Algebra for Year 7: Master the Basics of Variables, Expressions, and Equations

Question 1

A rectangular garden has a length of (x + 2) meters and a width of (x - 3) meters. What is the perimeter of the garden?

Accepted Answer

2(x + 2) + 2(x - 3)

Answer

2x + 1

Answer

x(x + 2) + x(x - 3)

Answer

4x - 1

Question 2

Explain the key differences between an algebraic expression and an algebraic equation. Provide clear examples to illustrate your explanation.

Accepted Answer

An algebraic expression is a mathematical phrase that includes variables, constants, and mathematical operations, while an algebraic equation is a mathematical statement that includes an equal sign.

Answer

An algebraic equation is a simplified form of an algebraic expression.

Answer

An algebraic expression is a statement that two mathematical expressions are unequal.

Question 3

Find the value of the expression: (2x - 3) * 5 + 10 when x equals 1

Accepted Answer

22

Answer

12

Answer

32

Answer

42

Question 4

Translate the statement into an inequality: The sum of a number x and 5 is greater than 10.

Accepted Answer

x + 5 > 10

Answer

x + 5 < 10

Answer

5 - x > 10

Question 5

Which of the following expressions is equivalent to 3(x - 2)?

Accepted Answer

3x - 6

Answer

6x - 3

Answer

x - 6

Answer

x + 6

Question 6

Simplify the algebraic expression: 3(x + 2)

Accepted Answer

3x + 6

Answer

3x + 2

Answer

6x + 2

Answer

6x + 6

Question 7

Which expression represents the sum of 5 and 3 times a number x?

Accepted Answer

5 + 3x

Answer

3 + 5x

Answer

5x + 3

Answer

3x + 5

Question 8

Find the area of a rectangle with length (x + 2) cm and width (x - 1) cm

Accepted Answer

x² + x - 2 cm²

Answer

x² + cm²

Answer

x² - x - 2 cm²

Answer

x² - 1 cm²

Question 9

Which of the following is NOT an algebraic expression?

Accepted Answer

10

Answer

2x + 5

Answer

y = 3x - 2

Answer

5(x - 1)

Question 10

Solve the equation: 2x - 5 = 13

Accepted Answer

x = 9

Answer

x = 4

Answer

x = 18

Answer

x = 25

Question 11

Which of the following graphs represents the equation y = 2x + 1?

Accepted Answer

A line passing through (0, 1) with a slope of 2

Answer

A parabola opening upwards

Answer

A circle with a radius of 1

Answer

A hyperbola with foci at (0, 1) and (0, -1)

Question 12

Simplify the expression: 2 * (x + 3)

Accepted Answer

2x + 6

Answer

5x

Answer

2x + 3

Answer

x + 6

Question 13

Which of the following represents the area of a rectangle with length x and width y?

Accepted Answer

x * y

Answer

x + y

Answer

2x + 2y

Answer

x / y

Question 14

Simplify the expression: 4(x + 3)

Accepted Answer

4x + 12

Answer

4x + 3

Answer

x + 12

Answer

x + 3

Question 15

Solve the inequality: x - 5 > 2

Accepted Answer

x > 7

Answer

x < 7

Answer

x > -3

Answer

x < -3

Question 16

Which of the following is an algebraic expression that involves variables (letters) and numbers?

Accepted Answer

x + y

Answer

2 + 3

Answer

5 - 2

Answer

10 / 5

Question 17

Solve the algebraic equation: x + 5 = 10

Accepted Answer

x = 5

Answer

x = 10

Answer

x = 15

Answer

x = 20

Question 18

Which of the following is a variable (a letter that represents an unknown value)?

Accepted Answer

x

Answer

5

Answer

10 + 5

Answer

a + b

Question 19

Expand the brackets in the algebraic expression: 2(x + 3)

Accepted Answer

2x + 6

Answer

2x + 3

Answer

x + 6

Answer

x + 9

Question 20

Which of the following is a quadratic equation that represents a parabola?

Accepted Answer

x^2 + 2x + 1 = 0

Answer

y = x + 3

Answer

y = 5x^3

Answer

y = 10

Question 21

What is the meaning of the expression 'x + 5'?

Accepted Answer

The sum of x and 5

Answer

The difference of x and 5

Answer

The product of x and 5

Answer

The quotient of x and 5

Question 22

Solve for x: x - 7 = 12

Accepted Answer

x = 19

Answer

x = 5

Answer

x = -5

Answer

x = -19

Question 23

What is the value of the expression 3(x + 2) when x is equal to 4?

Accepted Answer

24

Answer

18

Answer

12

Answer

15

Question 24

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

Accepted Answer

3x + 6

Answer

x + 5

Answer

3x + 2

Answer

6x + 2

Question 25

Which of the following is NOT an algebraic expression?

Accepted Answer

3

Answer

2x + 3y

Answer

(x - 2)(x + 3)

Answer

x squared + 2xy

Question 26

Write an algebraic expression for the distance around a rectangle with a length of x and a width of y.

Accepted Answer

2(x + y)

Answer

2x + y

Answer

x + 2y

Answer

xy

Question 27

Which of the following factors can be multiplied to equal x squared minus 4?

Accepted Answer

(x + 2)(x - 2)

Answer

x - 2

Answer

x + 2

Answer

x squared

Question 28

Expand the brackets: (x + 3)(x - 2)

Accepted Answer

x squared minus x minus 6

Answer

x squared plus x minus 6

Answer

2x squared minus x minus 6

Answer

x squared plus 5x minus 6

Question 29

Which of these is NOT a variable?

Accepted Answer

5

Answer

x

Answer

y

Answer

n

Question 30

Simplify this expression: 2x + 3x

Accepted Answer

6x

Answer

x + 3

Answer

5x

Answer

Cannot be simplified

Question 31

Solve for x: x + 5 = 10

Accepted Answer

5

Answer

10

Answer

15

Answer

20

Question 32

Expand the brackets: (x + 2)(x - 3)

Accepted Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + 5x - 6

Question 33

Which equation is a linear equation?

Accepted Answer

y = 2x + 1

Answer

y^2 = 4

Answer

x^3 - 2 = 0

Answer

y = x^2 - 1

Question 34

Find the value of x: x plus 5 equals 10

Accepted Answer

x is 5

Answer

x is 15

Answer

x is 10

Answer

x is -5

Question 35

Which of these is NOT a variable?

Accepted Answer

5

Answer

x

Answer

y

Answer

a

Question 36

Find the value of y: 3 multiplied by y equals 15

Accepted Answer

y is 5

Answer

y is 10

Answer

y is 20

Answer

y is 45

Question 37

What is the degree of the polynomial 2x^3 + 5x^2 - 3x + 1?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 38

Find a factor of the expression x^2 - 4.

Accepted Answer

x - 2

Answer

x + 2

Answer

x^2 + 4

Answer

x - 4

Question 39

Which of the following is an example of an algebraic expression?

Accepted Answer

2x + 5

Answer

The sum of two numbers

Answer

10 - 4 = 6

Answer

7 > 3

Question 40

If y = 4, what is the value of 3y - 2?

Accepted Answer

10

Answer

8

Answer

4

Answer

14

Question 41

Simplify the expression: 5a + 2b - 3a + b

Accepted Answer

2a + 3b

Answer

8a + 3b

Answer

8a - b

Answer

2a - b

Question 42

What is the solution to the equation: x + 7 = 12?

Accepted Answer

x = 5

Answer

x = 19

Answer

x = 7

Answer

x = -5

Question 43

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

Accepted Answer

2x + 10 cm

Answer

x + 10 cm

Answer

5x cm

Answer

2x + 5 cm

Question 44

Which of these inequalities is represented by the number line:  <img src='https://latex.codecogs.com/svg.latex?Large&space;egin{tikzpicture}[scale=0.8]  draw[thick,->] (-3,0) -- (4,0) node[anchor=north west] {x}; oreach x in {-2,-1,0,1,2,3}  draw (x cm,1pt) -- (x cm,-1pt) node[anchor=north] {$x$};  draw[fill=black] (1,0) circle (0.1); draw[thick,->] (1,0)--(4,0); end{tikzpicture}'>

Accepted Answer

x > 1

Answer

x ≤ 1

Answer

x ≥ 1

Answer

x < 1

Question 45

If 3 apples cost £1.20, how much do 5 apples cost?

Accepted Answer

£2.00

Answer

£1.80

Answer

£3.60

Answer

£2.40

Question 46

What is the coefficient of x in the expression: 7x² - 3x + 5?

Accepted Answer

-3

Answer

5

Answer

7

Answer

2

Question 47

The sum of three consecutive numbers is 24. What is the smallest of the three numbers?

Accepted Answer

7

Answer

8

Answer

6

Answer

9

Question 48

Which equation represents the following statement: 'Five less than twice a number is equal to eleven'?

Accepted Answer

2x - 5 = 11

Answer

2x + 5 = 11

Answer

2(x - 5) = 11

Answer

5 - 2x = 11