2nd Summative Test - Mathematics 9
1ST Grading
Name: ________________________ Grade & Section: ______________ Teacher: _____________
Date: ________
I.
Directions: Read and analyze each question. Solve the problem and write the letter of the best answer.
_____1. The sum and the product of the roots of a quadratic equation are 5 and 6, respectively. What is its equation?
A. x2 + 5x - 6 =0
B. x2 - 5x + 6 = 0
C. x2 + 6x – 5 = 0
D. x2+ 6x + 5 =0
____ 2. With the given equation 3𝑥 2 – 16𝑥 − 12 = 0, which of the following is the product of the roots?
A.
−12
B. −4
C. 4
D. 12
____ 3. If the product of roots of the quadratic equation given below is 2, then find the value of m in the equation
2𝑥 2 + 3𝑥 − 𝑚 = 0.
A.
-4
B. -2
C. 2
D. 4
____ 4. Which of the following are the roots of the quadratic equation 𝑥 2 – 5𝑥 − 24 = 0?
A.
-8 and -3
B. 8 and 3
C. -8 and 3
D. 8 and -3
____ 5. Find the roots of quadratic equation, x2 + 5x + 3 = 0.
−5+√13
−5−√13
5+√13
5−√13
√13−5
√13−5
5−√13
5+√13
A.
,
B.
,
C.
,D.
,
2
2
2
2
2
2
4
4
2
____ 6. Ian turns a page of a certain book and found out that it has an area of 96 𝑐𝑚 and a perimeter of 40𝑐𝑚.
What are the dimensions of the book?
A.8𝑐𝑚 𝑎𝑛𝑑 12𝑐𝑚
B. 6𝑐𝑚 𝑎𝑛𝑑 16𝑐𝑚
C. 4c𝑚 𝑎𝑛𝑑 24𝑐𝑚
D. 2𝑐𝑚 𝑎𝑛𝑑 48𝑐𝑚
____ 7 The sum of the ages of Ethan and Joy is 30 and the product is 224. What equation can be used to find their
ages?
A. 𝑥 2 + 30𝑥 + 224 = 0
C. 𝑥 2 − 30𝑥 − 224 = 0
2
B. 𝑥 − 30𝑥 + 224 = 0
D. 𝑥 2 + 30𝑥 − 224 = 0
2
____ 8. In y = x – 4, what are the values of y?
A. -4, -3, 0
B. 4, 3, 0
C. -3, 0, 5
D. -3, -4, 0
____ 9. Which of these represents a quadratic function?
A. y = x2
B. y = 2x
C. y = 2x
D. y = x3
____ 10. The graph of a quadratic function y = ax2 + bx + c is called __________.
A. bar graph
B. line
C. pie graph
D. parabola
____ 11. Which of the following graphs represent y = x2 - 2x?
____ 12. Express the quadratic function y = x2 + 2x – 1 in the form y = a (x – h)2 + k.
A. y = (x +1)2 + 1
C. y = (x + 1)2 - 2
2
B. y = (x + 1) + 2
D. y = (x + 1)2 – 1
2
____ 13. Pepe and Pedro transform y = 3x – 12x + 16 to vertex form. Pepe’s answer is y = 3(x-2)2 +4 and Pedro’s
answer is y = 3 (x +2)2 + 4. Who do you think got the correct answer?
A. Pepe
B. Pedro
C. Both of them
D. None of them
____ 14. What is f(x) = -3(x + 2)2 + 2 when written in the form of f(x) = ax2 + bx + c?
A. f(x) = -3x2 + 12x – 10
C. f(x) = -3x2 + 12x + 10
2
B. f(x) = 3x – 12x + 10
D. f(x) = -3x2 –12x – 10
____ 15. What is y = (x – 2)2 - 14 when written in the form y = ax2 + bx + c?
A. y = x2 + 4x + 10
C. y = x2 + 4x - 10
2
B. y = x – 4x + 10
D. y = x2 - 4x – 10
____ 16. Which statement is TRUE for the parabola whose equation is y = x2 – 6x + 15?
A. The parabola opens upward
C. The parabola contains the point (1,5)
B. The line of symmetry is x=1
D. The vertex is (1,16)
____ 17. What is the vertex of the graph of y= x2 - 2x – 1?
A. (-1,-2)
B.(1,2)
C.(1,-2)
D. (-1,2)
____ 18. The vertex of the graph given on the right is on the ___________.
A. base
C. origin
B. domain
D. range
____ 19. Which of the following equations represents the graph?
A. f(x) = -x2
C. f(x) = -(x+1)2
2
B. f(x) = x
D. f(x) = (x + 1)2
____20. In f(x) = x2 -4x -10, give the values of a, h and k.
A. a = 1, h = 2 k =-14
B. a = 1, h = 2 k =14
C. a = -1, h = 2 k =-14
____ 21. The graph of y = x2 – 7 is obtained by sliding the graph of y = x2
A. 7 units downward
B. 7 units upward
C. 7units to the right
D. a = 1, h = -2 k =-14
D. 7 units to the left
FOR NUMBER 22-23
From a 96-foot building, an object is thrown straight up into the air then follow a trajectory. The height S(t) of the ball above the
building after t seconds is given by the function S(t) = 80t – 16t2.
____ 22. What maximum height the object reach?
A. 196ft
B. 169ft
____ 23. Find the time at which the object is on the ground?
A. 5 seconds
B. 6 seconds
C. 100ft
D. 96ft
C. 7 seconds
D. 8 seconds
____24. Find the zeros of the quadratic function y = x2 – 3x + 2.
A. -1 and -2
B. 1 and 2
C. 1 and -2
D. -1 and 2
____25. Find the zeros of y = 2x2 + 2x -24
A. 3 and -4
B. -3 and -4
C. 3 and 4
D. -3 and 4
____26. In what direction does the graph of the quadratic function 𝑦 = 3𝑥 2 − 7𝑥 + 5 open?
A. upward
B. downward
C. to the left
D. to the right
____27. What is the vertex of the quadratic function 𝑦 = 𝑥 2 − 2𝑥 − 1?
A. (1, −2)
B. (−2, 3)
C. (−2, −1)
D. (2, −1)
____28. The graph of 𝑦 = 𝑥 2 − 9 is obtained by sliding the graph of 𝑦 = 𝑥 2 ________.
A.
B.
9 𝑢𝑛𝑖𝑡𝑠 𝑑𝑜𝑤𝑛𝑤𝑎𝑟𝑑
9 𝑢𝑛𝑖𝑡𝑠 𝑢𝑝𝑤𝑎𝑟𝑑
C. 9 𝑢𝑛𝑖𝑡𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑖𝑔ℎ𝑡
D. 9 𝑢𝑛𝑖𝑡𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑙𝑒𝑓𝑡
For questions 29-30. Refer to the figure below.
____29. What is the vertex of the graph?
A. (1, −3)
B. (−3,1)
C. (2, −3)
D. (2,3)
C. 𝑥 = 2
D. 𝑥 = 4
____30. What is the axis of symmetry?
A. 𝑥 = −3
B. 𝑥 = 1
II.Directions: Determine the nature, sum and product of the roots of the following quadratic.