Free UTMA Algebra Questions and Answers

Question 1

What is the solution to the equation 2𝑥+3=7?

Accepted Answer

x=2

Answer

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)

Accepted Answer

6x3y4

Answer

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?

Accepted Answer

(x-2) (x-3)

Answer

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

Accepted Answer

x<9

Answer

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)?

Accepted Answer

5

Answer

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.

UTMA - University of Toronto Math Assessment Practice Test

UTMA - University of Toronto Math Assessment Practice Test

Free UTMA Algebra Questions and Answers