The document contains a series of mathematical problems and answers related to algebraic expressions, translations of verbal sentences to mathematical sentences, polynomials, and operations on expressions. It includes multiple-choice questions and operations like addition, subtraction, and simplification. It also provides answers and explanations for problems, such as identifying which expressions are polynomials and solving equations.

1. Battle of the
brains

2. Write your final
answer on Show Me
Board

3. Translation of verbal sentence
to mathematical sentence
( 1 Point Each )

4. 6 increased by a number Y
6 + Y

5. Nine less than x
X – 9

6. The product of -5
and Y
-5Y

7. Thrice x added to
twice y
2y + 3x

8. Half of the sum of a
and b
𝑎 + 𝑏
2

9. Twice a number n increased by 5
2n + 5

10. Twice the sum of y and 7
2(y + 7)

11. The square of the sum
of x and y
(x + y ) 2

12. 2 subtracted from the square
of a number
X2 – 2

13. Seven times the number
diminished by 10
7N – 10

14. 3 more than twice a
number
2x + 3

15. Twice a number subtracted
from the square of a number.
X2 – 2x

16. Multiple Choice:
Choose the letter of the
correct answer.

17. Which of the following is equal to (22 + 32)3
A.(22)3 + (32)3
B.(52)3
C.43 + 93
D.(13)3
Answer: D

18. Which of the following is the same as a2b5?
A.A7
B.B7
C.(ab)7
D.None of the above
Answer: D

19. Which of the following is equivalent to 5-3?
A.- 53
B.-35
C. 𝟏
𝟓 𝟑
D.(-3)(5)
Answer: C

20. Which of the following is NOT a polynomial?
A. 𝟏
𝟓
x + 1
B. 𝟏
𝟓𝒙
+ 2
C. 2 𝑥 ÷
𝟕
𝟐
D. 𝟒𝒙+𝟏
𝟓
Answer: B

21. What is the degree of x3 – 10x + x4 ?
A.1
B.2
C.3
D.4
Answer: D

22. Which of the following is the difference when
2x2 – 5x – 1is subtracted from 7x2 – 4x + 8?
A.5x2 + x +9
B.5x2 – 9x +7
C.5x2 + x – 7
D.5x2 – x – 7
Answer: A

23. Which of th following is equivalent to 4x2 + 6x
– 2 +6 – 4x2 – 6x?
A.- 4
B.4
C.6
D.- 2
Answer: B

24. Which of the following is equivalent to 43?
A.25
B.34
C.26
D.4.3
Answer: C

25. Which of the following is not true?
A.6x3 + x3 = 7x3
B.(5x2 + 1) – (x2 + 1) = 4x2
C.3x4 – x4 = 2
D.7x2 + 3x – 2x + 1 = 7x2 + x + 1
Answer: C

26. Which of the following numbers is the
greatest?
A.1.23 x 103
B.1.75 x 103
C.1.03 x 104
D.11.4 x 103
Answer: D

27. Simplify
𝟔
𝟖
,
𝟗
𝟏𝟐
, and
𝟏𝟖
𝟐𝟒
a.
2
3
b.
3
5
c.
3
4
d.
5
8
Answer: C

28. Mr. Reyes decided to paint his house. He
wanted the paint light green. He mixed
7
8
of can of white to
2
3
of a can of blue paint.
How many can of paint did he use?
a.1
3
4
b.
36
24
c. 1
13
24
d.1
8
24
Answer: C

29. Three fourth of what number is 12?
a. 12 b. 24 c. 30 d. 16
Answer: D

30. Two Points Each

31. Divide:
𝑋−6
9
by
𝑋−6
3
-
𝟏
𝟑

32. The product of
𝒙
𝟒𝒚
times
𝟓𝒚
𝟐𝒙
is
𝟓
𝟒
or 1
𝟏
𝟒

33. Divide:
(𝒃−𝟑) 𝟐
𝟏𝟐
by
(𝒃−𝟑)
𝟔
𝒃 − 𝟑
𝟐

34. (2 )(
𝟒𝒙𝒚 𝟔
𝟔𝒙𝒚 𝟖)
=(
𝟒𝒚 𝟔
𝟑𝒚 𝟐)

35. 3(
𝟒
𝟔
𝒙 𝟐 -
𝟓
𝟑
𝒙 + 𝟓)
2x2 – 5x +15

36. What is the sum of 3x2 – 11x +
12 and 18x2 + 20x + 100?
21x2 + 9x +112

37. What must be added to -3x
+ 10 to get a result of 5x – 3
?
8x – 13

38. 2X5 – 8x3 + 10x – 4
2
= x5 – 4x3 +5x – 2

39. 8a5 – 16 a3 + 24 a
4a
= 2a4 – 4a3 + 6

40. (a +7) (a + 4)
= a2 + 11a + 28

41. (x + 10) (x – 10)
= x2 - 100

42. Perform the indicated operation
1 point each

43. 17xy + ( - 10xy)
7xy

44. -11a – 13a + 4a
= -20a

45. 5a + 16a – 11a
= 10a

46. -12 x + ( - 6x ) – 8x =
26x

47. - 4y +5y =
y

48. (x + 7 ) + ( x +8) + (3x +4)=
5x + 19

49. (-5x – 2) + (-3x – 6)
-8x – 8

50. (- 2)5 =
-32

51. (-5)2
25

52. (4)2
= 16

53. (-2)2 +(4)2 =
20

54. - 8x-5
−𝟖
𝒙 𝟓

55. 𝒄 𝟐
𝒄
− 𝟑
= c5

56. Y0 + 3x0 – 1
3

57. (-x)(-x) =
x2

58. (-3x4)( - 5x8) =
15 x12

59. (4a2)(3a5b)(2c4) =
24a7bc4

60. (-4a5)3 =
-64a15

61. (3a3b2c4)3 =
27a9b6c12

62. 2z3 (-4z)2 =
32 z5

63. (-8a)(2a)(-2a4) =
32 a6

64. −𝟐𝒙𝒚 𝟑
𝟔𝒙
-
𝑦3
3

65. 𝟒𝒙𝒚 𝟑
𝟐𝒙 𝟖 𝒚
=
𝟐𝒚 𝟐
𝒙 𝟕

66. (
−𝟑𝒙 𝟓
𝒚 𝟑
𝟒
) 𝟐
=
𝟗𝒙 𝟏𝟎
𝒚 𝟔
𝟏𝟔