Holt Algebra 1 - Chapter 01 Test PDF | PDF | Celsius | Function ... - Free Printable

Let's go through each problem step by step and solve them with explanations.

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Evaluate the expression.

1. $ 12 - q $ when $ q = 8 $

Substitute $ q = 8 $:
$ 12 - 8 = 4 $

✔ Answer: 4

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2. $ 3x $ when $ x = 9 $

Substitute $ x = 9 $:
$ 3 \times 9 = 27 $

✔ Answer: 27

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3. $ w^3 $ when $ w = 2 $

Cube $ w $:
$ 2^3 = 2 \times 2 \times 2 = 8 $

✔ Answer: 8

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4. $ \frac{24}{t} $ when $ t = 4 $

Divide:
$ \frac{24}{4} = 6 $

✔ Answer: 6

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Write the power as a product.

5. $ 10^4 $

This means $ 10 \times 10 \times 10 \times 10 $

✔ Answer: $ 10 \times 10 \times 10 \times 10 $

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6. $ (2.6)^3 $

This means $ 2.6 \times 2.6 \times 2.6 $

✔ Answer: $ 2.6 \times 2.6 \times 2.6 $

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7. $ n^6 $

This means $ n \times n \times n \times n \times n \times n $

✔ Answer: $ n \times n \times n \times n \times n \times n $

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8. The height of a horse is often measured in hands. You can estimate the height (in inches) of a horse by using the expression $ 4h $, where $ h $ is the number of hands. How tall is a horse that measures 14 hands?

Use the formula:
$ 4h = 4 \times 14 = 56 $ inches

✔ Answer: 56 inches

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Evaluate the expression.

9. $ 15 - 7 \cdot 2 $

Order of operations: multiplication first
$ 7 \cdot 2 = 14 $
Then: $ 15 - 14 = 1 $

✔ Answer: 1

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10. $ 2 + 2^3 \div 4 $

First, exponent: $ 2^3 = 8 $
Then division: $ 8 \div 4 = 2 $
Then addition: $ 2 + 2 = 4 $

✔ Answer: 4

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11. $ 5(3^2 - 4) $

Exponent: $ 3^2 = 9 $
Then subtraction: $ 9 - 4 = 5 $
Then multiplication: $ 5 \times 5 = 25 $

✔ Answer: 25

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Translate the verbal phrase into an algebraic expression.

12. The sum of a number $ x $ and 9

"Sum" means addition:
$ x + 9 $

✔ Answer: $ x + 9 $

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13. The number of quarters in $ d $ dollars

There are 4 quarters in a dollar, so:
$ 4d $

✔ Answer: $ 4d $

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Write an equation or an inequality.

14. Three more than twice a number $ b $ is equal to 13.

"Twice a number $ b $" → $ 2b $
"Three more than" → $ 2b + 3 $
"Is equal to 13" → $ = 13 $

So: $ 2b + 3 = 13 $

✔ Answer: $ 2b + 3 = 13 $

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15. The product of 5 and a number $ k $ is less than 60.

"Product" → $ 5k $
"Less than 60" → $ < 60 $

So: $ 5k < 60 $

✔ Answer: $ 5k < 60 $

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Check whether the given number is a solution of the equation or the inequality.

16. $ 10x - 3 = 27 $; check $ x = 3 $

Plug in $ x = 3 $:
$ 10(3) - 3 = 30 - 3 = 27 $ → True

✔ Answer: Yes, it is a solution

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17. $ 4y - 1 \geq 20 $; check $ y = 4 $

$ 4(4) - 1 = 16 - 1 = 15 $
Is $ 15 \geq 20 $? No.

✘ Answer: No, it is not a solution

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18. $ 2x + 1 < 17 $; check $ x = 8 $

$ 2(8) + 1 = 16 + 1 = 17 $
Is $ 17 < 17 $? No (it's equal)

✘ Answer: No, it is not a solution

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19. $ 4a - 7 = 3a - 4 $; check $ a = 3 $

Left side: $ 4(3) - 7 = 12 - 7 = 5 $
Right side: $ 3(3) - 4 = 9 - 4 = 5 $
Both sides equal → True

✔ Answer: Yes, it is a solution

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20. A bicycle travels at an average speed of 15 miles per hour. How many miles does the bicycle travel in 1.5 hours?

Use formula: distance = rate × time
$ 15 \times 1.5 = 22.5 $ miles

✔ Answer: 22.5 miles

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Tell whether the statement is always, sometimes, or never true.

21. For a given whole number $ x $, the expression $ 10x $ represents an even number.

- $ 10x = 2 \times 5x $ → always divisible by 2
- So $ 10x $ is always even

✔ Answer: Always true

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22. For any positive number $ x $, $ x^2 < x $

Test values:

- If $ x = 1 $: $ 1^2 = 1 $, so $ 1 < 1 $? No → false
- If $ x = 0.5 $: $ 0.25 < 0.5 $? Yes → true
- If $ x = 2 $: $ 4 < 2 $? No → false

So it's true for some values (like $ x < 1 $) but false for others

✔ Answer: Sometimes true

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 4 |
| 2 | 27 |
| 3 | 8 |
| 4 | 6 |
| 5 | $ 10 \times 10 \times 10 \times 10 $ |
| 6 | $ 2.6 \times 2.6 \times 2.6 $ |
| 7 | $ n \times n \times n \times n \times n \times n $ |
| 8 | 56 inches |
| 9 | 1 |
| 10 | 4 |
| 11 | 25 |
| 12 | $ x + 9 $ |
| 13 | $ 4d $ |
| 14 | $ 2b + 3 = 13 $ |
| 15 | $ 5k < 60 $ |
| 16 | Yes |
| 17 | No |
| 18 | No |
| 19 | Yes |
| 20 | 22.5 miles |
| 21 | Always true |
| 22 | Sometimes true |

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