Iraan-Sagpangan National High School

1st Quarterly Assessment in Mathematics IX

“All things bright and beautiful, all creatures great and small, all things wise and wonderful the Lord God made them all”

Direction: Choose the best letter that corresponds to your answer. Write your answer on the space provided before the number.

_______ 1. What is a polynomial equation of degree two that can be written in a form a x 2 + bx + c = 0,
where a, b, c are real numbers and a ≠ 0.
a. Quadratic Equation b. Linear Inequality c. Linear Equation d. Quadratic Inequality

_______ 2. Which of the following is a quadratic equation?

a. 2 x 2 + 4r – 1 b. 3t – 7 = 2 c. s2 + 5s – 4 = 0 d. 2 x 2 – 7 x ≥ 3

_______ 3. In the quadratic equation 3 x 2 + 7x – 4 = 0, which is the quadratic term?

a. x 2 b. 7x c. 3 x 2 d. -4

_______ 4. Which of the following equation is NOT a quadratic equation?

a. 2 x 2 + 5x – 3 = 0 b. 3x ( x-2 ) = 10 c. ( 2x + 5 ) ( x-1 ) = -6 d. 2x+x+2=0

_______ 5. In a quadratic equation 3 x 2 + 7x – 4 = 0, what is the linear term?

a. 3 b. 7x c. 7 d. -4

_______ 6. Refers to equation in no.5, what is the constant term?

a. x 2 b. 7x c. 3 x 2 d. -4

_______ 7. Which of the following quadratic equation is written in standard form?

a. 3x - 2 x 2 = 7 b. - 2 x 2 – 7 = -3x c. -2 x 2 – 7 + 3x = 0 d. -2 x 2 + 3x – 7 = 0

_______ 8. What is the arbitrary value of a, b, c in the equation -2 x 2 – 7 + 3x = 0.?

a. 2 , 7 ,3 b. -2, 3, -7 c. 2, 3, -7 d. -2, -3, -7

_______ 9. Which of the following quadratic equation is in a form a x 2 + c = 0?

a. 2 x 2 + 3x = 0 b. 2 x 2 = 3x c. 2 x 2 + 3 = 5 d. 2 x 2 + 3x + 0

_______ 10. The following are the values of a, b and c that Edna and Luisa got when they expressed 5 – 3x = 2 x 2 in standard form
( Edna: a = 2, b = 3, c = -5 ; Luisa: a= -2, b= -3; c =5 )
Who do you think got the correct values of a, b c?
a. Luisa c. Both of them are correct
b. Edna d. Both of them are wrong

_______ 11. What is √ 121?

a. 11 b. -11 c. ± 11 d. √ 11

________ 12. How many real roots does √ −16 have?

a. no real roots b. zero c. one real root d. two real roots

_________ 13. 3h2 – 147 = 0, find for the root.

a. +7, -7 b. -7, -7 c. +7, +7 d. 0, +7

_________ 14. Which of the following quadratic equation has two real roots.
a. x 2 – 16 = 0 b. x 2 + 16 = 0 c. x 2+2 = 2 d. x 2+3=3

_________ 15. What is the value of “x” when you extract the roots of x 2=225 ?
a. ±15 b. 15 c. ±16 d. ±17

______ 16. What is √ 5?

a. 25 b. ±25 c. √ 5 d. ± √ 5

______ 17. Which of the following values of x make the equation x 2+7x-18=0 true?
I. -9 II. 2 III. 9
a. I & II b. II & III c. I & III d. I, II, III

______ 18. The roots are -1 and -8, which of the following equations has this roots?
a. x 2 + 9x = -8 b. x 2 + 7x = 0 c. t 2 + 8 t + 16 = 0 d. h2 + 6h = 16

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______ 19. Factor: x 2+ 7 x+12=0. And equate to zero to find the value of the variable.
a. -3, -4 b. -7,0 c. 7,1 d. -7, -1

______ 20. Factor: n2 + 7n + 15 = 5

a. 5, 2 b. -5, 2 c. 5, -2 d. -5, -2

______ 21. Which of the following equations may be solved easily by factoring?
a. 2 x 2=72 c. w 2−64=0
b. t 2+ ¿ 12t + 36 = 0 d. 2 s 2+ 8 s−10=0

_______22. What must be the number that should be added to make the equation x 2+ 4 x ¿ to make it a perfect square
trinomial?
a. 2 b. 4 c.6 d.8

_______23. Solve: y 2 +4 y=32 by completing the square. What are the roots?
a. y = 4 & y = -8 c. y = -6 , y = -4
b. y =-4 & y = 8 d. y = 6 , y = 4

_______24. Solve by completing the square: 2 x 2+8 x−10=0 . What are the roots?
a. 1,5 b. -1,5 c.1,-5 d. -1,-5

_______25. Which of the following quadratic equations has no real roots?

a. 2 x 2+ 4 x=3 c.3 s 2−2 s=−5
b. t 2−8 t−4=0 d.−2 r 2 +r +7=0

_______26. One of the roots of x 2−8 x +16=0 is 4. What is the other root?
a. -4 b.−8 c.16 d.4

_______27. Observe the solution given below:

The equation is y 2 +4 y−32=0 is to be solved by completing the square.
Observe the solution;
2
y +4 y−32=0 1
2
y +4 y=32 2
2
y +4 y+ 16=32+16 3
2
( y + 4) =48 4

Something is wrong with the solution, which part of the solution?

a. 1 b.2 c.3 d.4

_______28. Use the quadratic formula to solve x2− 8x + 12 = 0. What is the first step?
a. Evaluate the given c. Determine the values of a, b, c.
b. Get the square of a given d. substitutes the given to formula

_______29. Use the quadratic formula to solve x2− 8x + 12 = 0. Which of the following is the correct in substituting the given to
the Quadratic Formula?
a. b. c. d.

______30. which of the following is the correct Quadratic Equation Formula?

a. b. c. d.

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God bless Never give up…
 Iraan-Sagpangan National High School
2nd Quarterly Assessment in Mathematics IX
“All things bright and beautiful, all creatures great and small, all things wise and wonderful the Lord God made them all”

Direction: choose the best letter that corresponds to your answer.

1. Translate into variation equation: “m varies direct as n”.
a. m=kn b. n=km c. k=n/m d. m=k/n
2. if x varies directly as y, and x=10 when y=2, find the constant of variation.
a. K=8 b. 12 c. 5 d. 10
3. The speed r of a moving object is inversely proportional to the time t travelled is written as
a. r=kt b. r=k/t c. t=kr d. r/k=r
4. a car travels a distance of d km in t hours. The formula that relates d to t is d=kt. What kind of variation is it?
a. direct b. inverse c. joint d. combined
5. y varies directly as x and y=32 when x=4. Find the constant of variation.
a. 8 b. 36 c. 28 d. 128
6. If y varies inversely as x and y=1/3 when x=8, find y when x=-4.
a. -2/3 b. 2/3 c. -32/3 d. 32/3
7. Wackie’s income varies directly as the number of days that she works. If she earns php 8000.00 in 20 days, how much will she earn if
she worked 3 times as long?
a. Php 26 000 b. php 24 000 c. php 20 000 d. php 16 000
8. If h varies jointly j2 and I and inversely as g, and h=50 when j=2, i=5, and g=1/2, find h when h when j=4, i=10, and g=1/4.
a. 25 b. 100 c. 800 d. 805
9. Translate into inverse variation: “the mass m of an object varies inversely as the acceleration due to gravity g.
a. y=k/x b. m=k/g c. k=mg d. g=km
10. if y varies inversely as x and y=3 when x=4, find y when x=6.
a. 2 b. 12 c. 6 d. 4
11. Find the equation of variation where a varies jointly as b and c, and a=36 when b=3 and c=4.
a. b=3ac b. k=abc c. a=3bc d. a=kbc
12. “z varies jointly as x and y” translate into variation statement.
a. Z=xy b. z=kxy c. k=xyz d. z=ky
13. Translate into combined variation: “t varies directly as a and inversely as b.
a. T=kab b. a=tk/b c. k=ta/b d. t=ka/b
14. If z varies directly as x and inversely as y, and z=9 when x=6 and y=2, find z when x=8 and y=12.
a. 3 b. 9 c. 12 d. 2
15. An encoder can type n words in t hours. The formula that relates n to t is n=k/t, what kind of variation is it?
a. Inverse b. direct c. joint d. combined
16. Given that y varies directly as x and y=56 when x=7, find the variation constant.
a. 7 b. 8 c. 28 d. 392
17. If two men can do a job in 8 days, how many men can do the same job in 4 days?
a. 7 b. 6 c. 5 d. 4
18. What is the simplified form of 405-26-110001/2-1?
a. 1 b. 1/75 c. 1/150 d. 1/6000
19. Which of the following is true?
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 a. 51/2 + 51/3 =53 b. 21/2 / 21/3=22/9 c. (31/3)2=92/3 d. 4-2/3=1/42/3
20. Simplify: (b ) (b )
5 3

a. 8b b. b8 c. b2 d. b8
21. 304-2 is equal to?
a. 16 b. 1 c. 1/16 d. 1/8
22. Which of the following is equal to 1/8?
a. 23 b. 2-3 c. -23 d. 4-2
23. 1/5 equivalent to?
-3

a. 125 b. 1/125 c. 15 d. 25
24. (81/2) (81/2) is equal to?
a. 1 b. 6 c. 8 d. 1/8

25. Evaluate: 6h0+(12d)0

a. 6 b. 1 c. 2 d. 7
26. Evaluate: b2/b-5
a. b7 b. b2 / 1/b5 c. b5 d. b2
27. evaluate: 1/(32x y )
3 5 -2

a. (32x3y5)2 b. 32x6y10 c. 1024xy d. 1024 x6y10

28. Evaluate: 8x y z
2 0 -1

a. 8 b. 8x2/z c. 8x2 d. 1
29. the symbol √ m is called _______.
n

a. Square root b. radical c. radicand d. index

30. Refer to item # 29 “n” is called _____.
a. radicand b. index c. radical d. root

31. given: √3
xy , determine the radicand.
a. 3 b. √ ❑ c. xy d. x2y2
32. The following will yield real roots, EXCEPT.
a. √ −8 b. √
3
−8 c. √
5
−32 d. √ 99
33. Simplify: √ 40
❑

a. 2√ 1 b. 2√ 5 c. 2√ 10 d. 2√ 1 0
34. What is the equivalent of 32/3?
a. √ 3
9 b. √
3
3 c.9 d. 27
35. Simplify: √ 250
3

a. 5 b. 2 √
3
5 c.5 √ 2 d.5 √
3
2

Part II. Simplify the following

36. √ 72 37. √ 200 38. √ 2539. √ 150 40. √3 54

41. 1001/2 42. -641/3 43. 93/2 44. d-2(xy0d)28a-1 45. (d0xy2)-1

Prepared by:

Wilma Rey Ledesma-Francisco

Teacher

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 Type equation here .
Iraan-Sagpangan National High School
3 Quarterly Assessment in Mathematics IX
rd

“Because of your smile, you make the world most beautiful”. -Thich nhat hanh
Direction: choose the best letter that corresponds to your answer.
1. The mathematician behind Radicals is?
a. Christoph Rudolff b. Christoph Rudolf c. Christoph Rudoff d. Christoph Rodolff
2. Convert into radical form: 42/3
a. √3 2
4 b. √
2 3
4 c. √
3
4 d. ❑√ 4 2
3. Add: √ 2 + 2 √ 2
a. 3√ 2 b. √ 2 c. 2 √ 2 d. 1 √ 2
4. Subtract: 6√ 5 x -4√ 5 x.
a. 6√ 5 x b. 4√ 5 x c. 2√ 5 x d. √ 5 x
5. Simplify: 4√ 3-9√ 3.
a. -√ 3 b −5 √ 3 c. √ 3 d. √ 3
6. Solve: 2√ 5+5√ 2-4 √ 5 .
a. 3√ 5 b. −2 √ 5 +5√ 2 c. 2 √ 5 +5√ 2 d. 5√ 2
7. Simplify: √ 75-√ 27
a. 2√ 75 b. 25 √ 27 c. 2 √ 3 d. 7 √ 3
8. Multiply: ( √ 7) ¿ ).
a. √ 10 b. √ 17 c. 3√ 7 d. √ 21
9. Which of the following should multiply to √ 3 to get 3 √ 5?
a. √ 9 b. √ 15 c. √ 5 d. √ 45
10. Give the product: -√ 3(√ 6-2 √ 15 )
a. -3√ 2+ 6 √ 5 b. -3√ 2+ √ 5 c. 3√ 2+ 6 √ 5 d. -√ 2+ 6 √ 5
11. Find the product: (√ 2+ √ 3 ¿ ¿- √ 3 ¿
a. -1 b. 2-3 c. 1 d. 2
12. Find the conjugate of ¿- √ 11¿ .
a. ¿- √ 11¿ b. ¿+√ 11¿ c. −4 d. ¿- √ 11¿
13. Find the product of ¿+√ 5 ¿(√ 2-√ 5).
a. √ 6-√ 15+ √ 10-5b. √ 6-√ 15+ √ 10+5 c. √ 6+√ 15+ √ 10-5 d. √ 6-√ 15− √ 10-5
14. Which binomial will give 8-4√ 3 as the product?
a. ¿-√ 5)2 b. ¿-√ 5)2 c. ¿-√ 2)2 d. ¿-√ 2)2
15. Divide: √ 8 ÷ √ 2 .
a. 2 b. √ 4 c. √ 8 d. √ 2
2
16. Simplify: .
√3
3 √2 2 √3 √3
a. b. c. d. 2 √ 3
√3 3 3 ❑
17. divide : √ 8 +√ 24 ¿ ÷ √ 2
a. 2+2√ 3 b. 2-2√ 3 c. 2√ 3 d. 2+2√ 2
18. find x∈ √ x =8
a. 64 b. 8 c. 16 d. 32
19. determine the value of x : √ x−7-7=8
a. 232 b. 322 c. 223 d. 225
20. Solve for x: √ 3 x+7 =7
a. 12 b. 14 c. 11 d. 7
21. Evaluate: √ 3 x+3 -√ 5 x−1=0.
a. 2 b. -4 c. 0 d. 8
22. :|√
3
2 x −1+3=0
a. 13 b. 11 c. -13 d. -26
23. Determine the solution for: √ 5 x+1 =1+3√ x
9 9
a. 0 b. c. -0 d.
4 −4

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 24. Which of the following is the simplified form of
√20 x +5 ?
√5 x
5 √ 4 x 2+5 √ 4 x 2+ 5
a. √ 4 x2 + x b. 5 x √ 4 x 4 + x c.
x
d. .
x
25. Which of the following is an incorrect characteristic of a radical in simplest form?
a. No fraction as radicals b. no radicand with variable
c. no radical appears in denominator of a fraction d. no radicands have perfect square factors other than 1
√
26. transformed into exponential form: √ √ 7 .
4

a. 771 /16 b. 71 /16 c. 71 /15 d. 71 /6

√
27. Evaluate: : √ x 6 .
3

a. X2 b. xy c. √ x d. x
28. What is y in : √3
y =5?
a. 25 b. 125 c. 5 d. 225
29. Which equation has x=64 as the value of x?
a. √ 3
y =5 b. ❑√ x =9 c. √
2
y =8 d. √ x =8
30. Find y: √ y =2.
4

a. 2 b. 4 c. 8 d. 16
31. A polygon of four sides is?
a. quadrilaterals b. parallelogram c. Square d. trapezoid
32. which of the following does not belong to the group?
a. b. c. d.

33. In a _______________ any two opposite sides are congruent.

a. Square b. rectangle c. rhombus d. parallelogram
34. In a parallelogram, any two consecutive angles are ________________.
a. Congruent b. supplementary c. bisects each other d. form triangles
35. __________ is a quadrilateral with two pairs of adjacent, congruent sides.
a. Kite b. trapezoid c. rectangle d. square
36. ___________ is a parallelogram with four right angles.
a. Kite b. trapezoid c. rectangle d. square
37. A quadrilateral with exactly one pair of opposite side parallel is?
a. Kite b. trapezoid c. rectangle d. square
38. A parallelogram with four right angles and four congruent sides is?
a. Kite b. trapezoid c. rectangle d. square
39. _________ is a parallelogram with four congruent sides.
a. Rhombus b. trapezoid c. rectangle d. square
40. Which of the following quadrilaterals has diagonals that do not bisect each other?
a. Rhombus b. trapezoid c. rectangle d. square

Prepared by:

Wilma Rey Ledesma-Francisco

Teacher

Iraan-Sagpangan National High School

4 Quarterly Assessment in Mathematics IX
th

“Success is the product of hard work”

Direction: Choose the best letter that corresponds to your answer. Write your answer before the number.
1. A polygon with four sides is?
a. quadrilateral b. kite c. trapezoid d. parallelogram

2. A _________ is a quadrilateral with exactly one pair of parallel opposite sides.

a. quadrilateral b. kite c. trapezoid d. parallelogram

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3. The diagonals of a kite are as follows, 6cm and 12cm find the area.
a. 36cm2 b. 36cm c. 72cm2 d. 72cm

4. The segment that joins the midpoints of the legs of a trapezoid is called the_______ .
a. median b. legs c. bases d. congruent

5. Given the figure at the left, find the median of a trapezoid.

a. 22 b. 28 c. 16 d. 44

6. which of the following is correct about Pythagorean theorem formula?

a. c2=a2+b2 b. c2=a2-b2 c. c2=a2-c2 d. c2=d2-b2

7. the square of hypotenuse of a _____________ is equal to the sum of the squares of the legs.
a. right triangle b. obtuse triangle c. acute triangle d. Pythagorean theorem

8. Using the figure at the left, what is side c?

c?
a=9 a. 225 b. 15 c. 14 d. 125

12
9. using Pythagorean theorem find a, if b=40 and c=50.
a. 36 b. 90 c. 30 d. 900

10.in a right triangle the length of each side are given as: a=5, c=13 using Pythagorean theorem find b.
a. 7 b. 13 c. 12 d. 5

11. what is the value of x?

45 a. 3 b. 3 √ 2 c. 12 d. 6√ 2
x 6
45
12. In a 45-45-90 right triangle, the length of one of its leg is 20cm, what is the length of the other leg?
a. 10cm b. 20cm c. 20√ 2 d. 20 √ 3

13. In a 45-45-90 special right triangle, what is the length of the hypotenuse?

x
a. 7√ 3 b. 10 c. 7 √ 2 d. 7

14. In a 30-60-90 right triangle, the hypotenuse is 21 find the length of the shorter leg.
a. 21√ 3 b. √ 3 c. 10.5 d.10.5√ 3

15. In a 30-60-90 right triangle the length of the hypotenuse is 4 √ 3 , find the longer leg.
a. 2 √ 3 b. 4√ 3 c. 6 d. 2√ 6

16. In a Right triangle, if the acute angles are 45 degrees, then the legs are equal and the hypotenuse equals the length of the leg
times square root of two. Which illustration fit to the theorem?
a. b. c. d.
17. A triangle is right if the square of the longest side is_________ to the sum of the squares of the shorter sides.
a. equal b. greater than c. less than d. more than

18. A triangle is obtuse if the square of the longest side is_________ the sum of the squares of the shorter sides.
a. equal b. greater than c. less than d. more than

items 19-24, enumerate the 6 trigonometric ratios.

19. 20. 21. 22. 23. 24.

25. sine θ is the ratio between _________ and _________.

a. opposite over hypotenuse b. adjacent over hypotenuse

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 c. opposite over adjacent d. SOH CAH TOA
26. cosine θ is the ratio between _______ and _______.
a. opposite over hypotenuse b. adjacent over hypotenuse
c. opposite over adjacent d. SOH CAH TOA
27. tangent θ is the ratio between ______ and _______.
a. opposite over hypotenuse b. adjacent over hypotenuse
c. opposite over adjacent d. SOH CAH TOA
28. Sine90 ° is equal to?
a. 0 b. ½ c.1 d. √ 3/2
29. Cosine 90° is equal to?
a. √ 3/2 b. 1 c. ½ d. 0
30. ___________ is a mnemonic code used for remembering the trigonometric equation
a. SOH-CAH-TOA B. SOO-CAH-TOA C. SOH-COH-TOA D. SOH-CAH-TAO

for items 31-42 complete the table below that summarizes the values of the trigonometric ratios of the angles
θ Sin Cos Tan Csc Sec Cot
30° 31. 34. 37. 41.
45° 32. 35. 38. 40.
60° 33. 36. 39. 42.

Item 42-50, solve the following using Trigonometric Ratios. Solve each triangle by finding all the missing side
lengths and angle measures.

42-45: Find sides a, b, angle B 45-46. Determine the angle A

B= ____
a=_____ c=16 a=3
3 0022’
A=____
b=_____ b=4
47-49 use the law of cosine: given a=10, b=8, angle C=55° find c. ______

50. What is the sum of all the angles of a triangle? ________.

Prepared by:
Wilma Rey Ledesma-Francisco
Subject Teacher
Congratulations…Welcome to Grade 10 Mathematics …be the best in everything you do. Love,learn, respect, obey and give thanks to God.

15. In a 30-60-90 right triangle the length of the hypotenuse is 4 √ 3 , find the longer leg.
a. 2 √ 3 b. 4√ 3 c. 6 d. 2√ 6

16. In a Right triangle, if the acute angles are 45 degrees, then the legs are equal and the hypotenuse equals the length of the leg
times square root of two. Which illustration fit to the theorem?
a. b. c. d.
17. A triangle is right if the square of the longest side is_________ to the sum of the squares of the shorter sides.
a. equal b. greater than c. less than d. more than

18. A triangle is obtuse if the square of the longest side is_________ the sum of the squares of the shorter sides.
a. equal b. greater than c. less than d. more than

items 19-24, enumerate the 6 trigonometric ratios.

19. 20. 21. 22. 23. 24.

25. sine θ is the ratio between _________ and _________.

a. opposite over hypotenuse b. adjacent over hypotenuse
c. opposite over adjacent d. SOH CAH TOA
26. cosine θ is the ratio between _______ and _______.
a. opposite over hypotenuse b. adjacent over hypotenuse

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 c. opposite over adjacent d. SOH CAH TOA
27. tangent θ is the ratio between ______ and _______.
a. opposite over hypotenuse b. adjacent over hypotenuse
c. opposite over adjacent d. SOH CAH TOA
28. Sine90 ° is equal to?
a. 0 b. ½ c.1 d. √ 3/2
29. Cosine 90° is equal to?
a. √ 3/2 b. 1 c. ½ d. 0
30. ___________ is a mnemonic code used for remembering the trigonometric equation
a. SOH-CAH-TOA B. SOO-CAH-TOA C. SOH-COH-TOA D. SOH-CAH-TAO

Item 31-40, solve the following using Trigonometric Ratios. Solve each triangle by finding all the missing side
lengths and angle measures.

31-35: Find sides a, b, angle B 36-39. Determine the angle A

B= ____
a=_____ c=16 a=3
3 0022’
A=____
b=_____ b=4
40. What is the sum of all the angles of a triangle? ________.

Prepared by:
Wilma Rey Ledesma-Francisco
Subject Teacher

11

38°
P 10 M
Q

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