1: Multiple Choice (20 items)

1. **Factor**: \( x^2 - 16 \)

- A. \( (x - 4)(x + 4) \)

- B. \( (x - 8)(x + 2) \)

- C. \( (x - 2)(x + 8) \)

- D. \( (x + 4)(x + 4) \)

2. **Factor**: \( 3x^2 - 12x \)

- A. \( 3x(x - 4) \)

- B. \( 3(x - 4) \)

- C. \( x(3x - 12) \)

- D. \( 3x(x - 3) \)

3. **Factor**: \( x^2 + 7x + 12 \)

- A. \( (x + 3)(x + 4) \)

- B. \( (x - 3)(x + 4) \)

- C. \( (x + 6)(x + 2) \)

- D. \( (x - 4)(x - 3) \)

4. **Factor**: \( x^2 - 10x + 21 \)

- A. \( (x - 3)(x - 7) \)

- B. \( (x + 3)(x - 7) \)

- C. \( (x - 1)(x - 21) \)

- D. \( (x + 1)(x - 21) \)

5. **Factor**: \( 2x^2 - 5x - 3 \)

- A. \( (2x + 1)(x - 3) \)
 - B. \( (2x - 1)(x + 3) \)

- C. \( (2x - 3)(x + 1) \)

- D. \( (2x + 3)(x - 1) \)

6. **Factor**: \( x^2 + 4x - 12 \)

- A. \( (x + 6)(x - 2) \)

- B. \( (x - 6)(x + 2) \)

- C. \( (x + 3)(x - 4) \)

- D. \( (x - 3)(x + 4) \)

7. **Factor**: \( 3x^2 + 13x + 4 \)

- A. \( (3x + 1)(x + 4) \)

- B. \( (3x + 4)(x + 1) \)

- C. \( (3x + 2)(x + 2) \)

- D. \( (3x - 1)(x + 4) \)

8. **Factor**: \( 6x^2 - 5x - 6 \)

- A. \( (3x - 2)(2x + 3) \)

- B. \( (3x + 2)(2x - 3) \)

- C. \( (6x - 1)(x + 6) \)

- D. \( (2x - 1)(3x + 6) \)

9. **Factor**: \( x^2 - 25 \)

- A. \( (x - 5)(x + 5) \)

- B. \( (x - 1)(x + 25) \)

- C. \( (x + 5)(x + 5) \)

- D. \( (x - 25)(x + 1) \)

10. **Factor**: \( 4x^2 - 12x + 9 \)

 - A. \( (2x - 3)(2x - 3) \)

- B. \( (2x - 3)(x - 3) \)

- C. \( (4x - 3)(x - 3) \)

- D. \( (2x + 3)(2x + 3) \)

11. **Factor**: \( x^2 - 4x - 21 \)

- A. \( (x - 7)(x + 3) \)

- B. \( (x - 3)(x + 7) \)

- C. \( (x + 7)(x - 3) \)

- D. \( (x + 4)(x - 5) \)

12. **Factor**: \( 5x^2 - 20x \)

- A. \( 5x(x - 4) \)

- B. \( 5(x - 4) \)

- C. \( x(5x - 20) \)

- D. \( 5x(x - 5) \)

13. **Factor**: \( x^2 + 2x - 35 \)

- A. \( (x + 7)(x - 5) \)

- B. \( (x - 7)(x + 5) \)

- C. \( (x + 5)(x - 7) \)

- D. \( (x - 5)(x + 7) \)

14. **Factor**: \( x^2 - 2x - 15 \)

- A. \( (x - 5)(x + 3) \)

- B. \( (x + 5)(x - 3) \)

- C. \( (x - 3)(x + 5) \)

- D. \( (x + 3)(x - 5) \)
15. **Factor**: \( 3x^2 + 7x - 6 \)

- A. \( (3x - 1)(x + 6) \)

- B. \( (3x + 2)(x - 3) \)

- C. \( (3x - 2)(x + 3) \)

- D. \( (3x + 1)(x - 6) \)

16. **Factor**: \( 4x^2 + 4x - 15 \)

- A. \( (4x - 3)(x + 5) \)

- B. \( (4x + 5)(x - 3) \)

- C. \( (2x + 3)(2x - 5) \)

- D. \( (2x - 3)(2x + 5) \)

17. **Factor**: \( x^2 + 6x + 9 \)

- A. \( (x + 3)(x + 3) \)

- B. \( (x + 3)(x - 3) \)

- C. \( (x - 3)(x - 3) \)

- D. \( (x + 1)(x + 9) \)

18. **Factor**: \( x^2 - x - 12 \)

- A. \( (x - 4)(x + 3) \)

- B. \( (x + 4)(x - 3) \)

- C. \( (x - 3)(x + 4) \)

- D. \( (x - 6)(x + 2) \)

19. **Factor**: \( 2x^2 + 7x - 3 \)

- A. \( (2x - 1)(x + 3) \)

- B. \( (2x + 1)(x - 3) \)

- C. \( (2x - 3)(x + 1) \)

- D. \( (2x + 3)(x - 1) \)
20. **Factor**: \( x^2 + 5x + 6 \)

- A. \( (x + 2)(x + 3) \)

- B. \( (x + 1)(x + 6) \)

- C. \( (x - 2)(x - 3) \)

- D. \( (x + 3)(x - 2) \)

#### Section 2: Identification (20 items)

1. **Identify the factored form of** \( x^2 - 9 \).

- **Answer**: \( (x - 3)(x + 3) \)

2. **Identify the factored form of** \( 6x^2 - 5x - 6 \).

- **Answer**: \( (3x + 1)(2x - 3) \)

3. **Identify the factored form of** \( x^2 + 8x + 15 \).

- **Answer**: \( (x + 3)(x + 5) \)

4. **Identify the factored form of** \( 2x^

Certainly! Here is a comprehensive test questionnaire covering factoring polynomials, factoring general
quadratic trinomials, and simplifying algebraic expressions. The test is divided into three sections:
multiple choice, identification, and problem-solving.

---

### Test Questionnaire

#### Section 1: Multiple Choice (20 items)

1. **Factor**: \( x^2 - 16 \)

- A. \( (x - 4)(x + 4) \)

- B. \( (x - 8)(x + 2) \)

- C. \( (x - 2)(x + 8) \)

- D. \( (x + 4)(x + 4) \)

2. **Factor**: \( 3x^2 - 12x \)

- A. \( 3x(x - 4) \)

- B. \( 3(x - 4) \)

- C. \( x(3x - 12) \)

- D. \( 3x(x - 3) \)

3. **Factor**: \( x^2 + 7x + 12 \)

- A. \( (x + 3)(x + 4) \)

- B. \( (x - 3)(x + 4) \)

- C. \( (x + 6)(x + 2) \)

- D. \( (x - 4)(x - 3) \)

4. **Factor**: \( x^2 - 10x + 21 \)

- A. \( (x - 3)(x - 7) \)

- B. \( (x + 3)(x - 7) \)

- C. \( (x - 1)(x - 21) \)

- D. \( (x + 1)(x - 21) \)

5. **Factor**: \( 2x^2 - 5x - 3 \)

- A. \( (2x + 1)(x - 3) \)

- B. \( (2x - 1)(x + 3) \)

- C. \( (2x - 3)(x + 1) \)

- D. \( (2x + 3)(x - 1) \)
6. **Factor**: \( x^2 + 4x - 12 \)

- A. \( (x + 6)(x - 2) \)

- B. \( (x - 6)(x + 2) \)

- C. \( (x + 3)(x - 4) \)

- D. \( (x - 3)(x + 4) \)

7. **Factor**: \( 3x^2 + 13x + 4 \)

- A. \( (3x + 1)(x + 4) \)

- B. \( (3x + 4)(x + 1) \)

- C. \( (3x + 2)(x + 2) \)

- D. \( (3x - 1)(x + 4) \)

8. **Factor**: \( 6x^2 - 5x - 6 \)

- A. \( (3x - 2)(2x + 3) \)

- B. \( (3x + 2)(2x - 3) \)

- C. \( (6x - 1)(x + 6) \)

- D. \( (2x - 1)(3x + 6) \)

9. **Factor**: \( x^2 - 25 \)

- A. \( (x - 5)(x + 5) \)

- B. \( (x - 1)(x + 25) \)

- C. \( (x + 5)(x + 5) \)

- D. \( (x - 25)(x + 1) \)

10. **Factor**: \( 4x^2 - 12x + 9 \)

- A. \( (2x - 3)(2x - 3) \)

- B. \( (2x - 3)(x - 3) \)

- C. \( (4x - 3)(x - 3) \)
 - D. \( (2x + 3)(2x + 3) \)

11. **Factor**: \( x^2 - 4x - 21 \)

- A. \( (x - 7)(x + 3) \)

- B. \( (x - 3)(x + 7) \)

- C. \( (x + 7)(x - 3) \)

- D. \( (x + 4)(x - 5) \)

12. **Factor**: \( 5x^2 - 20x \)

- A. \( 5x(x - 4) \)

- B. \( 5(x - 4) \)

- C. \( x(5x - 20) \)

- D. \( 5x(x - 5) \)

13. **Factor**: \( x^2 + 2x - 35 \)

- A. \( (x + 7)(x - 5) \)

- B. \( (x - 7)(x + 5) \)

- C. \( (x + 5)(x - 7) \)

- D. \( (x - 5)(x + 7) \)

14. **Factor**: \( x^2 - 2x - 15 \)

- A. \( (x - 5)(x + 3) \)

- B. \( (x + 5)(x - 3) \)

- C. \( (x - 3)(x + 5) \)

- D. \( (x + 3)(x - 5) \)

15. **Factor**: \( 3x^2 + 7x - 6 \)

- A. \( (3x - 1)(x + 6) \)

- B. \( (3x + 2)(x - 3) \)
 - C. \( (3x - 2)(x + 3) \)

- D. \( (3x + 1)(x - 6) \)

16. **Factor**: \( 4x^2 + 4x - 15 \)

- A. \( (4x - 3)(x + 5) \)

- B. \( (4x + 5)(x - 3) \)

- C. \( (2x + 3)(2x - 5) \)

- D. \( (2x - 3)(2x + 5) \)

17. **Factor**: \( x^2 + 6x + 9 \)

- A. \( (x + 3)(x + 3) \)

- B. \( (x + 3)(x - 3) \)

- C. \( (x - 3)(x - 3) \)

- D. \( (x + 1)(x + 9) \)

18. **Factor**: \( x^2 - x - 12 \)

- A. \( (x - 4)(x + 3) \)

- B. \( (x + 4)(x - 3) \)

- C. \( (x - 3)(x + 4) \)

- D. \( (x - 6)(x + 2) \)

19. **Factor**: \( 2x^2 + 7x - 3 \)

- A. \( (2x - 1)(x + 3) \)

- B. \( (2x + 1)(x - 3) \)

- C. \( (2x - 3)(x + 1) \)

- D. \( (2x + 3)(x - 1) \)

20. **Factor**: \( x^2 + 5x + 6 \)

- A. \( (x + 2)(x + 3) \)
 - B. \( (x + 1)(x + 6) \)

- C. \( (x - 2)(x - 3) \)

- D. \( (x + 3)(x - 2) \)

#### Section 2: Identification (20 items)

1. **Identify the factored form of** \( x^2 - 9 \).

- **Answer**: \( (x - 3)(x + 3) \)

2. **Identify the factored form of** \( 6x^2 - 5x - 6 \).

- **Answer**: \( (3x + 1)(2x - 3) \)

3. **Identify the factored form of** \( x^2 + 8x + 15 \).

- **Answer**: \( (x + 3)(x + 5) \)

4. **Identify the factored form of** \( 2x^

2 + 7x + 3 \).

- **Answer**: \( (2x + 1)(x + 3) \)

5. **Identify the factored form of** \( 4x^2 - 4 \).

- **Answer**: \( (2x - 2)(2x + 2) \)

6. **Identify the factored form of** \( x^2 + 3x - 10 \).

- **Answer**: \( (x + 5)(x - 2) \)

7. **Identify the factored form of** \( x^2 - 2x - 15 \).

- **Answer**: \( (x - 5)(x + 3) \)
8. **Identify the factored form of** \( 5x^2 + 7x - 6 \).

- **Answer**: \( (5x - 1)(x + 6) \)

9. **Identify the factored form of** \( x^2 - 6x + 8 \).

- **Answer**: \( (x - 2)(x - 4) \)

10. **Identify the factored form of** \( 2x^2 - 5x + 2 \).

- **Answer**: \( (2x - 1)(x - 2) \)

11. **Identify the factored form of** \( x^2 + 2x - 35 \).

- **Answer**: \( (x + 7)(x - 5) \)

12. **Identify the factored form of** \( 3x^2 - 4x - 4 \).

- **Answer**: \( (3x + 2)(x - 2) \)

13. **Identify the factored form of** \( x^2 - 16x + 64 \).

- **Answer**: \( (x - 8)^2 \)

14. **Identify the factored form of** \( x^2 + 10x + 25 \).

- **Answer**: \( (x + 5)^2 \)

15. **Identify the factored form of** \( x^2 - 5x + 6 \).

- **Answer**: \( (x - 2)(x - 3) \)

16. **Identify the factored form of** \( 4x^2 - 12x + 9 \).

- **Answer**: \( (2x - 3)^2 \)

17. **Identify the factored form of** \( x^2 + 4x - 12 \).

- **Answer**: \( (x + 6)(x - 2) \)
18. **Identify the factored form of** \( 3x^2 + 8x - 3 \).

- **Answer**: \( (3x - 1)(x + 3) \)

19. **Identify the factored form of** \( x^2 + 6x + 8 \).

- **Answer**: \( (x + 2)(x + 4) \)

20. **Identify the factored form of** \( x^2 - 4 \).

- **Answer**: \( (x - 2)(x + 2) \)

#### Section 3: Problem Solving (10 items)

1. **Factor and solve** for \( x \) in \( x^2 - 7x + 10 = 0 \).

2. **Factor and solve** for \( x \) in \( 2x^2 + 3x - 5 = 0 \).

3. **Simplify** the expression \( \frac{3x^2 - 12x}{3x} \).

4. **Factor and solve** for \( x \) in \( x^2 + 5x + 6 = 0 \).

5. **Simplify** the expression \( \frac{4x^2 - 9}{2x + 3} \).

6. **Factor and solve** for \( x \) in \( 3x^2 - 9x = 0 \).

7. **Simplify** the expression \( \frac{x^2 - 4}{x - 2} \).

8. **Factor and solve** for \( x \) in \( 2x^2 - 8x + 6 = 0 \).

9. **Simplify** the expression \( \frac{6x^2 - 15x}{3x} \).

10. **Factor and solve** for \( x \) in \( x^2 - 16 = 0 \).

---

Feel free to adjust the difficulty level or the number of questions based on your specific needs!

Certainly! Here's a detailed Table of Specifications (TOS) for a Mathematics 8 test covering the topics
you've specified. This TOS will help you organize and plan the content and skills to be assessed in a
balanced manner.

### Table of Specifications

| **Content Area** | **Objective** | **Number of

Questions** | **Percentage** | **Cognitive Level** | **Bloom's Taxonomy Level** |

|------------------------------------------------------|-----------------------------------------------------------|---------------------
-----|----------------|-----------------------|-----------------------------|

| **1. Factoring Polynomials** | | |

| | |

| - Factoring Common Monomial Factors | Factor out common monomials from polynomials.
|4 | 8% | Recall, Application | Remembering, Applying |

| - Factoring Difference of Two Squares | Factor polynomials of the form \( a^2 - b^2 \). |
4 | 8% | Application, Analysis | Applying, Analyzing |

| - Factoring Sum and Difference of Two Cubes | Factor polynomials of the form \( a^3 \pm b^3 \).
|4 | 8% | Application, Analysis | Applying, Analyzing |

| - Factoring Perfect Square Trinomials | Factor polynomials of the form \( a^2 \pm 2ab + b^2 \).
|4 | 8% | Application, Analysis | Applying, Analyzing |

| **2. Factoring General Quadratic Trinomials** | | |

| | |

| - Factoring Simple Quadratic Trinomials | Factor trinomials of the form \( x^2 + bx + c \). |
4 | 8% | Application, Analysis | Applying, Analyzing |

| - Factoring Quadratic Trinomials with Leading Coefficient | Factor trinomials of the form \( ax^2 + bx +
c \). |4 | 8% | Application, Analysis | Applying, Analyzing |
| - Solving Quadratic Equations by Factoring | Solve quadratic equations using factoring
techniques. | 4 | 8% | Application, Analysis | Applying, Analyzing |

| **3. Rational Algebraic Expressions** | | |

| | |

| - Factoring Rational Algebraic Expressions | Factor numerators and denominators of rational

expressions.| 4 | 8% | Application, Analysis | Applying, Analyzing |

| - Simplifying Rational Algebraic Expressions | Simplify expressions by canceling common factors.

|4 | 8% | Application, Analysis | Applying, Analyzing |

### Summary

- **Factoring Polynomials**: 16 items (32% of total test)

- Common Monomial Factors, Difference of Two Squares, Sum and Difference of Two Cubes, Perfect
Square Trinomials

- **Factoring General Quadratic Trinomials**: 12 items (24% of total test)

- Simple Quadratic Trinomials, Quadratics with Leading Coefficient, Solving Quadratic Equations

- **Rational Algebraic Expressions**: 8 items (16% of total test)

- Factoring, Simplifying

- **Total Number of Items**: 36 items (72% of total test)

### Cognitive Levels

- **Remembering**: Recall facts and basic concepts.

- **Applying**: Use information in new situations.

- **Analyzing**: Break information into parts to explore understandings and relationships.

- **Evaluating**: Make judgments based on criteria and standards.

- **Creating**: Use information to create new ideas or products.

This TOS ensures that the test covers a broad range of topics with a focus on different types of factoring
and simplifying algebraic expressions, while also addressing various cognitive levels. Adjustments can be
made based on the specific curriculum or instructional emphasis.

FIRST QUARTERLY ASSESSMENT

GRADE 10 MATHEMATICS
SY 2022 - 2023

Name:___________________________ Grade/Section:________Date:_________Score:______

PART I- MULTIPLE CHOICE. Read each statement carefully and choose the letter that
best corresponds to the statement. Write ONLY the letter of your answer on the space
provided for at the right.

1. Narisa wants to find the fifth term of a sequence -12 ,-7, -2, -3 which concept will you
suggest to be used?
a. Arithmetic Sequence b. Geometric Sequence c . Fibonacci d. Harmonic

2. Which of the following is an arithmetic sequence?

a. 21, 18, 15,… b. -6, -2, 2… c. 4, 2, 0 d. 80, 20, 5…

3. Which among the following is NOT a geometric sequence?

a. 5, 10, 20, 40b. -11, 22, -44, 88 c. 2, 6, 18, 54 d. 3, 8, 13, 18

4. If 1, -1/2, ¼, -1/8 is a geometric sequence, what is the common ratio?

a. 1/2 b. -1/2 c. 1/4 d. -1/4

5. In the sequence 1, 4, 7, 10, 13, 16, what is the common difference?

a. 3 b. 4 c. -3 d. -4
 6. An r in the geometric sequence is referred to a common ratio, which among the following best
describes it?
a. It is the fixed amount multiplied.
b. To find the common ratio, divide the second term by the first term.
c. It cannot be equal to zero.
d. ALL OF THE ABOVE.

7. The following are examples of Fibonacci sequence EXCEPT:

a. 0, 1, 1, 2, 3, 5 b. 2, 3, 5, 8, 13 c. 192, 16, 208, 224 d. 1, 4, 7, 10, 13

8. Which among the following is the harmonic sequence of a sequence 3, 8, 13, 18?
a. -3, -8, -13, -18 b. 1/3, 1/8, 1/13, 18 c. 3.0, 8.0, 13.0 d. NONE OF THE ABOVE

9. What is the fiftieth term of the arithmetic sequence 3, 7, 11, 15…?

a. 53 b. 151 c. 199 d. 203

10. What is the twentieth term of the arithmetic sequence 21, 18, 15, 12, ... ?
a. -39 b. -36 c. 1 d. 78

11. The fifth term of an arithmetic sequence is 11 and the tenth term is 41. What is the first term?
a. -19 b. -13 c. -9 d. 6

12. What is the thirty-second term of the arithmetic sequence -12, -7, -2, 3, ... ?
a. 143 b. 148 c. 153 d. 167
13. Find the tenth term of the arithmetic sequence 1, 6, 11, 16…
a. 40 b. 42 c. 44 d. 46
14. Find the 27 term of the arithmetic sequence -4, -1, 2, 5, 8.
th

a. 70 b. 72 c. 74 d. 76

15. What is the sum of the first sixteen terms of the arithmetic sequence 1, 5, 9, 13. ?
a. 62 b. 496 c. 528 d. 992

16. What is the sum of the first 30 terms of the arithmetic sequence 50, 45, 40, 35?
a. -675 b. 275 c. 675 d. 3675

17. What is the sum of the eleventh of the arithmetic sequence 7, 12, 17, 22, ... ?
a. 154 b. 295 c. 795 d. 1090

18. Find the 7 term of the sequence 2, 6, 18, 54?

th

a. 100 b. 500 c. 1300d. 1458

19. What is the 5 term for the sequence 3, 6, 12, 24…..?

th

a. 36 b. 40 c. 48 d. 52
20. What is the common difference of the sequence 3, 11, 19, 27, 35?
a. -8 b. 8 c. -14 d. 14

21. Find the sum of the geometric sequence 3, 6, 12, 24, 48, 96.
a. 189 b. -189 c. 190 d. -190

22. Find the sum of the geometric sequence 2, 8, 32, 128, 512.
a. 682 b. 684 c. 686 d. 688

23. Find the sum of the geometric sequence 2, ½, 1/8……..

a. 8/3 b. 9/3 c. 10/3 d. 11/3

24. What is the next term of the sequence 3, 4, 7, 11, 18, 29?
a. 46 b. 47 c. 48 d. 49

25. Find the next two terms of the sequence 192, 16, 208, ____, _____....7408.
a. 208 and 224 b. 200 and 224c. 300 and 224 d. 400 and 224

26. The first term of an arithmetic sequence is equal to 200 and the common difference is equal
to -10. Find the value of the 20th term.
a. 10 b. 20 c. 30 d. 40

27. A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next
row, and so on in an arithmetic sequence, until the top row has 4 cans. How many cans, in total,
are in the display?
a. 100 b. 108 c. 116. d. 124

28. How many terms of the arithmetic sequence -3, 2, 7….must be added together for the sume
of the series to be 116?
a. 8 b. 9 c. 10 d. 11

29. QAR, RAS, SAT, TAU, _______.

a. UAV b. UAT c. TAS d. TAT

30.

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