ISEE Upper Level Word Problems: Other Math Concepts Practice Test 22

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1. What type of number could result from the product of two irrational numbers?

  • A. rational or irrational
  • B. rational only
  • C. irrational only
  • D. integer only

2. Which expression is equivalent to the expression (x – 4)(x + 5)?

  • A. x2 – 20
  • B. x2 + 1
  • C. x2 – x – 20
  • D. x2 + x – 20

3. If k is a positive integer, and (x + 11)2 = x2 + kx + 121, what is the value of k ?

  • A. 121
  • B. 55
  • C. 22
  • D. 11

4. If the sum of all integers from 1 to 400, inclusive, is x, then which expression represents the sum of all integers from 1 to 397, inclusive?

  • A. x + 1,197
  • B. x + 397
  • C. x – 397
  • D. x – 1,197

5. What is the solution set for x2 + 64 = 0?

  • A. 8
  • B. 8i
  • C. ±8
  • D. ±8i

6. If x2 + y2 = 73, and 2xy = 48, what is the value of (x – y)2?

  • A. 5
  • B. 11
  • C. 25
  • D. 121

7. The first six terms of an arithmetic sequence of numbers are shown.

–7, –4, –1, 2, 5, 8

Which expression gives the value of the xth term of the sequence?

  • A. x – 8
  • B. x – 6
  • C. 3x – 10
  • D. 3x + 7

8. There are 1,760 yards in a mile. If Elena is walking at a speed of 4 miles per hour, which of the following expressions gives her speed in yards per second?

  • A.
  • B.
  • C.
  • D.

9. Perry and Esther are driving towards each other, each at a constant rate. Perry began his drive two hours before Esther began hers. Esther is driving at a slower speed than Perry. Which additional piece of information, if given, would allow a determination of how long Perry had been driving before he and Esther met?

  • A. the difference between Perry and Esther's speeds
  • B. the sum of Perry and Esther's speeds
  • C. Perry's speed
  • D. Esther's speed

10. What is the result of the following expression?

  • A.
  • B.
  • C.
  • D.

11. For what value(s) of y does = 0?

  • A. y = 3 and y = –7
  • B. y = 7 and y = –3
  • C. y = 8 only
  • D. y = 8 and y = –8

12. For all integers x and y, let x y be defined as x y = (x + y)2 – x – y. For example, 2 3 = 52 – 2 – 3 = 20. Which one of the following is an odd number?

  • A. 3 4
  • B. 3 5
  • C. 4 6
  • D. none of the above

13. In a certain city, the average height for men over 18 years old is 70 inches. All men in the city are within 5 inches of the average height. If m represents the height of a man in the city, which best describes the man's height?

  • A. |m – 5| ≤ 70
  • B. |m – 5| ≥ 70
  • C. |m – 70| ≥ 5
  • D. |m – 70| ≤ 5

14. The value of a varies directly as the square root of b and varies inversely as c. If b is multiplied by 4 and c is divided by 2, then by what factor does a change from its original value?

  • A.
  • B.
  • C. 4
  • D. 8

15. In the formula z = , x > 0, and y > 0. If one of the three variables does not change, which of the following is true?

  • A. as x decreases, z increases
  • B. as x increases, z decreases
  • C. as y decreases, z increases
  • D. as y increases, z increases