Sacred Heart College
Second Quarterly Examination
Integrated Basic Education Department
Lucena City
MATHEMATICS 9
Mr. Alcantara/Mr. De La Torre
I. Multiple Choices. Read the questions carefully then choose the best answer from the
choices.
1. What law of exponent can it be justified that a0
Zero Exponent Rule
Product to a
Power Rule
=1?
Power to a Power Rule
Negative
Exponent Rule
2. Of all the 7 laws of exponents, which two laws required the exponential expressions to have
the same base?
Product Rule & Quotient Power to a
Quotient to a Power & Zero Exponent
Rule
Power &
Product to a Power Rule
Rule & Negative
Negative
Exponent Rule
Exponent Rule
3. What is the representation of the radical expression?
𝑛
𝑦 = 𝑘𝑥
𝑎𝑥 2 + 𝑏𝑥 + 𝑐
√𝑎
𝑦
= 𝑎(𝑥 − ℎ)2 + 𝑘
4. In writing expressions from radical to rational, what part of the expression will become the
index?
Denominator
of
the Numerator of
Radicand
Base
exponent
the exponent
5. What do you call the process of eliminating the radicals in the denominator?
Rationalizing
the Extracting the
Solving
Simplifying
denominator
roots
6. Which of the following equations is an example of product law of radicals?
4
4
√2 ∙ √3 = √6
√121 = 11
( √𝑎𝑏) = 𝑎𝑏
7. In dividing two numbers as radicand, which of the following laws applies?
Quotient Law
Zero Law
Product Law
2 √6
√ =
3
3
Exponential
Law
8. What conditions are involved in adding and subtracting radicals?
Indices and radicands are the same.
Only radicands are the same.
Only indices are the same.
Indices and radicands are different.
9. What is the first step in solving quadratic inequalities?
Write the inequality as an Apply the
Plot the roots in the number Determine the
equation.
quadratic formula. line.
testing points
10. What is the simplest form of (𝑎𝑏 3 𝑐 5 )−3 (𝑎4 𝑏 7 𝑐 5 )?
𝑎
𝑏 2 𝑐 10
𝑐 10
𝑎𝑏 2
2
11. What is the simplest form of
17 6
81𝑐 𝑑
𝑏3
2 2
[(𝑐 3 ) (3𝑑3 ) ]
(𝑐 −3 𝑏 3 )(𝑐𝑑)0
17 6 3
81𝑐 𝑑 𝑏
𝑏2
𝑎𝑐 10
𝑎𝑏 2 𝑐 10
?
𝑏3
81𝑐 17 𝑑 6
81𝑐 17 𝑏 3
𝑑6
Sacred Heart College
Second Quarterly Examination
Integrated Basic Education Department
Lucena City
MATHEMATICS 9
Mr. Alcantara/Mr. De La Torre
12. Which of the following is the rational form of 3√(3𝑥𝑦)?
1
3𝑥𝑦
9𝑥 3 𝑦 3
(3𝑥𝑦)3
27𝑥𝑦
13. Numerators of exponents in exponential form become what part of the radical form?
Exponent of the Radicand
Index
Radicand
Radicand
6
14. What is the simplest form of √64𝑥18 𝑦 6 ?
2𝑥 3 𝑦
2𝑥 3 𝑦 2
2𝑥 3 𝑦 3
2𝑥 3 𝑦 4
4
15. Which of the following process can be used to simplify √9𝑥 2 𝑦 2?
Lowering the index
Rationalizing
Product law
the denominator
Other rules
16. Which of the following is NOT the condition in multiplying radicals?
Indices and radicands are Indices are
Indices are the same but Indices and
the same
different but
radicands are different
radicands are
radicand are
different
different
17. Which of the following inequalities is a quadratic inequality?
𝑥 3 + 𝑥 2 ≤ 2𝑥 2 + 𝑥 3 − 4
3𝑥(𝑥 + 2) > 3𝑥 2
𝑥(𝑥 + 5)(𝑥 − 4) ≤ 4
(𝑥 + 2)(𝑥 − 3)
− 𝑥2 < 0
18. Which of following is the graph of the interval 2 ≤ 𝑥 ≤ 4?
19. Simplify (−4)−2 𝑥 −1 𝑦 2 𝑧 3
𝑦2𝑧3
16𝑥
−𝑦 2 𝑧 3
16𝑥
16𝑦 2 𝑧 3
𝑥
−16𝑦 2 𝑧 3
𝑥
5
20. Write into radicand (3𝑥 + 1)4 and simplify if possible.
4
3𝑥 + 1 √3𝑥 + 1
4
√(3𝑥 + 1)5
√3𝑥 + 1
4𝑥 3 𝑦 2
4𝑥 3 𝑦 3
5
√(3𝑥 + 1)4
3
21. Simplify: √64𝑥 9 𝑦 3
4𝑥 3 𝑦
22. Which of the following is the conjugate surd of (√2 + √5)?
(√2 − √5 )
(√5 − √2 )
(−√2 − √5 )
23. Solve: 5√𝑥 − 1 = 40.
65
63
4𝑥 3 𝑦 4
(√2 + √5)
84
86
24. Which of the following is the solution set of the quadratic inequality 𝑥2 − 𝑥 − 12 > 0?
−3 > 𝑥 > 4
−3 < 𝑥 < 4
−3 > 𝑥 < 4
4 > 𝑥 < −3
Sacred Heart College
Second Quarterly Examination
Integrated Basic Education Department
Lucena City
36
MATHEMATICS 9
Mr. Alcantara/Mr. De La Torre
−2
25. Evaluate ( 5 )
3
1
9
−
1
9
9
81
4
8
−25𝑥 8
25𝑥 8
1
26. What value of k will make 64𝑘 = 2
6
2
27. Evaluate √(−5𝑥 4 )2 .
5𝑥 4
−5𝑥 4
28. What is the number when the square root of the sum of a number and 9 is 12?
135
144
153
29. If 𝑥 ≥ 1, what would be the other solution of the inequality 2𝑥 2 − 3𝑥 ≤ 5?
5
5
𝑥 ≥ −1
𝑥≤2
𝑥≥2
30. If 𝑥 ≥ 2, what is the solution of 𝑥 2 − 6𝑥 + 8 ≤ 0?
𝑥≤4
𝑥≥4
𝑥 ≤ −4
276
𝑥 ≤ −1
𝑥 ≥ −4