Topic Review — Integers #2

Review Questions

1. Absolute value and ordering Fluency

   1. |−9|
   2. |−4| + |3|
   3. Order from smallest to largest: −7, 2, −3, 0, 5, −1
   4. Which is larger: −2 or −11?
   5. List two integers with absolute value 15.

2. Multiply and divide integers Fluency

   1. (−5) × 8
   2. (−6) × (−7)
   3. 9 × (−4)
   4. (−40) ÷ 8
   5. (−36) ÷ (−4)
   6. 72 ÷ (−9)

3. Powers of negative numbers Fluency

   1. (−4)²
   2. (−3)³
   3. (−1)¹⁰
   4. (−2)⁵
   5. (−5)²

4. Comparing and reasoning Understanding

   1. Compare using <, > or =:   (−3) × 4 __ (−2) × (−6)
   2. True or false: |−5| > |−3|. Explain.
   3. Without calculating, predict the sign of (−2) × (−3) × (−4). Explain.
   4. Give an example of two different integers whose product is +24.

5. Multi-step problems Understanding

   1. Calculate: [(−4) × 3] ÷ (−6)
   2. Calculate: (−2)³ × (−1)⁴
   3. What value of n makes (−5) × n = 45 true?
   4. What value of n makes n ÷ (−3) = −8 true?

6. Word problems Problem Solving

   1. Five cities have these temperatures: −8°C, −3°C, 4°C, −15°C, 2°C. Which is coldest? Which two have the smallest difference in temperature?
   2. A lift descends 3 floors per second. After 7 seconds, what floor is it on if it started at floor 0?
   3. A company’s profit changes by −$500 each month. Starting from $0, what is the balance after 6 months?
   4. A diver records her depth every minute: −5 m, −10 m, −15 m, −20 m. Describe the pattern using multiplication. What depth at 8 minutes?
   5. The temperature drops 4°C each hour. Starting at 12°C, when does it reach −12°C?

7. Order of operations with negative numbers: Understanding

   1. (−3)² + 4 × (−2)
   2. [(−5) × 2] − (−3)²
   3. (−2) × [3 + (−7)]
   4. −4² + (−4)² — note the difference!

8. Evaluate expressions given integer values: Fluency

   Let a = −3 and b = 4. Evaluate:

   1. 2a + b
   2. ab − a
   3. a² − b²
   4. b − 2a

9. Is each statement always, sometimes, or never true? Explain with an example. Understanding

   1. A negative number multiplied by a negative number is positive.
   2. The absolute value of a number is always positive.
   3. The product of two integers with different signs is negative.

10. Stock market: a share price starts at $50. Problem Solving

    1. It rises by $3 each day for 5 days. What is the new price?
    2. Then it falls by $7 each day for 4 days. What is the price now?
    3. Express the overall change from the starting price as an integer.
    4. Is the overall change a gain or a loss?