G8 U1 Assessment
Name: _________________________________________ Date:________________
Grade 8 Unit 1 Rational and Irrational Numbers 1. For each of the following, circle yes if the number is a rational and no if they are not.
A B
√2 3
Yes/no Yes/No
4
C
𝜋
D
6.54841 Yes/No
Yes/No
2. For each of the following, circle yes if the number is a rational and no if they are not.
A
6.846
Yes/No
B
√16
Yes/No
C D
518 13 12 83
Yes/No Yes/No
3. In order to make this number an irrational, what would go into the blank? 8 ⧠ A
.57
B
5
C D
1 8
none of the above Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 1
4.
Which of the following is not a rational number?
A
1.5
B
1.5
C D
5.
5
√15
What is the fractional equivalent of .89?
A B C D
6.
1
8 9 89 10 89 100 1 89
What is 1.2929 in fraction form?
A B C D
128 99 128 100 132 99 132 100
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 2
7.
8.
9.
Johan converts the repeating decimal 4.206206 to a fraction. He has calculated the answer 4202 to be ⧠ . What is the correct denominator?
A
1000
B
999
C
1100
D
800
Estimate the value of √46. In between what two integers does your estimate lie?
A
9 and 10
B
7 and 8
C
6 and 7
D
5 and 6
In the following, circle the number whose value is larger.
A
√42 and 𝜋
B
√91 and √33
C
√104 and √63
D
√29 and √45 Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 3
10. What does the following expression simplify to? 𝜋 2 + 𝜋 + 4𝜋 2
A
6𝜋
B
6𝜋 2
C
4 + 6𝜋
D
5𝜋 2 + 𝜋
11. What does the following expression simplify to? 6√38 − 2√19 + √38 A
7√38 − 2√19
B
4√8 − 6√12
C
6√15 − 5√21
D
10√32 − 3√11
12. What does the following expression simplify to? √39 + 4√80 + √39 - √15
A
2√39 − √3(√3 − 16)
B
2√39 − √5(√3 − 16)
C
2√39 − √5(√5 − 16)
D
2√49 − √5(√3 − 16) Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 4
13. Approximate √43 − 2√46 + 5√43 − 𝜋. Between what two integers does the value lie?
A
5.2 dollars/ car washed
B
6 dollars/car washed
C
5.5 dollars/ car washed
D
4.8 dollars/ car washed
14. Simplify the following expression, you do not have to make an approximation. Show your work. √23 + 𝜋 3 + 2𝜋 + 4√23 − 𝜋
15. Which irrational number is larger? Why? 2√15 or √50?
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 5
16.
Estimate √97 to the nearest hundredth. Show your work.
2
17. Sketch a line going through (0, 3) with a slope of 5. Label another point on the line (x, y). Draw two similar triangles formed by the line and the y-axis. Set up proportions and find an equation relating x and y.
18. How can this mixed fraction be written as a compound fraction. Then after finding this, write it in its decimal form. Show your work. 6
4 8
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 6
19. Convert 0.44 to a fraction. Is it irrational? Why?
20.
Approximate(√88)2 + 88 + 3𝜋 2 . Show work.
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 7
Grade 8 Unit 1 Rational and Irrational Numbers 1. For each of the following, circle yes if the number is a rational and no if they are not.
A B
√2 3
Yes/no Yes/No
4
C
𝜋
D
6.54841 Yes/No
Yes/No
2. For each of the following, circle yes if the number is a rational and no if they are not.
A
6.846
Yes/No
B
√16
Yes/No
C D
518 13 12 83
Yes/No Yes/No
3. In order to make this number an irrational, what would go into the blank? 8 ⧠ A
.57
B
5
C D
1 8
none of the above Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 1
4.
Which of the following is not a rational number?
A
1.5
B
1.5
C D
5.
5
√15
What is the fractional equivalent of .89?
A B C D
6.
1
8 9 89 10 89 100 1 89
What is 1.2929 in fraction form?
A B C D
128 99 128 100 132 99 132 100
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 2
7.
8.
9.
Johan converts the repeating decimal 4.206206 to a fraction. He has calculated the answer 4202 to be ⧠ . What is the correct denominator?
A
1000
B
999
C
1100
D
800
Estimate the value of √46. In between what two integers does your estimate lie?
A
9 and 10
B
7 and 8
C
6 and 7
D
5 and 6
In the following, circle the number whose value is larger.
A
√42 and 𝜋
B
√91 and √33
C
√104 and √63
D
√29 and √45 Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 3
10. What does the following expression simplify to? 𝜋 2 + 𝜋 + 4𝜋 2
A
6𝜋
B
6𝜋 2
C
4 + 6𝜋
D
5𝜋 2 + 𝜋
11. What does the following expression simplify to? 6√38 − 2√19 + √38 A
7√38 − 2√19
B
4√8 − 6√12
C
6√15 − 5√21
D
10√32 − 3√11
12. What does the following expression simplify to? √39 + 4√80 + √39 - √15
A
2√39 − √3(√3 − 16)
B
2√39 − √5(√3 − 16)
C
2√39 − √5(√5 − 16)
D
2√49 − √5(√3 − 16) Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 4
13. Approximate √43 − 2√46 + 5√43 − 𝜋. Between what two integers does the value lie?
A
5.2 dollars/ car washed
B
6 dollars/car washed
C
5.5 dollars/ car washed
D
4.8 dollars/ car washed
14. Simplify the following expression, you do not have to make an approximation. Show your work. √23 + 𝜋 3 + 2𝜋 + 4√23 − 𝜋
15. Which irrational number is larger? Why? 2√15 or √50?
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 5
16.
Estimate √97 to the nearest hundredth. Show your work.
2
17. Sketch a line going through (0, 3) with a slope of 5. Label another point on the line (x, y). Draw two similar triangles formed by the line and the y-axis. Set up proportions and find an equation relating x and y.
18. How can this mixed fraction be written as a compound fraction. Then after finding this, write it in its decimal form. Show your work. 6
4 8
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 6
19. Convert 0.44 to a fraction. Is it irrational? Why?
20.
Approximate(√88)2 + 88 + 3𝜋 2 . Show work.
Copyright © Swun Math Grade 8 Unit 1 Assessment, Page 7
