International School
Grade 8
www.Klassenarbeiten.de Seite 1
Quiz # 1
1.) Simplify:
a) x5 ∙ x4 b) 𝑎6
𝑎 c) (𝑎2
𝑏3)3
d) (𝑎
𝑏)−1
e) [(𝒂𝟑)𝟐𝟓]𝟎 (2 pts. each)
2.) Simplify
a) (-5a2b3)(4ab2) b) 6𝑎3𝑏4
3𝑎𝑏2
c) (-2x3)3 d) (𝑦2
2𝑥)4
(3 pts. each)
3.) Evaluate
a) 5-2 b) -52
c) [(𝟏
𝟐)−𝟏
]
𝟑
d) (-5)-3 (2 pts. each)
Bonus
(2-1 + 2-2)-2 (5 pts.)
Quiz # 2
1. Write the following numbers in scientific notation! (2 pts. each)
a) 3 520 000 000 b) 0.0000148
c) 0.025 ∙ 10-4 d) 156 ∙ 103
Grade 8
www.Klassenarbeiten.de Seite 1
Quiz # 1
1.) Simplify:
a) x5 ∙ x4 b) 𝑎6
𝑎 c) (𝑎2
𝑏3)3
d) (𝑎
𝑏)−1
e) [(𝒂𝟑)𝟐𝟓]𝟎 (2 pts. each)
2.) Simplify
a) (-5a2b3)(4ab2) b) 6𝑎3𝑏4
3𝑎𝑏2
c) (-2x3)3 d) (𝑦2
2𝑥)4
(3 pts. each)
3.) Evaluate
a) 5-2 b) -52
c) [(𝟏
𝟐)−𝟏
]
𝟑
d) (-5)-3 (2 pts. each)
Bonus
(2-1 + 2-2)-2 (5 pts.)
Quiz # 2
1. Write the following numbers in scientific notation! (2 pts. each)
a) 3 520 000 000 b) 0.0000148
c) 0.025 ∙ 10-4 d) 156 ∙ 103
International School
Grade 8
www.Klassenarbeiten.de Seite 2
2. Write the approximations of the following numbers as stated. (2 pts. each)
a) Write 3.4956
(I) nearest tenth (II) in three significant figures
b) Write 786.832
(I) nearest hundreds (II) nearest hundredth
Bonus
Evaluate and give your answer in scientific notation! (4 pts.)
8 ∙ 106 ∙ 8 ∙ 102
2 ∙ 103
Quiz # 3
1.) 53
59 2.) 5a5
3a3
3.) (-46x2y3z)0
4a) 1
𝑥−3 b) 𝑥−3
𝑥−7
5.) (-3x-1y2)2 6.) (-5x-2y)(-2x-3y2)
7a) (3
𝑥)−2
b) x6x5
c) −6
𝑥−2 d) 3𝑥−2𝑦
𝑥𝑦
Grade 8
www.Klassenarbeiten.de Seite 2
2. Write the approximations of the following numbers as stated. (2 pts. each)
a) Write 3.4956
(I) nearest tenth (II) in three significant figures
b) Write 786.832
(I) nearest hundreds (II) nearest hundredth
Bonus
Evaluate and give your answer in scientific notation! (4 pts.)
8 ∙ 106 ∙ 8 ∙ 102
2 ∙ 103
Quiz # 3
1.) 53
59 2.) 5a5
3a3
3.) (-46x2y3z)0
4a) 1
𝑥−3 b) 𝑥−3
𝑥−7
5.) (-3x-1y2)2 6.) (-5x-2y)(-2x-3y2)
7a) (3
𝑥)−2
b) x6x5
c) −6
𝑥−2 d) 3𝑥−2𝑦
𝑥𝑦
International School
Grade 8
www.Klassenarbeiten.de Seite 3
Results
Quiz # 1
1.) a) x5 ∙ x4 = x5 + 4 = x9 b) 𝑎6
𝑎 = a6 – 1 = a5
c) (𝑎2
𝑏3)3
= 𝑎2 ∙3
𝑏3 ∙3 = 𝒂𝟔
𝒃𝟗 d) (𝑎
𝑏)−1
= 1
(𝑎
𝑏)1 = 1 : 𝑎
𝑏 = 1 ∙ 𝑏
𝑎 = 𝒃
𝒂
e) [(𝒂𝟑)𝟐𝟓]𝟎 = 1
2a) (-5a2b3)(4ab2) = -20a2 + 1b3 + 2 = -20a3b5 b) 6𝑎3𝑏4
3𝑎𝑏2 = (6 : 3)a3 – 1b4-2 = 2a2b2
c) (-2x3)3 = (-2)3x3 ∙ 3 = -8x9 d) (𝑦2
2𝑥)4
= 𝑦2 ∙4
24𝑥4 = 𝒚𝟖
𝟏𝟔𝒙𝟒
3a) 5-2 = 1
52 = 𝟏
𝟐𝟓 b) -52 = -25
c) [(𝟏
𝟐)−𝟏
]
𝟑
= (𝟏
𝟐)−𝟏 ∙𝟑
= 𝟏−𝟑
𝟐−𝟑 = 𝟏
𝟏
𝟐𝟑
= 1: 1
8 = 1 ∙ 8 = 8 d) (-5)-3 = 1
(−5)3 = - 𝟏
𝟏𝟐𝟓
Bonus: (2-1 + 2-2)-2 = (1
2 + 1
22)−2
= (1
2 + 1
4)−2
= (3
4)−2
= 1
(3
4)2 = 1 : 32
42 = 1 ∙ 16
9 = 1𝟕
𝟗
Quiz # 2
1. a) 3 520 000 000 = 3.52 ∙ 109 b) 0.0000148 = 1.48 ∙ 10-5
c) 0.025 ∙ 10-4 = 2.5 ∙ 10-6 d) 156 ∙ 103 = 1.56 ∙ 105
2a) (I) nearest tenth 3.4956 ≈ 3.5 (II) in three significant figures 3.4956 ≈ 3.50
b) (I) nearest hundreds 786.832 ≈ 800 (II) nearest hundredth 786.832 ≈ 786.83
Bonus 8 ∙ 106∙ 8 ∙ 102
2 ∙ 103 = 64
2 ∙ 106 + 2 – 3 = 32 ∙ 105 = 3.2 ∙ 106
Quiz # 3
1.) 53
59 = 53-9 = 5-6 = 𝟏
𝟓𝟔 2.) 5a5
3a3 = 12
3 a5-3 = 𝟏𝟐
𝟑 a2 3.) (-46x2y3z)0 = 1
4a) 1
𝑥−3 = 1 : 1
𝑥3 = 1 ∙ x3 = x3 b) 𝑥−3
𝑥−7 = 1
𝑥3 ∶ 1
𝑥7 = 1
𝑥3 ∙ x7 = x7 –3 = x4
5.) (-3x-1y2)2 = (-3)2x-1 ∙ 2y2 ∙ 2 = 9𝒚𝟒
𝒙𝟐 6.) (-5x-2y)(-2x-3y2) = 10x-2 + (-3)y1 + 2 = 10𝒚𝟑
𝒙𝟓
7a) (3
𝑥)−2
= 3−2
𝑥−2 = 𝟏
𝟗 ∙ x2 b) x6x5 = x6 + 5 = x11
c) −6
𝑥−2 = -6 : 1
𝑥2 = -6x2 d) 3𝑥−2𝑦
𝑥𝑦 = 3x-2 – 1y1 – 1 = 3 ∙ 𝟏
𝒙𝟑
Grade 8
www.Klassenarbeiten.de Seite 3
Results
Quiz # 1
1.) a) x5 ∙ x4 = x5 + 4 = x9 b) 𝑎6
𝑎 = a6 – 1 = a5
c) (𝑎2
𝑏3)3
= 𝑎2 ∙3
𝑏3 ∙3 = 𝒂𝟔
𝒃𝟗 d) (𝑎
𝑏)−1
= 1
(𝑎
𝑏)1 = 1 : 𝑎
𝑏 = 1 ∙ 𝑏
𝑎 = 𝒃
𝒂
e) [(𝒂𝟑)𝟐𝟓]𝟎 = 1
2a) (-5a2b3)(4ab2) = -20a2 + 1b3 + 2 = -20a3b5 b) 6𝑎3𝑏4
3𝑎𝑏2 = (6 : 3)a3 – 1b4-2 = 2a2b2
c) (-2x3)3 = (-2)3x3 ∙ 3 = -8x9 d) (𝑦2
2𝑥)4
= 𝑦2 ∙4
24𝑥4 = 𝒚𝟖
𝟏𝟔𝒙𝟒
3a) 5-2 = 1
52 = 𝟏
𝟐𝟓 b) -52 = -25
c) [(𝟏
𝟐)−𝟏
]
𝟑
= (𝟏
𝟐)−𝟏 ∙𝟑
= 𝟏−𝟑
𝟐−𝟑 = 𝟏
𝟏
𝟐𝟑
= 1: 1
8 = 1 ∙ 8 = 8 d) (-5)-3 = 1
(−5)3 = - 𝟏
𝟏𝟐𝟓
Bonus: (2-1 + 2-2)-2 = (1
2 + 1
22)−2
= (1
2 + 1
4)−2
= (3
4)−2
= 1
(3
4)2 = 1 : 32
42 = 1 ∙ 16
9 = 1𝟕
𝟗
Quiz # 2
1. a) 3 520 000 000 = 3.52 ∙ 109 b) 0.0000148 = 1.48 ∙ 10-5
c) 0.025 ∙ 10-4 = 2.5 ∙ 10-6 d) 156 ∙ 103 = 1.56 ∙ 105
2a) (I) nearest tenth 3.4956 ≈ 3.5 (II) in three significant figures 3.4956 ≈ 3.50
b) (I) nearest hundreds 786.832 ≈ 800 (II) nearest hundredth 786.832 ≈ 786.83
Bonus 8 ∙ 106∙ 8 ∙ 102
2 ∙ 103 = 64
2 ∙ 106 + 2 – 3 = 32 ∙ 105 = 3.2 ∙ 106
Quiz # 3
1.) 53
59 = 53-9 = 5-6 = 𝟏
𝟓𝟔 2.) 5a5
3a3 = 12
3 a5-3 = 𝟏𝟐
𝟑 a2 3.) (-46x2y3z)0 = 1
4a) 1
𝑥−3 = 1 : 1
𝑥3 = 1 ∙ x3 = x3 b) 𝑥−3
𝑥−7 = 1
𝑥3 ∶ 1
𝑥7 = 1
𝑥3 ∙ x7 = x7 –3 = x4
5.) (-3x-1y2)2 = (-3)2x-1 ∙ 2y2 ∙ 2 = 9𝒚𝟒
𝒙𝟐 6.) (-5x-2y)(-2x-3y2) = 10x-2 + (-3)y1 + 2 = 10𝒚𝟑
𝒙𝟓
7a) (3
𝑥)−2
= 3−2
𝑥−2 = 𝟏
𝟗 ∙ x2 b) x6x5 = x6 + 5 = x11
c) −6
𝑥−2 = -6 : 1
𝑥2 = -6x2 d) 3𝑥−2𝑦
𝑥𝑦 = 3x-2 – 1y1 – 1 = 3 ∙ 𝟏
𝒙𝟑
