Algebra for 5th Graders: Patterns and Equations Made Easy

Question 1

To solve the equation 3(x - 2) = 15, what should you do first?

Accepted Answer

Distribute the 3 to the terms inside the parentheses.

Answer

Multiply 3 to the terms inside the parentheses.

Answer

Add 2 to both sides of the equation.

Answer

Divide both sides of the equation by 3.

Question 2

A rectangle has a length of 5 cm and a width of 2x cm. What is the perimeter of the rectangle?

Accepted Answer

10 cm + 4x cm

Answer

5x cm

Answer

5 cm + 2x cm

Answer

2x cm

Question 3

What is the algebraic expression for 'the product of 7 and a number, x'?

Accepted Answer

7x

Answer

x + 7

Answer

7 - x

Question 4

Combine like terms to simplify the expression: 2x + 5 + 3x - 2

Accepted Answer

5x + 3

Answer

5x - 3

Answer

3x + 3

Answer

3x - 3

Question 5

What is the algebraic expression for 'the total after adding nine to a number'?

Accepted Answer

n + 9

Answer

9 - n

Answer

n - 9

Question 6

You have a number. When you add double that number to the original number, the total is 21. Write this as an equation.

Accepted Answer

x + 2x = 21

Answer

2x + 1 = 21

Answer

x - 2x = 21

Answer

2x - 1 = 21

Question 7

In the equation 3x + y = 6, what does the number '3' represent?

Accepted Answer

The coefficient of the x-term

Answer

The y-intercept

Answer

The x-intercept

Answer

The solution to the equation

Question 8

Examine the pattern: 1, 4, 9, 16, 25, ... Write an algebraic expression that represents the nth term of this pattern.

Accepted Answer

n^2

Answer

n + 1

Answer

2n

Answer

n + 2

Question 9

A farmer starts with 12 sheep. He buys 6 more sheep and then sells half of his total number of sheep. How many sheep does the farmer have left?

Accepted Answer

9

Answer

6

Answer

12

Answer

18

Question 10

A rectangular garden has a length of x meters and a width of y meters. What equation represents the total distance around the garden, which is 20 meters?

Accepted Answer

2x + 2y = 20

Answer

x + y = 20

Answer

x - y = 20

Answer

2xy = 20

Question 11

What is an example of a mathematical pattern?

Accepted Answer

Adding 2 to each number in a sequence

Answer

The number of sides on a polygon

Answer

The number of days in a week

Answer

Rolling a dice

Question 12

If x = 2, what is the value of the expression: 3x + 5?

Accepted Answer

11

Answer

5

Answer

15

Answer

20

Question 13

What is the missing number in the pattern: 2, 4, 8, 16, ___, 64

Accepted Answer

32

Answer

24

Answer

40

Answer

48

Question 14

Which of the following is a letter that represents an unknown number?

Accepted Answer

x

Answer

2

Answer

5 + 3

Answer

ABC

Question 15

In the equation: y - 7 = 12, what is the value of y?

Accepted Answer

19

Answer

5

Answer

12

Answer

24

Question 16

Which of the following is an algebraic expression?

Accepted Answer

5x + 2y

Answer

2 + 3

Answer

x = 5

Answer

10 - 5

Question 17

How is an algebraic expression different from an equation?

Accepted Answer

An equation has an equals sign, while an expression does not.

Answer

An expression is a statement, while an equation is a question.

Answer

An equation is true for all numbers, while an expression is not.

Answer

An expression has variables, while an equation does not.

Question 18

Which step is NOT used to solve the equation 2x - 5 = 7?

Accepted Answer

Multiply both sides by 2.

Answer

Add 5 to both sides.

Answer

Divide both sides by 2.

Answer

Subtract 5 from both sides.

Question 19

What is the value of n in the equation 3(n - 2) = 15?

Accepted Answer

7

Answer

3

Answer

5

Answer

9

Question 20

What is the next number in the sequence 2, 5, 8, 11, ...?

Accepted Answer

13

Answer

14

Answer

15

Answer

16

Question 21

A farmer has 12 sheep. He buys more sheep and now has 25 sheep in total. Write an equation to show this.

Accepted Answer

12 + x = 25

Answer

25 - 12 = x

Answer

12x = 25

Answer

x - 12 = 25

Question 22

Write an algebraic expression for the following sentence: The product of 3 and a number, x.

Accepted Answer

3 * x

Answer

x + 3

Answer

x - 3

Answer

x / 3

Question 23

In the expression 3x - 4, what does the number in front of the variable represent?

Accepted Answer

The coefficient of x

Answer

The value of x

Answer

The result of multiplying x by 3

Question 24

In the pattern 2, 5, 8, 11, ..., what is the rule that generates each term? Express the rule as an algebraic expression for the nth term.

Accepted Answer

Add 3 to the previous term

Answer

Multiply the previous term by 3

Answer

Add 5 to the previous term

Answer

The pattern is random

Question 25

In the equation 3x + y = 6, what does the number in front of the variable x represent?

Accepted Answer

The coefficient of the variable term

Answer

The number of solutions to the equation

Answer

The constant term

Question 26

A farmer has 10 chickens. Each chicken lays 2 eggs per day. How many eggs do the farmer's chickens lay in 7 days?

Accepted Answer

140 eggs

Answer

20 eggs

Answer

280 eggs

Answer

70 eggs

Question 27

Translate this sentence into an algebraic expression: The difference between 10 and a number, represented by 'x'

Accepted Answer

10 - x

Answer

x + 10

Answer

x - 10

Answer

10x

Question 28

What is the algebraic expression for the perimeter of a rectangle with a length of (x + 2) cm and a width of (x - 1) cm?

Accepted Answer

2(x + 2 + x - 1) cm

Answer

2x + 1 cm

Answer

4x - 2 cm

Answer

x(x + 2 + x - 1) cm

Question 29

A farmer has 10 sheep. He buys more sheep and now has 18 sheep in total. How many sheep did he buy?

Accepted Answer

8

Answer

2

Answer

10

Question 30

Solve for x: |x - 3| = 5

Accepted Answer

x = 2 or x = 8

Answer

x = 5

Answer

x = -2 or x = -8

Answer

x = 0

Question 31

What is the perimeter of a square with a side length of s?

Accepted Answer

2s

Answer

s^2

Answer

s/4

Answer

4s^2

Question 32

We have a number pattern: 4, 8, 12, 16, ... What comes next?

Accepted Answer

24

Answer

20

Answer

28

Answer

32

Question 33

Which of these is NOT an algebraic expression?

Accepted Answer

10

Answer

2x added to 5

Answer

y minus 3

Answer

4 multiplied by 7

Question 34

Simplify the expression: 3 multiplied by (x plus 2)

Accepted Answer

3x plus 6

Answer

3x

Answer

3x plus 2

Answer

6x

Question 35

What is the opposite operation of multiplication?

Accepted Answer

Division

Answer

Addition

Answer

Subtraction

Answer

Exponents

Question 36

A farmer has 12 sheep. She sells some sheep and now has 7 sheep left. How many sheep did she sell?

Accepted Answer

12 - 7

Answer

7 + 12

Answer

7 - 12

Answer

12 x 7

Question 37

Which expression represents the following phrase: "5 more than a number x"?

Accepted Answer

x + 5

Answer

x - 5

Answer

5x

Answer

x/5

Question 38

Which of the following is an example of a variable?

Accepted Answer

x

Answer

5

Answer

100

Answer

pizza

Question 39

Which of the following represents the inverse operation of subtraction?

Accepted Answer

Addition

Answer

Multiplication

Answer

Division

Answer

Squaring

Question 40

Factor the expression: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x - 3)(x - 3)

Answer

(x + 3)(x + 3)

Question 41

Determine the domain and range of the function: f(x) = |x - 2|.

Accepted Answer

Domain: All real numbers, Range: Non-negative real numbers

Answer

Domain: Non-negative real numbers, Range: All real numbers

Answer

Domain: Values greater than -2, Range: Non-negative real numbers

Answer

Domain: Values less than -2, Range: Non-positive real numbers

Question 42

Which equation represents a line with a slope of 2 and a y-intercept of -3?

Accepted Answer

y = 2x - 3

Answer

y = x - 3

Answer

y = 2x + 3

Answer

y = -2x - 3

Question 43

Which expression shows one number added to another number?

Accepted Answer

x + 5

Answer

12

Answer

y = 2

Answer

5^2

Question 44

What number comes next in the sequence: 5, 10, 15, ___, 25?

Accepted Answer

20

Answer

18

Answer

22

Answer

24

Question 45

Which letter in an equation can stand for any number?

Accepted Answer

x

Answer

5

Answer

y = 3

Answer

10 + 2

Question 46

In the expression 3x + 2, what number tells us how many times x is used?

Accepted Answer

3

Answer

2

Answer

5

Answer

6

Question 47

Which of these is NOT a math operation used in algebra?

Accepted Answer

Squaring

Answer

Adding

Answer

Subtracting

Answer

Multiplying

Question 48

In the equation 2y - 5 = 9, what number makes the equation true?

Accepted Answer

7

Answer

2

Answer

9

Answer

11

Question 49

Which word problem can you solve using an equation?

Accepted Answer

Two numbers add up to 10.

Answer

A rectangle has an area of 24 square units.

Answer

A square has a perimeter of 16 inches.

Answer

A cube has a volume of 64 cubic units.

Question 50

Which expression represents '5 less than a number x'?

Accepted Answer

x - 5

Answer

x / 5

Answer

5 - x

Answer

5x

Question 51

Which property is used in the equation: (2 + 3) + 4 = 2 + (3 + 4)?

Accepted Answer

Associative Property of Addition

Answer

Identity Property of Addition

Answer

Distributive Property

Answer

Commutative Property of Addition

Question 52

Which of the following is a linear equation?

Accepted Answer

y = 2x + 3

Answer

3x - 7 > 10

Answer

y = 5x^2

Answer

x^2 - 4 = 0

Question 53

Which expression shows the perimeter of a rectangle with length x and width y?

Accepted Answer

2x + 2y

Answer

x + y

Answer

x * y

Question 54

What is the slope of the line that connects the points (2, 4) and (6, 10)?

Accepted Answer

3

Answer

1

Answer

2

Question 55

What is a pattern?

Accepted Answer

A series of numbers, shapes, or objects that follow a specific rule

Answer

A set of letters that form a word

Answer

A collection of numbers that add up to 10

Answer

A group of shapes that make a picture

Question 56

Evaluate the expression 3x + 5 for x = 2

Accepted Answer

11

Answer

15

Answer

8

Answer

20

Question 57

Which equation represents the sentence 'The sum of a number and 7 is 15'?

Accepted Answer

x + 7 = 15

Answer

7 - x = 15

Answer

15 + x = 7

Answer

x / 7 = 15

Question 58

Simplify the expression: 2(x + 5)

Accepted Answer

2x + 10

Answer

5x + 2

Answer

10x + 2

Answer

x + 10

Question 59

Which equation is equivalent to 2x - 5 = 15?

Accepted Answer

2x = 20

Answer

x + 5 = 15

Answer

5x = 15

Answer

x - 5 = 15

Question 60

Which of the following is a variable?

Accepted Answer

A letter that represents an unknown number

Answer

A number that is always the same

Answer

A symbol that represents an operation

Answer

A word that describes a shape

Question 61

Which of the following is an expression with a variable?

Accepted Answer

5 + x

Answer

5 + 5

Answer

5 - 5

Answer

5 x 5

Question 62

What is the value of x in the equation x + 5 = 10?

Accepted Answer

5

Answer

20

Answer

15

Answer

10

Question 63

Which of the following patterns follows the rule 'add 3'?

Accepted Answer

2, 5, 8, 11, ...

Answer

2, 4, 8, 16, ...

Answer

2, 4, 6, 8, ...

Answer

2, 6, 12, 24, ...

Question 64

What is the next term in the sequence 1, 4, 9, 16, ...?

Accepted Answer

25

Answer

31

Answer

19

Answer

36