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Mathematics

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

Introductory Algebra (variables, expressions, properties, perimeters, and patterns)
100 pts
40 questions • ~35 min
Aayush Nayak
6-B
Grade 6
YBIS
Home
Read each question carefully and answer to the best of your ability. Show all working for word problems.
1.
True / False A symbol like k used to represent a changing quantity is called a variable.
1 pt
True
False
Answer: True
2.
True / False The expression 4 + x represents 4 multiplied by x.
1 pt
True
False
Answer: False
3.
True / False In the expression 9p - 6, 9 is a coefficient.
1 pt
True
False
Answer: True
4.
True / False The perimeter of a square with side s equals 2s.
1 pt
True
False
Answer: False
5.
True / False If a = 3, then 2a + 1 equals 7.
1 pt
True
False
Answer: True
6.
True / False The distributive property lets us rewrite 7(m + 2) as 7m + 14.
1 pt
True
False
Answer: True
7.
True / False For whole-number n, the product 3n can be an even number only.
1 pt
True
False
Answer: False
8.
True / False The expressions y + y + y and 3y are equivalent.
1 pt
True
False
Answer: True
9.
True / False If each box has q pens, then 5 boxes contain q + 5 pens.
1 pt
True
False
Answer: False
10.
True / False For any numbers a and b, a + b = b + a is an example of the associative property.
1 pt
True
False
Answer: False
11.
Multiple Choice Which expression represents “12 more than a number t”?
2 pts
A. t + 12
B. 12t
C. t - 12
D. 12 - t
Answer: A. t + 12
12.
Multiple Choice “Subtract 9 from the product of m and n” is written as:
2 pts
A. 9mn
B. mn - 9
C. m - 9n
D. 9 - mn
Answer: B. mn - 9
13.
Multiple Choice Which is equivalent to 6(x + 4)?
2 pts
A. 6x + 24
B. 10x
C. 6x + 4
D. 24x
Answer: A. 6x + 24
14.
Multiple Choice Find the value of 3x - 5 when x = 4.
2 pts
A. 7
B. 12
C. -1
D. 17
Answer: A. 7
15.
Multiple Choice Identify the property: (p + q) + r = p + (q + r).
2 pts
A. Commutative of addition
B. Associative of addition
C. Distributive over addition
D. Additive identity
Answer: B. Associative of addition
16.
Multiple Choice Perimeter of a rectangle with length L and breadth B is:
2 pts
A. L + B
B. 2(L + B)
C. 4(L + B)
D. LB
Answer: B. 2(L + B)
17.
Multiple Choice If each packet holds 25 cookies, how many cookies are in k packets?
2 pts
A. k + 25
B. 25 - k
C. 25k
D. 25/k
Answer: C. 25k
18.
Multiple Choice Which inequality represents “x is at least 7”?
2 pts
A. x = 7
B. x > 7
C. x >= 7
D. x < 7
Answer: C. x >= 7
19.
Multiple Choice Which pair could represent two consecutive even integers?
2 pts
A. 2n and 2n + 1
B. 2n and 2n + 2
C. n and n + 1
D. 2n - 1 and 2n + 1
Answer: B. 2n and 2n + 2
20.
Multiple Choice If s is the side length of a square, which expression gives its area?
2 pts
A. 4s
B. s + s
C. s^2
D. 2s
Answer: C. s^2
21.
Fill in the Blank A number that does not change in value is called a _____.
2 pts
Answer: constant
22.
Fill in the Blank The expression for “7 multiplied by n” is _____.
2 pts
Answer: 7n
23.
Fill in the Blank The coefficient of x in 5x + 2 is _____.
2 pts
Answer: 5
24.
Fill in the Blank The perimeter of a square with side a is _____.
2 pts
Answer: 4a
25.
Fill in the Blank The expression “the sum of y and 11” can be written as _____.
2 pts
Answer: y+11
26.
Fill in the Blank When like terms are combined, 4k + 3k becomes _____.
2 pts
Answer: 7k
27.
Fill in the Blank If x = 2 and y = 3, then x + 2y equals _____.
2 pts
Answer: 8
28.
Fill in the Blank Using the distributive property, 9(t + 1) is rewritten as _____.
2 pts
Answer: 9t+9
29.
Fill in the Blank “r exceeds s” can be expressed as _____.
2 pts
Answer: r>s
30.
Fill in the Blank If each letter in a pattern uses 4 matchsticks, the total for n letters is _____.
2 pts
Answer: 4n
31.
Word Problem 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.
5 pts
Working:
Answer:
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 The side length of an equilateral triangle is x cm. Write a rule for its perimeter and evaluate it for x = 9 cm.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Perimeter of an equilateral triangle = 3x
Step 2: Substitute x = 9 → 3(9)
Answer: 27 cm
33.
Word Problem 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.
5 pts
Working:
Answer:
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 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.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Fare expression = 50 + 15d
Step 2: Substitute d = 8 → 50 + 15(8) = 50 + 120
Answer: 170 rupees
35.
Word Problem Let the smaller of two consecutive odd integers be 2n + 1. Their sum is 40. Find n and the two integers.
5 pts
Working:
Answer:
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 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.
5 pts
Working:
Answer:
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 Evaluate 4a + 2(3a - 5) for a = 7, showing the use of the distributive property.
5 pts
Working:
Answer:
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 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.
5 pts
Working:
Answer:
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 A pattern uses M(n) = 5n + 2 matchsticks for the nth figure. How many matchsticks are needed for the 12th figure?
5 pts
Working:
Answer:
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 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.
5 pts
Working:
Answer:
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
40
Total Questions
100
Total Points
~35
Minutes