Grade 7 Math Chapter 1 Test featuring six questions on algebra, patterns, and equations.

Let's solve each question step by step and explain the reasoning.

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Question 1:

Which expression has a value of 74 when x = 10, y = 8, and z = 12?

We'll substitute the values into each option:

- A) 4xyz
$ 4 \times 10 \times 8 \times 12 = 4 \times 960 = 3840 $ → Not 74

- B) x + 5y + 2z
$ 10 + 5(8) + 2(12) = 10 + 40 + 24 = 74 $ ✔

- C) 2xz - 3y
$ 2(10)(12) - 3(8) = 240 - 24 = 216 $ → Not 74

- D) 6xyz + 8
$ 6 \times 10 \times 8 \times 12 + 8 = 5760 + 8 = 5768 $ → Not 74

✔ Answer: B

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Question 2:

Which of the following is an example of the commutative property?

The commutative property states that changing the order of numbers in addition or multiplication does not change the result.
For example: $ a + b = b + a $

- A) 20 + 10 = 2(10 + 5)
Left: 30, Right: 2(15) = 30 → True, but this is not commutative; it's distributive.

- B) 20 + 10 = 10 + 20
This shows switching order → Yes, this is the commutative property of addition. ✔

- C) 5 + (20 + 10) = (5 + 20) + 10
This is associative property (grouping changes), not commutative.

- D) 20 + 0 = 20
Identity property of addition.

✔ Answer: B

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Question 3:

What are the next two numbers in the pattern?
75, 70, 60, 55, 45, 40 ...

Let’s look at the pattern:

- 75 → 70: –5
- 70 → 60: –10
- 60 → 55: –5
- 55 → 45: –10
- 45 → 40: –5

Pattern: Alternating subtraction of 5 and 10

So:
- After 40: subtract 10 → 30
- Then subtract 5 → 25

Sequence: 75, 70, 60, 55, 45, 40, 30, 25

✔ Answer: C) 30, 25

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Question 4:

Benjamin spends $78 for n shirts. Which equation can be used to show the cost of one shirt?

Total cost = $78
Number of shirts = n
Cost per shirt = Total ÷ Number = $78 ÷ n

So, the equation is:
78/n

✔ Answer: D) 78/n

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Question 5:

Solve the equation: 20 = n - 12

Add 12 to both sides:
$ 20 + 12 = n $
$ n = 32 $

✔ Answer: A) 32

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Question 6:

Find the value: $6^2$

$6^2 = 6 \times 6 = 36$

✔ Answer: D) 36

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✔ Final Answers:

1. B
2. B
3. C
4. D
5. A
6. D

Let me know if you'd like these explained further!