Free UTMA Algebra Questions and Answers — Questions and Answers
Question 1: What is the solution to the equation 2𝑥+3=7?
- x=2 (Correct answer)
- x=−2
- x=1
- x=3
Correct answer: x=2
To solve the equation 2x + 3 = 7, first subtract 3 from both sides, which gives 2x = 4. Next, divide both sides by 2. This isolates x, resulting in x = 2.
Question 2: Simplify the expression (3𝑥2𝑦)⋅(2𝑥𝑦3)
- 6x3y4 (Correct answer)
- 5𝑥2𝑦2
- 6𝑥3𝑦3
- 5𝑥3𝑦4
Correct answer: 6x3y4
To simplify the expression (3x^2y) * (2xy^3), multiply the coefficients (3 * 2 = 6) and add the exponents of the like bases. For x, x^2 * x^1 becomes x^(2+1) = x^3. For y, y^1 * y^3 becomes y^(1+3) = y^4. Combining these terms yields 6x^3y^4.
Question 3: What is the factorization of the quadratic expression x2-5x+6?
- (x-2) (x-3) (Correct answer)
- (x+2) (x+3)
- (x-1) (x-6)
- (x+1) (x+6)
Correct answer: (x-2) (x-3)
To factor the quadratic expression x^2 - 5x + 6, we need to find two numbers that multiply to +6 and add up to -5. These two numbers are -2 and -3. Therefore, the factorization is (x-2)(x-3).
Question 4: Solve the inequality 3𝑥−4<2𝑥+5
- x<9 (Correct answer)
- 𝑥>9
- 𝑥<1
- x>1
Correct answer: x<9
To solve the inequality 3x - 4 < 2x + 5, first subtract 2x from both sides to get x - 4 < 5. Then, add 4 to both sides of the inequality. This results in x < 9.
Question 5: If 𝑓 (𝑥) =2𝑥2−3𝑥+4, what is 𝑓 (−1)?
- 9
- -1
- 5 (Correct answer)
- 1
Correct answer: 5
To find f(-1), substitute x = -1 into the function f(x) = 2x^2 - 3x + 4. This gives f(-1) = 2(-1)^2 - 3(-1) + 4. Evaluating this, we get 2(1) - (-3) + 4, which simplifies to 2 + 3 + 4 = 9.
Free UTMA Algebra Questions and Answers
What is the solution to the equation 2𝑥+3=7?