Algebra Basics: Variables, Expressions, and Patterns — Practice Worksheet

1. True / False (1 pts)

A symbol like k used to represent a changing quantity is called a variable.

✓ Answer

True

2. True / False (1 pts)

The expression 4 + x represents 4 multiplied by x.

✓ Answer

False

3. True / False (1 pts)

In the expression 9p - 6, 9 is a coefficient.

✓ Answer

True

4. True / False (1 pts)

The perimeter of a square with side s equals 2s.

✓ Answer

False

5. True / False (1 pts)

If a = 3, then 2a + 1 equals 7.

✓ Answer

True

6. True / False (1 pts)

The distributive property lets us rewrite 7(m + 2) as 7m + 14.

✓ Answer

True

7. True / False (1 pts)

For whole-number n, the product 3n can be an even number only.

✓ Answer

False

8. True / False (1 pts)

The expressions y + y + y and 3y are equivalent.

✓ Answer

True

9. True / False (1 pts)

If each box has q pens, then 5 boxes contain q + 5 pens.

✓ Answer

False

10. True / False (1 pts)

For any numbers a and b, a + b = b + a is an example of the associative property.

✓ Answer

False

11. Multiple Choice (2 pts)

Which expression represents “12 more than a number t”?

✓ Answer

A. t + 12

12. Multiple Choice (2 pts)

“Subtract 9 from the product of m and n” is written as:

✓ Answer

B. mn - 9

13. Multiple Choice (2 pts)

Which is equivalent to 6(x + 4)?

✓ Answer

A. 6x + 24

14. Multiple Choice (2 pts)

Find the value of 3x - 5 when x = 4.

✓ Answer

A. 7

15. Multiple Choice (2 pts)

Identify the property: (p + q) + r = p + (q + r).

✓ Answer

B. Associative of addition

16. Multiple Choice (2 pts)

Perimeter of a rectangle with length L and breadth B is:

✓ Answer

B. 2(L + B)

17. Multiple Choice (2 pts)

If each packet holds 25 cookies, how many cookies are in k packets?

✓ Answer

C. 25k

18. Multiple Choice (2 pts)

Which inequality represents “x is at least 7”?

✓ Answer

C. x >= 7

19. Multiple Choice (2 pts)

Which pair could represent two consecutive even integers?

✓ Answer

B. 2n and 2n + 2

20. Multiple Choice (2 pts)

If s is the side length of a square, which expression gives its area?

✓ Answer

C. s^2

21. Fill in the Blank (2 pts)

A number that does not change in value is called a _____.

✓ Answer

constant

22. Fill in the Blank (2 pts)

The expression for “7 multiplied by n” is _____.

✓ Answer

7n

23. Fill in the Blank (2 pts)

The coefficient of x in 5x + 2 is _____.

✓ Answer

5

24. Fill in the Blank (2 pts)

The perimeter of a square with side a is _____.

✓ Answer

4a

25. Fill in the Blank (2 pts)

The expression “the sum of y and 11” can be written as _____.

✓ Answer

y+11

26. Fill in the Blank (2 pts)

When like terms are combined, 4k + 3k becomes _____.

✓ Answer

7k

27. Fill in the Blank (2 pts)

If x = 2 and y = 3, then x + 2y equals _____.

✓ Answer

8

28. Fill in the Blank (2 pts)

Using the distributive property, 9(t + 1) is rewritten as _____.

✓ Answer

9t+9

29. Fill in the Blank (2 pts)

“r exceeds s” can be expressed as _____.

✓ Answer

r>s

30. Fill in the Blank (2 pts)

If each letter in a pattern uses 4 matchsticks, the total for n letters is _____.

✓ Answer

4n

31. Word Problem (5 pts)

A student buys 3 notebooks at p rupees each and one pen for 12 rupees. Write an expression for the total cost and find the amount when p = 18.

✎ Worked Solution

Step 1: Total cost expression = 3p + 12

Step 2: Substitute p = 18 → 3(18) + 12 = 54 + 12

Answer: 66 rupees

32. Word Problem (5 pts)

The side length of an equilateral triangle is x cm. Write a rule for its perimeter and evaluate it for x = 9 cm.

✎ Worked Solution

Step 1: Perimeter of an equilateral triangle = 3x

Step 2: Substitute x = 9 → 3(9)

Answer: 27 cm

33. Word Problem (5 pts)

There are b bags with 6 apples in each. If 4 apples are eaten, how many apples remain? Also find the number when b = 7.

✎ Worked Solution

Step 1: Total apples = 6b

Step 2: Apples remaining = 6b - 4

Step 3: For b = 7 → 6(7) - 4 = 42 - 4

Answer: 38 apples

34. Word Problem (5 pts)

A taxi charges a base fare of 50 rupees plus 15 rupees per kilometer for d kilometers. Write the expression for the fare and compute it for d = 8.

✎ Worked Solution

Step 1: Fare expression = 50 + 15d

Step 2: Substitute d = 8 → 50 + 15(8) = 50 + 120

Answer: 170 rupees

35. Word Problem (5 pts)

Let the smaller of two consecutive odd integers be 2n + 1. Their sum is 40. Find n and the two integers.

✎ Worked Solution

Step 1: Consecutive odd integers = 2n + 1 and 2n + 3

Step 2: Sum = (2n + 1) + (2n + 3) = 4n + 4

Step 3: Set 4n + 4 = 40 → 4n = 36 → n = 9

Answer: n = 9; integers are 19 and 21

36. Word Problem (5 pts)

A rectangular garden has width w meters and length that is 3 meters more than the width. Write the perimeter in terms of w and find it when w = 10.

✎ Worked Solution

Step 1: Length = w + 3

Step 2: Perimeter P = 2(w + (w + 3)) = 2(2w + 3)

Step 3: Simplify P = 4w + 6; for w = 10 → 4(10) + 6

Answer: 46 meters

37. Word Problem (5 pts)

Evaluate 4a + 2(3a - 5) for a = 7, showing the use of the distributive property.

✎ Worked Solution

Step 1: Expand 2(3a - 5) = 6a - 10

Step 2: 4a + (6a - 10) = 10a - 10

Step 3: Substitute a = 7 → 10(7) - 10 = 70 - 10

Answer: 60

38. Word Problem (5 pts)

A jar has 500 mL of juice. After pouring 4 glasses of g mL each, how much juice is left? Also find the amount left when g = 120.

✎ Worked Solution

Step 1: Total poured = 4g

Step 2: Juice left = 500 - 4g

Step 3: For g = 120 → 500 - 4(120) = 500 - 480

Answer: 20 mL

39. Word Problem (5 pts)

A pattern uses M(n) = 5n + 2 matchsticks for the nth figure. How many matchsticks are needed for the 12th figure?

✎ Worked Solution

Step 1: Use the rule M(n) = 5n + 2

Step 2: Substitute n = 12 → M(12) = 5(12) + 2 = 60 + 2

Answer: 62 matchsticks

40. Word Problem (5 pts)

On a class trip, each of x students pays 320 rupees. The bus costs 4500 rupees. Write an expression for the money left after paying for the bus and evaluate it for x = 20.

✎ Worked Solution

Step 1: Total collected = 320x

Step 2: Money left = 320x - 4500

Step 3: For x = 20 → 320(20) - 4500 = 6400 - 4500

Answer: 1900 rupees