Republic of the Philippines Department of Education Region III SCHOOLS DIVISION OF BULACAN SAN MIGUEL NATIONAL HIGH SCHOOL MATHEMATICS 8 1st QUARTER 4TH SUMMATIVE TEST S.Y. 2021 – 2022 Name: _____________________________________ Section: _____________________ Date: __________________ Direction: Read each question carefully. Choose the letter of the correct answer and type it on the box before the number. _____1. Which of the following is true about the system of linear equations in two variables? I. Any set of linear equations. II. A set of two or more linear equations in two variables. III. A system of linear equations may have only one solution, infinitely many solutions, or no solution at all. IV. A system of linear equations in two variables can be solved algebraically or graphically. A. I and II B. I, II, and III C. II and III D. II, III, and IV _____ 2. Which of the following equations could NOT be considered as system of linear equation in two variables? 7x − y = 8 −x + 6y = 2 y = x − 8 4???? 2 − 3x − 4 = 0 A. { B. { C. { D. { 2x + 4y = 8 7x = y − 12 5???? + 4y = 8 x???? 2 = −9 _____ 3. What is the graph of a system of linear equations in two variables which shows only one solution? A. intersecting B. coinciding C. parallel D. perpendicular _____ 4. How do you describe the graphs of the system of linear equations in two variables which has no solution? A. coinciding B. intersecting C. parallel D. perpendicular _____ 5. All the following are graphs of the system of linear equations in two variables EXCEPT: A. coinciding B. intersecting C. parallel D. perpendicular _____ 6. What is the solution to the system of equations shown in the graph? A. (0, −1) C. (0,3) B. (0,2) D. (3,0) _____ 7. How many solutions does a system of linear equation in two variables has if the slopes of the lines are equal and the y-intercepts are also equal? A. one C. no solution B. two D. infinitely many _____ 8. In the equation ???????? + ???????? = ???? where A and B are not equal to zero is a linear equation in what form? A. point- slope form C. standard form B. slope-intercept form D. two-point form _____ 9. What is the slope and ???? − ???????????????????????????????????? of the equation ???? = 2???? − 4? A. ???? = 2 ???????????? ???? = 4 C. ???? = 2 ???????????? ???? = – 4 B. ???? = 4 ???????????? ???? = 2 D. ???? = – 4 ???????????? ???? = 2 _____ 10. What is the equation of a line that passes through the points (1, 3) ???????????? (−2, 5)? A. −2???? + 3???? = 11 B. 2???? − 3???? = 11 C. 2???? + 3???? = 11 D. 3???? + 2???? = 11 _____ 11. If the graph of a linear equation passes through a point (1, −2) and a slope of 3, what form is being illustrated? A. point-slope B. standard C. slope-intercept D. two-point _____ 12. The line passes through the point (0,3) and has a slope of 2. What is the equation of a line in slope-intercept form? A. ???? = 1/2 ???? B. ???? = 3 C. ???? = 2???? + 3 D. ???? = 3???? + 2
_____ 13. What is the standard form of the equation ???? = −2???? + 1? A. 2???? − ???? = 1 B. −2???? + ???? = 1 C. 2???? + ???? = 1 D. −2???? − ???? = 1 _____ 14. Which of the following pair of points have a slope of −2? A. (2, 4) ???????????? (5, −2) C. (2 ,5) ???????????? (4, −2) B. (4, 2) ???????????? (−2, 5) D. (−2, 2) ???????????? (4, 5) _____ 15. Write the equation of a line whose slope is 2 and am intercept of 4 in standard form. A. 2x – y = -4 B. 2x + y = -4 C. 2x – y = 4 D. y = 2x + 4 _____ 16. Which system of equation has intersecting graphs? x + y = 3 3x − 2y = 5 2x − y = 2 3x + y = 2 A. { B. { C. { D. { x+y = 2 6x − 4y = 10 3???? + ???? = 2 3x + y = −2 _____ 17. Which system of equation has coinciding graphs? 2x + 5 y = 10 2x − 3y = 5 x + y = −2 5x − 2y = 7 A. { B. { C. { D. { 2x + 5y = −10 x + 3y = 1 3???? + 3???? = −6 3x + 2y = 9 x − 3y = 5 _____ 18. Which of the following ordered pair satisfies the given system { ? 3x − 4y = −5 A. (7,4) B. (−7, −4) C. (7, −4) D. (−7, 4) 2x − y = 4 _____ 19. All the following ordered pairs satisfy the system { , EXCEPT: 4x − 2y = 8 A. (0, −4) B. (2, 0) C. (4, 4) D. (0,2 ) For items 20-21, consider the graph at the right. _____ 20. What are the slopes of graph? A. 2/3 and -1/3 C. 3 and -2/3 B. -2/3 and 1/3 D. -2/3 and -3 _____ 21. What are the ????-intercepts? A. (0, 2) ???????????? (0, −1) C. (3, 0) ???????????? (1,0) B. (−2,0) ???????????? (0,1) D. (−3,0) ???????????? (1, 0) _____ 22. What do you call the process of adding the equations to eliminate either ???? or ???? from the system of linear equations? A. cancellation B. elimination C. graphing D. substitution 5x − 3y = −2 _____ 23. What is the first step to solve this system of linear equations { ? 4x + 3y = 20 A. Add the 2 equations. C. Multiply the second equation by 3. B. Subtract the 2 equations. D. Multiply the first equation by 1/5. 2x − 3y = 6 _____ 24. Which of the following shows the graph of the system { ? 6x − 9y = 36 A. B. C. D. _____ 25. Jessie has 2 apples and 3 oranges with a total cost of ₱105.00 while his friend has 1 apple and 4 oranges cost ₱90.00. Which of the following steps would be the best way to begin with in finding the cost of an apple and the cost of an orange? 2???? + 3???? = 105 (equation 1) ???? + 4???? = 90 (equation 2) A. Multiply equation 2 by −2. C. Add equation 1 and 2. B. Multiply equation 1 by 4 and 2. D. Multiply equation 2 by 2 and add. y = 2x − 9 _____ 26. The system of linear equation { is solved by substitution. After the initial x + 3y = 8 substitution in the second equation, which of the following is the resulting expanded equation? A. ???? + 3???? − 9 = 8 C. ???? + 3(2????) − 9 = 8 B. ???? + 3(2????) − 9 = 8 D. ???? + 3(2???? − 9) = 8 _____ 27. Which of the following equations can best be solved using elimination by addition? 2x + y = 10 x+y =5 x + y = 10 x − 3y = 5 A. { B. { C. { D. { 2x + y = 8 x−y =7 2x + y = 8 3 + x = −2y
_____ 28. A farmyard has dogs and chickens. The owner said that his dogs and chickens had a total of 148 legs and 60 heads. How many dogs and chickens were in the farmyard? A. 22 dogs and 38 chickens C. 14 dogs and 46 chickens B. 38 dogs and 22 chicken D. 46 dogs and 14 chickens For items 29-30: A tricycle passenger is charged Php10.00 for the first 4 kilometers and an additional of Php1.50 per succeeding kilometer. _____ 29. What equation can be used to model the situation? A. ???? = 1.50???? + 10 C. ???? = 1.50???? + 4 B. ???? = 10???? + 1.50 D. ???? = 1.50 + 4???? _____ 30. How much should be paid for a total travel of 35 kilometers? A. Php 56.50 C. Php 72.50 B. Php 62.50 D. Php 82.50