Math 9 P.E FINAL
Math 9 P.E FINAL
Math 9 P.E FINAL
NAME: DATE:
KNOWLEDGE
A B C D
A. 2 C. 7
B. -5 D. 3
A. 7 C. 5
B. 2 D. 9
A. -5 C. 2
B. -8 D. -3
2
A . 6 x −8 x−5=0 C. 7 x 2−7 x−5=8 x+ 9
B. 9 x 2−x−5=5 x2−4 x D. 2x +8 = 0
3 2
A . 4 x + x =0 C. 1 – 4x = 0
B. 4x – 3 = 0 D. 4 x2 +3=0
O O O O 6. When can you say that the roots are real, rational and unequal?
A. If D = 0. C. If D < 0.
B. If D > 0 D. None of these
O O O O 7. Which of the following is the formula in getting the sum of the roots?
−a −c
A. C.
b b
−b a
B. D.
a b
O O O O 8. Which of the following is the formula in getting the product of the roots?
c −c
A. C.
a a
a −a
B. D.
c c
O O O O 9. In the quadratic equation ax 2 +bx +c=0 , if b 2−4 ac< 0 , then the equation has
O O O O 10. In the quadratic equation ax 2 +bx +c=0 , if b 2−4 ac=0 , then the equation has
O O O O 11. The equation of the axis of symmetry of the parabola represented by the function
2
y=( x−2 ) is:
A. x = -2 B. x = 2 C. x -= 0 D. y = 2
2
O O O O 12. The axis of symmetry for the parabola defined by y=x −8 x+12 is
A. x = -4 B. x = 4 C. x = 8 D. x = 12
O O O O 13. Which of the following is the formula in getting the axis of symmetry of a quadratic
function?
−b
x=
A. 2a B. x = c/a C. x = -b/c D. x = -c/ 2a
O O O O 15. Which of the following will be the graph of a quadratic function if the value of a is negative?
PROCESS
O O O O 1. Which of the following is the standard form of the equation6 x 2−2 x+ 9=6 x +4 ?
2
A . 6 x −8 x+5=0
B. 6 x 2+ 8 x+5=0
C. 6 x 2−8 x−5=0
D. 6 x 2+ 8 x−5=0
O O O O 2. When can you say that the equation is a quadratic?
A. When it is written in the form ax 2 +bx +c=0
B. When it is written in the form ax 2 +bx +c=0 , where a, b, and c are real numbers and a is
not equivalent to zero.
C. When it is written in the form ax 2 +bx +c=0 , where a, b, and c are real numbers and a is
equivalent to zero.
D. When it is written in the form ax 2 +bx +c=0 , where a, b, and c are real numbers and b is
not equivalent to zero.
A. 25 B. 100 C. 40 D. 400
O O O O 4. Which of the following is √ 175 ?
A . 7 √5 B. 5 √ 7 C. 7 √ 6 D. 6 √ 7
O O O O 6. Which of the following is/are the solution set/s of the quadratic equation x 2+ 5 x−24=0?
A. (-8, 3) B. (8, -3) C. (-8, -3) D. (8, 3)
A. 24 C. 5
B. -24 D. -5
A. 21 C. 31
B. 41 D. 51
2
Mathematics9 – 1st Periodic
x
Examination 3
–6 –4 –2 2 4 6
–2
–4
–8
–10
2
C. y=a ( x +h ) −k
2
D. y=a ( x−h ) +k
2
O O O O 12. The axis of symmetry for the parabola defined by y=x −8 x+12 :
A. x = -4 B. x = 4 C. x = 8 D. x = 12
A. C.
10 y y
9 x
8 –4 –3 –2 –1 1 2 3 4
7
6
5
4 –5
3
2
1
x
–4 –3 –2 –1 1 2 3 4 –10
B. 10 y
D. 10 y
9
8
7
6 5
5
4
3 x
2 –4 –3 –2 –1 1 2 3 4
1
x
–2 –1 1 2 3 4 5 6
4 4
2 2
–8 –6 –4 –2 O 2 4 6 8 x –8 –6 –4 –2 O 2 4 6 8 x
–2 –2
–4 –4
–6 –6
–8 –8
y y
8 8
6 Mathematics9 – 1st Periodic Examination
6 4
4 4
2 2
–2 –2
–4 –4
–6 –6
B. –8 –8
O O O O 16. Identify the vertex and the y-intercept of the graph of the function .
A. vertex: (–2, 5); C. vertex: (2, 5);
y-intercept: –7 y-intercept: –7
–8 –6 –4 –2 O 2 4 6 8 x
–2
–4
–6
–8
B. D.
-1 2 -1 2
UNDERSTANDING
I. Directions: Read the following statements carefully, and then choose the best answer for
what is asked in each item. Shade the letter of the correct answer on the circle provided
before the number.
O O O O 1.1 Larry can do a certain task 6 h longer than Rita. If they work together, they can finish the
task in 4 hours. How long will it take each of them to do the task alone?
A. Rita will take 6 hours to do the task alone while Larry will need 12 hours to do the task
alone.
B. Rita will take 12 hours to do the task alone while Larry will need 6 hours to do the task
alone.
C. Rita will take 5 hours to do the task alone while Larry will need 12 hours to do the task
alone.
D. Rita will take 11 hours to do the task alone while Larry will need 5 hours to do the task
alone.
O O O O 1.2 This is because
A. Let x be the number of hours it takes Rita to do the task, and x + 5 be the number of
hours it takes Larry to do the task.
B. Let x + 6 be the number of hours it takes Rita to do the task, and x be the number of
hours it takes Larry to do the task.
C. Let x be the number of hours it takes Rita to do the task, and x + 6 be the number of
hours it takes Larry to do the task.
D. Let x + 5 be the number of hours it takes Rita to do the task, and x be the number of
hours it takes Larry to do the task.
O O O O 1.3 What is the best method of quadratic equation is applicable in this situation?
A. Completing the Square B. Quadratic Formula
B. Extracting Square Roots D. Factoring
O O O O 2.1 The difference between 2 positive numbers is 7 while their product is 60. Find the 2
numbers.
A. The smaller number is 4 and the larger number is 11.
B. The smaller number is 5 and the larger number is 12.
C. The smaller number is 3 and the larger number is 13.
D. The smaller number is 5 and the larger number is 11.
O O O O 2. 2 This is because
A. Let x be the smaller and x + 6 be the larger number.
B. Let x be the smaller and x + 5 be the larger number.
C. Let x be the smaller and x - 7 be the larger number.
D. Let x be the smaller and x + 7 be the larger number.
O O O O 2. 3 What property of equality is being used in solving the problem?
O O O O 4. 1 The product of two consecutive whole numbers is 812. What are the numbers?
A. The two whole numbers are 27 and 28.
B. The two whole numbers are 24 and 25.
C. The two whole numbers are 26 and 27.
D. The two whole numbers are 28 and 29.
O O O O 4. 2 This is because
A. Let x be the first number and let x + 2 be the second number.
B. Let x be the first number and let x - 2 be the second number.
C. Let x be the first number and let x + 1 be the second number.
D. Let x be the first number and let x - 1 be the second number.
O O O O 4. 3 What type of problem is being asked?
A. Age problem C. Number Problem
B. Work Problem D.Distance Problem
O O O O 5. Formulate a quadratic equation if the roots are 2 and -1.
A. x2 – x – 2 = 0 B. x2 + x + 2 = 0 C. x2 –2x + 2= 0 D. x2 – 3x – 2 = 0
O O O O 6. What are the roots of x2 = 18?
A. x = ±2√ 3 B. x = ±3√ 2 C. x = ±16 D. x = ±9
2
O O O O 7. When deriving the quadratic formula, a student starts with y=ax +bx+c , then solves
0=ax 2 +bx +c . Why?
O O O O 8. 2 This is because
A. { } B. ( ) C. [ ] D. < >
“MATHEMATICS
It may not teach us how to breathe oxygen
And how to exhale carbon dioxide
Or to love a friend and forgive an enemy
It may not even help us find our way to
Our one true love
But it gives us every reason to hope that
EVERY PROBLEM HAS A SOLUTION.”
GOD BLESS!!!!!