TSIA2 Algebra Fundamentals 3 — Questions and Answers
Question 1: Solve the system: x + y = 10 and x - y = 4. What is x?
- x = 3
- x = 5
- x = 7 (Correct answer)
- x = 9
Correct answer: x = 7
Adding the equations gives 2x = 14, so x = 7.
Question 2: What is the simplified form of (3x²y)(4xy³)?
- 12x²y³
- 12x³y⁴ (Correct answer)
- 7x³y⁴
- 12x³y³
Correct answer: 12x³y⁴
Multiply coefficients (3×4=12) and add exponents: x^(2+1)=x³ and y^(1+3)=y⁴.
Question 3: A store marks up items by 25%. If an item costs the store $48, what is the selling price?
- $54
- $58
- $60 (Correct answer)
- $62
Correct answer: $60
Selling price = 48 × 1.25 = $60.
Question 4: Which of the following is a factor of x² - 9x + 18?
- (x - 2)
- (x - 3) (Correct answer)
- (x + 6)
- (x + 9)
Correct answer: (x - 3)
x² - 9x + 18 = (x - 3)(x - 6), so (x - 3) is a factor.
Question 5: What is the solution to |2x - 4| = 10?
- x = 7 only
- x = -3 only
- x = 7 or x = -3 (Correct answer)
- x = 3 or x = -7
Correct answer: x = 7 or x = -3
Set 2x - 4 = 10 (x = 7) and 2x - 4 = -10 (x = -3).
Question 6: If 5x + 2y = 20 and y = 5, what is x?
- x = 1
- x = 2 (Correct answer)
- x = 3
- x = 4
Correct answer: x = 2
Substituting y = 5: 5x + 10 = 20, so 5x = 10 and x = 2.
Question 7: What is the degree of the polynomial 4x³ - 7x⁵ + 2x - 9?
- 3
- 4
- 5 (Correct answer)
- 6
Correct answer: 5
The degree is determined by the highest exponent, which is 5 in -7x⁵.
TSIA2 Algebra Fundamentals 3
Solve the system: x + y = 10 and x - y = 4.
What is x?