Free Printable Grade 8 Mathematics — Third Quarter Examination (SY 2025

1.

Which of the following is the first step in solving the equation $3x + 5 = 14$ ?

a)

Divide both sides by 3

b)

Subtract 5 from both sides

c)

Add 5 to both sides

d)

Multiply both sides by 3

2.

What does it mean when a number is a solution of a linear equation in one variable?

a)

It makes the left side greater than the right side

b)

It makes the equation true when substituted for the variable

c)

It removes all variables from the equation

d)

It changes the form of the equation

3.

During a math game, a student thinks of a number. The teacher asks the student to triple the number and then subtract 9. After taking these steps, the student gets a final result of 21. How will you represent this in an equation?

a)

$3(x - 9) = 21$

b)

$3x + 9 = 21$

c)

$3x - 9 = 21$

d)

$x - 9 = 21$

4.

The perimeter of a triangle is 54 cm. Two sides are equal, and the third side is 6 cm. Let the length of each equal side be $x$ cm. Which equation represents the situation?

a)

$2x + 6 = 54$

b)

$2(x - 6) = 54$

c)

$3x + 6 = 54$

d)

$2x + (x + 6) = 54$

5.

A school club collected ₱1,200 from selling tickets at ₱50 each. How many tickets were sold?

a)

20

b)

24

c)

28

d)

32

6.

Which of the following inequalities involves only one variable?

a)

$x + 5 > 10$

b)

$2y - 3 \le 7z$

c)

$3x + 2y < 8$

d)

$25y = 130x - z$

7.

Juan is buying notebooks. Each notebook costs ₱15, and he has only ₱100. Which inequality represents the maximum number of notebooks ( $x$ ) he can buy?

a)

$15x > 100$

b)

$15x \le 100$

c)

$x + 15 \le 100$

d)

$x - 15 < 100$

8.

Solve the inequality: $3x - 5 > 10$ . Which of the following represents the solution set?

a)

$x > 5$

b)

$x > \dfrac{15}{3}$

c)

$x > \dfrac{10}{3}$

d)

$x > \dfrac{15}{2}$

9.

A local bakery is preparing boxes of cupcakes for a charity event. Each volunteer should receive at least 5 boxes. Which graph shows the number of boxes ( $x$ ) that each volunteer should receive?

a)

Open circle at 5, shading to the right

b)

Closed circle at 5, shading to the right

c)

Open circle at 5, shading to the left

d)

Closed circle at 5, shading to the left

10.

Reyes NHS teachers are preparing gifts for the Matigsalog community. They wanted each family to receive at least 4.5 kilos of rice. Which graph shows the kilos of rice each family should receive?

a)

Graph of $x > 4$

b)

Graph of $x \ge 4$

c)

Graph of $x \le 4$

d)

Graph of $x < 4$

11.

A student graphs the inequality $x \ge 2$ using an open circle at 2 and shading to the right. What is the student’s error?

a)

The shading direction is incorrect

b)

The inequality should be $x > 2$

c)

The circle should be closed, not open

d)

The graph should be shaded to the left

12.

Which of the following is a linear inequality in two variables?

a)

$x^2 + y \le 5$

b)

$2x + 3y > 7$

c)

$xy < 10$

d)

$x^2 - y^2 \ge 0$

13.

Which value of $x$ satisfies $x > 6$ ?

a)

5

b)

6

c)

7

d)

-2

14.

Solve the inequality: $x + 5 > 9$ .

a)

$x > 14$

b)

$x > 4$

c)

$x < 14$

d)

$x = 4$

15.

Which statement best describes a linear equation in two variables and how its solution is expressed?

a)

A linear equation in two variables represents a straight line, and its solutions are expressed as ordered pairs $(x,y)$

b)

A linear equation in two variables has only one solution, written as a fraction

c)

A linear equation in two variables contains exponents greater than 1, and its solution is a single number

d)

A linear equation in two variables has no variables, and its solution is written using an inequality

16.

The equation $2x + y = 7$ represents a relationship between two variables. Which ordered pair is a solution of the equation?

a)

$(2,4)$

b)

$(4,1)$

c)

$(1,6)$

d)

$(3,1)$

17.

A line is represented by the equation $y = 3x + 5$ . What is the slope of the line?

a)

5

b)

3

c)

-3

d)

-5

18.

The equation of a line is $y = -2x + 4$ . Which ordered pair represents the $y$ -intercept of the line?

a)

$(-2, 0)$

b)

$(0, -2)$

c)

$(4, 0)$

d)

$(0, 4)$

19.

Which formula is used to find the equation of a line given two points $(x_1, y_1)$ and $(x_2, y_2)$ ?

a)

$y - y_1 = m(x - x_1)$ , where $m = \dfrac{y_2 - y_1}{x_2 - x_1}$

b)

$y = mx + c$ , where $m = x_1 + x_2$

c)

$y = x + y$

d)

$y = x_1y_1 + x_2y_2$

20.

In the equation $y = mx + b$ , what does the value of $b$ represent?

a)

The $x$ -intercept

b)

The slope of the line

c)

The point where the line crosses the $y$ -axis

d)

The distance between two points

21.

Find the equation of the line passing through the point $(2,3)$ with a slope of 4.

a)

$y = 4x + 11$

b)

$y = 4x - 5$

c)

$y = 4x - 1$

d)

$y = 4x + 3$

22.

A line passes through the point $(2,3)$ with slope $m = -2$ . Which of the following points also lies on this line?

a)

$(3, 1)$

b)

$(4, 0)$

c)

$(1, 5)$

d)

$(0, 7)$

23.

A student wants to sketch a line with an $x$ -intercept of 6 and a $y$ -intercept of $-3$ . Which approach will correctly generate the graph?

a)

Plot the points $(6, 0)$ and $(0, -3)$ , then draw a straight line through them

b)

Plot the points $(0, 6)$ and $(0, -3)$ , then draw a straight line through them

c)

Plot the $x$ -intercept twice, then draw a line through the two points

d)

Plot the $y$ -intercept only, then draw a vertical line

24.

A city planner is mapping a straight bike lane on a coordinate grid. The bike lane must pass through two checkpoints located at $(1,2)$ and $(4,8)$ . Which plan will most effectively produce an accurate graph of the bike lane?

a)

Plot one checkpoint and draw a horizontal line

b)

Plot both checkpoints and draw a straight line

c)

Find the midpoint and draw a line through it

d)

Plot the checkpoints and draw a curve

25.

Which of the following is an example of a system of linear equations in two variables?

a)

$x + y = 5$

b)

$x^2 + y = 6$

c)

$\begin{cases} x + y = 4 \ 2x - y = 1 \end{cases}$

d)

$3x > 2y$

26.

Which ordered pair is a solution of the system $\begin{cases} x + y = 6 \ x - y = 2 \end{cases}$ ?

a)

$(2,4)$

b)

$(4,2)$

c)

$(3,3)$

d)

$(1,5)$

27.

For numbers 27–29. In a school canteen, a student buys pencils and pens. A pencil costs ₱5 and a pen costs ₱10. The student buys a total of 6 items and spends ₱40. Let $x =$ number of pencils, $y =$ number of pens. The situation is modeled by the system: $\begin{cases} x + y = 6 \ 5x + 10y = 40 \end{cases}$ . Two lines are represented by the above equations $x + y = 6$ and $5x + 10y = 40$ . When these lines are graphed on the same coordinate plane, what does their point of intersection represent?

a)

The slope of both lines

b)

The solution of the system

c)

The $y$ -intercept of the first line

d)

The $x$ -intercept of the second line

28.

What does the equation $5x + 10y = 40$ represent in this situation?

a)

The total number of pencils and pens bought by the student

b)

The total cost of pencils only

c)

The total amount of money spent on pencils and pens

d)

The difference between the cost of pencils and pens

29.

When these equations are graphed, at what point do the lines intersect?

a)

$(2, 4)$

b)

$(4, 2)$

c)

$(6, 0)$

d)

$(3, 3)$

30.

A system of linear equations may have one solution, no solution, or infinitely many solutions. Which type of system has exactly one solution?

a)

Inconsistent system

b)

Consistent and Dependent system

c)

Consistent and Independent system

d)

Parallel system

31.

For this item, refer to the graph shown at the right. The graph shows two linear equations represented on the same coordinate plane. Based on the graph, how is the system of linear equations classified?

a)

Independent system

b)

Dependent system

c)

Consistent and Independent system

d)

Inconsistent system

32.

For numbers 32–34. A tricycle driver earns money from short trips and long trips. A short trip costs ₱20, and a long trip costs ₱35. One morning, the driver completed 10 trips and earned ₱290. Let $x =$ number of short trips and $y =$ number of long trips. The situation is modeled by the system: $\begin{cases} x + y = 10 \ 20x + 35y = 290 \end{cases}$ . In the system of linear equations shown above, what does the ordered pair $(x, y)$ that satisfies both equations represent?

a)

Any point on the $x$ -axis

b)

A value that makes only one equation true

c)

The common solution of the two equations

d)

The slope of each equation

33.

Using an algebraic method, how many short trips did the driver make?

a)

3

b)

4

c)

6

d)

7

34.

How many long trips did the driver make?

a)

6

b)

4

c)

10

d)

35

35.

For item nos. 35–37. The barangay staff recorded the following information: The total of Faye’s age and Jeson’s age is 20 years. The difference in their ages is 8 years. Faye is older than Jeson. To check the accuracy of the records, the barangay staff asked Faye and Jeson’s mathematics teacher to verify the information using systems of linear equations. Which system of equations correctly represents the information recorded by the barangay staff?

a)

$\begin{cases} x + y = 20 \ x - y = 8 \end{cases}$

b)

$\begin{cases} 2x + y = 20 \ x + y = 8 \end{cases}$

c)

$\begin{cases} x + y = 8 \ x - y = 8 \end{cases}$

d)

$\begin{cases} x - y = 20 \ x + y = 8 \end{cases}$

36.

Using the correct system of equations, what are the ages of Faye and Jeson?

a)

Faye = 18 years, Jeson = 2 years

b)

Faye = 12 years, Jeson = 8 years

c)

Faye = 16 years, Jeson = 4 years

d)

Faye = 14 years, Jeson = 6 years

37.

Which statement best explains why the ages found in Question 2 are correct?

a)

The sum of their ages is 20 and Faye is 8 years older than Jeson

b)

The sum of their ages is 20 and Faye is 6 years older than Jeson

c)

Jeson’s age is greater than Faye’s age

d)

The difference in their ages is 20 years

38.

For numbers 38–40. Maria is a public-school teacher living in Davao City. After work, she goes to Bankerohan Public Market to buy food for her family. She plans to buy fish and chicken, but she must stay within her limited budget. At the market, the fish costs ₱350 per kilogram and the chicken costs ₱250 per kilogram. Maria has at most ₱1,500 to spend on fish and chicken combined. She also wants to buy at least 3 kilograms of fish for her family. Let $x =$ number of kilograms of fish, $y =$ number of kilograms of chicken. Which system of linear inequalities represents Maria’s situation?

a)

$\begin{cases} x + y \le 1500 \ x \ge 3 \end{cases}$

b)

$\begin{cases} x + y = 1500 \ x \le 3 \end{cases}$

c)

$\begin{cases} 350x + 250y \le 1500 \ x \ge 3 \end{cases}$

d)

$\begin{cases} 350x + 250y \le 1500 \ x \le 3 \end{cases}$

39.

Maria considers buying 5 kg of fish and 3 kg of chicken. Which statement correctly evaluates this choice?

a)

This choice is acceptable because it meets both the budget limit and the minimum fish requirement

b)

This choice is not acceptable because it exceeds the budget

c)

This choice is not acceptable because it does not meet the minimum fish requirement

d)

This choice is acceptable because it meets Maria’s needs for today

40.

Which of the following combinations best satisfies Maria’s budget and buying conditions?

a)

2 kg of fish and 3 kg of chicken

b)

3 kg of fish and 1 kg of chicken

c)

4 kg of fish and 2 kg of chicken

d)

5 kg of fish and 2 kg of chicken

Grade 8 Mathematics — Third Quarter Examination (SY 2025–2026)

Total questions: 40

Worksheet time: 37mins

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