Page 1 of 37 Secondary 2 Workbook Answer Key Chapter 1 Real Numbers and Its Operations 1.1 Square Roots A. Definition of Square Roots 1. C 2.(1)Yes (2)Yes (3)No (4)Yes Reasoning: The numbers under the square root must be non-negative. 3.(1) 14 (2) 5 3 (3) 3 1 10 (4) 0.04 4. 4 5. (1) 1.2 (2) 9 (3) 7 2 (4) 6 5 6. 49 B. Definition of Principal Square Root 1. (1)1.1 (2)0.2 (3) 5 6 (4)10 2. 0 or 1 , 0 3. 0.4, 6 5 ,3,0.5 4. -1 or 7 C. Application of Principal Square Root 1. 3 , - 2 2. < , > 3. 9 4. 1 5. -6
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Page 1 of 37
Secondary 2 Workbook Answer Key
Chapter 1 Real Numbers and Its Operations
1.1 Square Roots
A. Definition of Square Roots
1. C
2.(1)Yes (2)Yes (3)No (4)Yes
Reasoning: The numbers under the square root must be non-negative.
3.(1) 14 (2)5
3 (3)
3
1
10 (4) 0.04
4. 4
5. (1) 1.2 (2) 9 (3)7
2 (4)
6
5
6. 49
B. Definition of Principal Square Root
1. (1)1.1 (2)0.2 (3)5
6 (4)10
2. 0 or 1 , 0
3. 0.4,6
5,3,0.5
4. -1 or 7
C. Application of Principal Square Root
1. 3 , - 2 2. < , >
3. 9 4. 1 5. -6
Page 2 of 37
1.2 Cube Roots
A. Definition of Cube Roots
1. A 2. B 3. A
4.(1) -0.3 (2)2
-3
(3)3
4 (4)
1-
2
5. (1)3
-2
(2)1
2 6. (1)5 (2)
7-
4
B. Application to Cube Roots
1. B 2. (1)1 (2)5
3
3. 1𝑐𝑚 4. 2, 3, 3 n 5. 4
1.3 Understanding Real Numbers Again
A. Understanding 4th Root and nth Root
1. (1) 1 (2) 3 (3)Has no real solution. (4)0
2. 3
2 3. - 1 0
B. Real Numbers and Number Line
1. C 2. B 3. D 4. B 5. C 6. D 7. 2 3
1.4 Operations on Quadratic Radicals
1.4.1 Definition of Quadratic Radicals
1. A 2. D 3. C
4.(1) 3- 2 (2)4-2x (3)𝜋 − 3 (4)1
Page 3 of 37
5. 2 6. 1 7. 2+ 3-2
1.4.2 Multiplying and Dividing Quadratic Radicals
A. Multiplying Quadratic Radicals
1. C 2. -4 3a
3.(1) 24 2x (2) 2 5 b ab (3)2 3b
4.(1)8 6 (2)5 5
2 (3) 24 a b
(4)20 (5)2 30
25 (6)3 3 2
5. 2 11 3 5 4 3
B. Dividing Quadratic Radicals
1. 2 2a 2.(1)5
3 (2)
3 2
4 (3)
2
x
3.(1)2 (2)2 3 (3)1 (4)1
9 (5)
3 3
2 (6)45 6
C. Simplifying Quadratic Radicals
1. C
2.(1)3
6 (2)
30
10 (3)
10
5 (4)
15
5
ab
a (5)
2
x x (6)
10 5
5
3. 4x xy . The value is 25
3.
1.4.3 Adding and Subtracting Quadratic Radicals
1.(1)3𝑎 (2) 3 2 (3)2 13 3
4 3
Page 4 of 37
(4)6 3 5 (5)13 3 (6)2 3
1.4.4 Mixed Operations on Quadratic Radicals
1.(1)8 7 (2)2 3 1 (3)6 10 6 (4)9
(5)2 (6)0 (7) 32
ab (8)
7 23
2
2. 2
Page 5 of 37
Quiz Yourself (A)
I. Multiple choice questions.
1. A 2. C 3. D 4. C 5. D 6. A 7. A 8. C 9. C
II. Fill in the blanks.
10. 4 , 6 ,2,2
5 11. 0.5,
1
3,
1
3 ,18
12. 2 13. 3a 14. 2, 1,0,1,2 15. <
III. Short answer questions.
16.(1)7 (2)2
3 (3)
2
3 (4) 23a
(5) 1 (6) 2 (7) 3 2
17. 81
Quiz Yourself (B)
I. Multiple choice questions.
1. A 2. C 3. C 4. A 5. B 6. B
II. Fill in the blanks.
7. 1
2x 8. a 9. 3, 1 2x x 10. 2x 11. 1
III. Short answer questions.
12. 1
2a . The minimized value is 1.
13.(1)2
b
ab (2)2 3 (3)60 3 (4) 3 (5)
9 2
8 (6)3 x
14. 1
Page 6 of 37
Chapter 2 Polynomial Operations
2.1 Adding and Subtracting Polynomials
A. Definition of Polynomials
1. ③④⑤,①②⑥,①②③④⑤⑥
2. Degree: 2. Terms: 3. The 1st term: −2𝑥. The 2nd term: −5. The 3rd
term: 3
3. Answer not provided.
4.(1) 8 92 x y (2) 1 1( 1) 2n n nx y
B. Like Terms
1. B 2. D 3. 30𝑥, 60 4. 2,3,1
5. 3
C. Combining Like Terms
1.(1)3ab (2) 2 23 20 17ab a b (3)5
3y (4) 214 10
23 3
ab a
2. 8 3. 11
D. Removing and Inserting Parenthesis
1.(1) 12 6x (2) 5 x
2. 3 26 1x x x 3. 3 2 1x x 4. 1
2b a 5. 0
6.(1) 2 22 2x y (2) 2 218 22x y (3) 2 23 4a b ab
(4)5 1y (5) 2 23 4a b ab (6) 25 2 3x x 7. 7
E. Adding and Subtracting Polynomials
1.(1) 14 (2) 6
Page 7 of 37
2. 22 7 3x x
3. 𝐴 − 𝐵 = 21 54
6 2x y xy ,2𝐴 − 3𝐵 = 2 13
2 112
x y xy
2.2 Multiplying Polynomials
A. Multiplying Monomials
1.(1) 9 6125x y z (2) 4 8 312 16x y x y (3) 3 26x y (4) 6 334a b
2. 22
B. Multiplying with Monomial and Polynomial—Multiplication
Involving 𝒂(𝒎 + 𝒏 + 𝒑)
1.(1) 3 28 12 4a a a (2) 2 3 2 21
3a b a b (3) 4 2 3 3 2 420 8 12x y x y x y
(4) 4 5 3 5 2 712 8 16a b a b a b (5) 3 23 4 14x x x
2. 36 3. 19
34
C. Multiplication with Polynomial and Polynomial—Multiplication
Involving (𝒂 + 𝒃)(𝒎 + 𝒏)
1.(1) 2 2 35x x (2) 23 5 2x x (3) 2 24 9m n
(4) 2 24 +12 9a ab b (5) 2 2x y x y
2. 1 2x 3. 0x 4. 222 24x x
2.3 Multiplication Formulas
A. Square of Sums or Difference of Two Numbers—Multiplication
Involving (𝒂 ± 𝒃)𝟐
Page 8 of 37
1. (1) 9𝑚2 − 24𝑚𝑛 + 16𝑛2 (2) 𝑚2 +2
3𝑚𝑛 +
1
9𝑛2
(3) 4
9𝑥2 − 2𝑥𝑦 +
9
4𝑦2 (4) 32𝑎2 = 2𝑏2
(5) −33𝑥2 + 33 (6) 7921
9
2. (𝑎 + 𝑏)2 and (−𝑎 − 𝑏)2 are equal because (−𝑎 − 𝑏)2 = [−(𝑎 +
𝑏)]2 = (𝑎 + 𝑏)2.
(𝑎 − 𝑏)2 and (𝑏 − 𝑎)2 are equal because (𝑏 − 𝑎)2 = [−(𝑎 − 𝑏)]2 =
(𝑎 − 𝑏)2.
(𝑎 − 𝑏)2 and 𝑎2 − 𝑏2 are not equal because (𝑎 − 𝑏)2 = (𝑎 − 𝑏)(𝑎 −
𝑏) while 𝑎2 − 𝑏2 == (𝑎 + 𝑏)(𝑎 − 𝑏).
3. 𝑎2 + 𝑏2 =5
2, 𝑎𝑏 =
1
4.
4. 9
2
B. Multiplication with sum and Difference of two Numbers—
Multiplication Involving (𝒂 + 𝒃)(𝒂 − 𝒃)
1. A 2. B
3.(1) 2 249 9y x (2) 2 216x y (3) 2 125
16x (4) 2 21 1
9 4m n
4.(1)9996 (2)24
39925
5. (1) 220 20m (2) 42 16x
2.4 Dividing Polynomials
2.4.1 Dividing Monomials
1.(1) 2 22x y (2) 11ac (3) 25m (4) 3 36a b (5) 26 ( )a m n
2.(1) 3a (2) 3 33( )
2x a b 3. 2, 1m n 4. 4x
Page 9 of 37
2.4.2 Dividing a Polynomial by a Monomial
1.(1) 5 a (2) 3 2 34
2x x (3)
22
7a b
2. (1) 3 44
3x x (2) 2 28 6 12xy x y (3)
14
2x
3. 4
2.4.3 Dividing a Polynomial by a Polynomial
1. 2 2 1x x 2. 2 3x x 3. 1
2k 4. 1
2.5 Factoring
2.5.1 Factoring by Common Factor—Factoring Involving 𝒂𝒎 + 𝒂𝒏 +
𝒂𝒑
1. ( )m a b c , 2 (1 2 )x y ,2 ( 2 1)xy x y , 3( 2 )m m n n
2.(1) 2 22 (2 )x x y (2) (3 6 1)x xy y (3) 2 24 2 3 )ab a bc(
(4) ( 2 )( 2)x y x (5) ( 2)(2 3 )a x y (6) 22(1 ) ( 1)p q pq
(7) )(2 3x y xy ( ) (8) (2 )( 3 )a b a b
3. 1999
2.5.2 Difference of Squares—Factoring Involving 𝒂𝟐 − 𝒃𝟐
(1) 2(2 2 1)x y (2) xy z xy z ( ) ( ) (3)1 2 1 2
3 11 3 11x y x y ( ) ( )
(4) 2 2mn m n m n 2 ( ) ( ) (5) 0.6 -0.6xy xy( ) ( ) (6)1 1