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Mathematics

Introduction to Algebra: Variables, Expressions, and Perimeter — Practice Worksheet

Introductory Algebra: variables vs. constants, coefficients, properties, expressions, evaluation, and perimeter rules
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 Algebra uses variables to represent quantities that can change.
1 pt
True
False
Answer: True
2.
True / False In the term 9k, 9 is the variable.
1 pt
True
False
Answer: False
3.
True / False The perimeter of a square with side s is 3s.
1 pt
True
False
Answer: False
4.
True / False The distributive property allows you to expand a(b + c) into ab + ac.
1 pt
True
False
Answer: True
5.
True / False For all real numbers a and b, a + b = b + a.
1 pt
True
False
Answer: True
6.
True / False Variables must always be lowercase letters.
1 pt
True
False
Answer: False
7.
True / False Evaluating 4t − 1 at t = 0 gives 4.
1 pt
True
False
Answer: False
8.
True / False An algebraic expression may include more than one variable.
1 pt
True
False
Answer: True
9.
True / False In 6m + 2n, m and n are the literal coefficients.
1 pt
True
False
Answer: True
10.
True / False Two consecutive even integers differ by 1.
1 pt
True
False
Answer: False
11.
Multiple Choice In 12p, which identifies the variable and the numerical coefficient?
2 pts
A. Variable: 12; Coefficient: p
B. Variable: p; Coefficient: 12
C. Variable: 12p; Coefficient: 1
D. Variable: 12; Coefficient: 1
Answer: B. Variable: p; Coefficient: 12
12.
Multiple Choice Which statement shows the commutative property of multiplication?
2 pts
A. a + (b + c) = (a + b) + c
B. a(b + c) = ab + ac
C. ab = ba
D. (ab)c = a(bc)
Answer: C. ab = ba
13.
Multiple Choice If a = 5, what is the value of 3a + 4?
2 pts
A. 11
B. 19
C. 17
D. 34
Answer: B. 19
14.
Multiple Choice Which expression represents “twice a number decreased by seven”?
2 pts
A. 2x + 7
B. 2x − 7
C. 7 − 2x
D. x/2 − 7
Answer: B. 2x − 7
15.
Multiple Choice A rectangle has length 3x and width x + 2. Which expression equals its perimeter?
2 pts
A. 6x + 2x
B. 2(3x + x + 2)
C. 8x + 4
D. 3x(x + 2)
Answer: C. 8x + 4
16.
Multiple Choice Which of the following is an algebraic expression?
2 pts
A. 4 + 7
B. x/5 + 2
C. 18 × 3
D. 9 − 1
Answer: B. x/5 + 2
17.
Multiple Choice Which property lets you rewrite 7(n + 3) as 7n + 21?
2 pts
A. Commutative property of addition
B. Associative property of multiplication
C. Distributive property
D. Identity property of 0
Answer: C. Distributive property
18.
Multiple Choice For an equilateral triangle with side y, the perimeter is:
2 pts
A. y^2
B. 2y
C. 3y
D. 4y
Answer: C. 3y
19.
Multiple Choice What is the constant term in 9 − 5q + 2?
2 pts
A. -5
B. 11
C. 9
D. -5q
Answer: B. 11
20.
Multiple Choice If x = 1 and y = 4, what is 2x + 3y?
2 pts
A. 10
B. 14
C. 12
D. 18
Answer: B. 14
21.
Fill in the Blank A symbol that can take different values is called a _____.
2 pts
Answer: variable
22.
Fill in the Blank A number that stays the same in an expression is a _____.
2 pts
Answer: constant
23.
Fill in the Blank In 14z, 14 is the numerical _____.
2 pts
Answer: coefficient
24.
Fill in the Blank The rule a × (b + c) = ab + ac is the _____ property.
2 pts
Answer: distributive
25.
Fill in the Blank The perimeter of a polygon is the sum of the lengths of all its _____.
2 pts
Answer: sides
26.
Fill in the Blank The perimeter of a square with side s is _____.
2 pts
Answer: 4s
27.
Fill in the Blank When x = 3, the value of 2x + 1 is _____.
2 pts
Answer: 7
28.
Fill in the Blank Consecutive odd integers differ by _____.
2 pts
Answer: 2
29.
Fill in the Blank An expression built from variables, constants, and operations is an algebraic _____.
2 pts
Answer: expression
30.
Fill in the Blank In 5p + 3q, p and q are the _____ coefficients.
2 pts
Answer: literal
31.
Word Problem A herb garden is planted in rows. The first row has 6 plants, and each following row has 4 more plants than the previous row. The number of plants in row r is given by 6 + 4(r − 1). How many plants are in row 8? Show your working.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Substitute r = 8 into 6 + 4(r − 1): 6 + 4(8 − 1)
Step 2: Compute inside parentheses: 6 + 4(7) = 6 + 28
Step 3: Add: 6 + 28 = 34
Answer: 34 plants
32.
Word Problem A rectangle has length 3x + 2 and width x − 1. If x = 4, find its perimeter. Use P = 2(l + w).
5 pts
Working:
Answer:
Worked Solution:
Step 1: Compute length l = 3(4) + 2 = 12 + 2 = 14
Step 2: Compute width w = 4 − 1 = 3
Step 3: Find l + w = 14 + 3 = 17
Step 4: Perimeter P = 2(17) = 34
Answer: 34 units
33.
Word Problem Mira has n stickers. Leo has 2n + 3 stickers. If n = 12, how many stickers does Leo have?
5 pts
Working:
Answer:
Worked Solution:
Step 1: Substitute n = 12 into 2n + 3: 2(12) + 3
Step 2: Multiply and add: 24 + 3 = 27
Answer: 27 stickers
34.
Word Problem Evaluate 5(a + 2) − 3a when a = 4. Show each algebraic step.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Expand using distributive property: 5a + 10 − 3a = 2a + 10
Step 2: Substitute a = 4: 2(4) + 10 = 8 + 10
Step 3: Add: 18
Answer: 18
35.
Word Problem Notebooks cost $2.25 each and pens cost $0.75 each. Write an expression for the total cost of 4 notebooks and 6 pens, then compute its value.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Form the expression: Total = 4(2.25) + 6(0.75)
Step 2: Multiply: 4(2.25) = 9.00 and 6(0.75) = 4.50
Step 3: Add: 9.00 + 4.50 = 13.50
Answer: $13.50
36.
Word Problem An equilateral triangle has side length 12.3 cm. Find its perimeter.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Use P = 3a for equilateral triangle with side a
Step 2: Substitute a = 12.3: P = 3(12.3) = 36.9
Answer: 36.9 cm
37.
Word Problem A square has side length y + 1 meters. If y = 6, find the perimeter of the square.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Compute side: y + 1 = 6 + 1 = 7
Step 2: Perimeter of a square P = 4s = 4(7) = 28
Answer: 28 meters
38.
Word Problem The sum of two consecutive odd integers is 36. Find the two integers.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Let the integers be n and n + 2
Step 2: Write equation: n + (n + 2) = 36 → 2n + 2 = 36
Step 3: Solve: 2n = 34 → n = 17; next is n + 2 = 19
Answer: 17 and 19
39.
Word Problem A row of n adjacent squares is built from matchsticks. The total number of matchsticks is M = 3n + 1. How many matchsticks are needed for 9 squares?
5 pts
Working:
Answer:
Worked Solution:
Step 1: Substitute n = 9 into M = 3n + 1
Step 2: Compute: M = 3(9) + 1 = 27 + 1 = 28
Answer: 28 matchsticks
40.
Word Problem A rectangle’s length is triple its width. If its perimeter is 64 units, find the rectangle’s width and length.
5 pts
Working:
Answer:
Worked Solution:
Step 1: Let width be w and length be 3w; perimeter P = 2(l + w) = 64
Step 2: Set up equation: 2(3w + w) = 64 → 2(4w) = 64 → 8w = 64
Step 3: Solve for w: w = 8; then l = 3w = 24
Answer: Width = 8 units, Length = 24 units
40
Total Questions
100
Total Points
~35
Minutes