UA · Unit 6 review

1. 1.

   Evaluate √36.

   Answer. 6

   6² = 36.

2. 2.

   Write 0.4 as a fraction in simplest form.

   Answer. 25

   0.4 = 25 = 25.

3. 3.

   Between which two consecutive integers does √10 lie?

   Answer. 3 and 4

   3² = 9 and 4² = 16, and 9 < 10 < 16.

4. 4.

   Is a triangle with sides 12, 16, 20 a right triangle?

   Answer. yes

   Check 12² + 16² = 20².

5. 5.

   A rectangle is 12 by 35. How long is a diagonal? Then Sam needs 3 of that amount. What is the total they need?

   Answer. 111

   Diagonal² = 12² + 35² = 37², so the diagonal is 37. Then multiply by 3: 111.

6. 6.

   A sphere has radius 3 cm. Volume in terms of π? Write a complete answer — Jonah will compare with a partner.

   Answer. 36π cubic cm

   V = (43)πr³ = (43)π(27) = 36π.

7. 7.

   Evaluate √36. Then Theo needs 2 of that amount. What is the total they need?

   Answer. 12

   6² = 36. Then multiply by 2: 12.

8. 8.

   Write 18 as a decimal. Then Nora needs 2 of that amount. What is the total they need?

   Answer. 0.25

   1 ÷ 8 = 0.125. Then multiply by 2: 0.25.

9. 9.

   Between which two consecutive integers does √11 lie? Then Luis needs 3 of that amount. What is the total they need?

   Answer. 9 and 4

   3² = 9 and 4² = 16, and 9 < 11 < 16. Then multiply by 3: 9 and 4.

10. 10.

    A right triangle has legs 5 and 12. What is the hypotenuse? Then Owen needs 2 of that amount. What is the total they need?

    Answer. 26

    5² + 12² = 169 = 13². Then multiply by 2: 26.

11. 11.

    Think

    Grace tried this problem:
    Find the missing leg of a right triangle with leg 6 and hypotenuse 10.
    Grace wrote 16. That is not correct. What is the right answer?

    Answer. 8

    Grace’s answer 16 is off. x² + 6² = 10² → x² = 64 → x = 8.

12. 12.

    Think

    Malik tried this problem:
    A sphere has radius 3 cm. Volume in terms of π?
    Malik wrote 72π cubic cm. That is not correct. What is the right answer?

    Answer. 36π cubic cm

    Malik’s answer 72π cubic cm is off. V = (43)πr³ = (43)π(27) = 36π.

Original extra practice. Keys are computed from the items, not guessed.