Mathematics Sample Passages and Items

Guidelines for Use of Calculators

Pre-Algebra (Basic Skills)

  1. How much greater is the product of –3, –7, and 5 than their sum?
    1. –110
    2. –100
    3. 90
    4. 100
    5. 110

Pre-Algebra (Application)

  1. Mark bought 3 shirts at a clothing store. If he paid a total of $15.00 for 2 shirts and the average (arithmetic mean) cost of the 3 shirts was $8.00, how much did Mark pay for the third shirt?
    1. $7.00
    2. $7.67
    3. $8.50
    4. $9.00
    5. $11.50

Coordinate Geometry (Basic Skills)

  1. A straight line in the coordinate plane passes through the points with (x,y) coordinates
    (–1,1) and (2,3). What are the (x,y) coordinates of the point at which the line passes through the y-axis?
    1. [ordered pair: zero, two thirds]
    2. [ordered pair: zero, five thirds]
    3. [ordered pair: zero, two]
    4. [ordered pair: zero, five halves]
    5. [ordered pair: negative two, zero]

Intermediate Algebra (Application)

Items 4–5 are based on the following information.

Astonville currently has a property tax of 2% of the market value of each house. Senator Smith has proposed a change in the property tax. Under this Smith proposal, there would be no tax on a house unless the market value of the house was above $20,000. The tax on a house whose market value was over $20,000 would be 2.5% of the difference between the house's market value and $20,000.

  1. Sue Miller would pay the same tax on her house under the Smith proposal as under the current plan. What is the market value of her house?
    1. $ 10,000
    2. $ 40,000
    3. $100,000
    4. $120,000
    5. $400,000
  1. What percentage of Senator Smith's constituents would save money under this new tax proposal?
    1. 25%
       
    2. 33 1/3
       
    3. 50%
       
    4. 66 2/3
    5. The answer cannot be determined from the given information.

College Algebra (Basic Skills)

  1. If –4x2 + 4x + 3 > 0, then which of the following inequalities must be true?spacer
    1. x > 0spacer
    2. x < 0spacer
    3. x < [negative one half] or x > [three halves]
    4. [negative one half] < x < [three halves]
    5. [negative two thirds] < x < [one half]

Trigonometry (Basic Skills)

  1. Which of the following is equivalent to [figure: sin x tan squared x plus sin x over tan x] for 0 < x < 90o ?
    1. sin x + cos x
    2. 2 sin x tan x
    3. sec x
    4. cos x
    5. [figure: sin squared x over cos cubed x]
Answers:
1. E. 2. D. 3. B. 4. C. 5. E. 6. D. 7. C.