    2. G. 
    3. H.   
    4. J.    7
    5. K.    9
11. A DVD player with a list price of $100 is marked down 30%. If John gets an employee discount of 20% off the sale price, how much does John pay for the DVD player ?
    1. A. $86.00
    2. B. $77.60
    3. C. $56.00
    4. D. $50.00
    5. E. $44.00
12.  = ?
    (Note: i =  )
    1. F.  9i
    2. G.  9 + i
    3. H.  9 – i
    4. J.  9
    5. K. –9