College Readiness Math Flashcards

Simplify: (2x³y²)(3x²y⁴)

Answer: 6x⁵y⁶

Multiply coefficients (2 × 3 = 6) and add exponents: x^(3+2) = x⁵, y^(2+4) = y⁶.

What are the solutions to x² + 5x − 6 = 0?

Answer: x = 1 and x = −6

Factor: (x + 6)(x − 1) = 0, so x = −6 or x = 1.

What is the y-intercept of the line 4x − 2y = 10?

Answer: −5

Set x = 0: −2y = 10, so y = −5.

The table shows (1, 3), (2, 6), (3, 12), (4, 24). Which function best models this data?

Answer: f(x) = 3 · 2^(x−1)

Each output doubles, indicating exponential growth: f(x) = 3 · 2^(x−1).

Solve the system: x + y = 8 and x − y = 2

Answer: x = 5, y = 3

Adding the equations: 2x = 10, x = 5; substituting: y = 3.

Which value of k makes 4x² + kx + 9 a perfect square trinomial?

Answer: 12

For a perfect square (2x + 3)², the middle term is 2(2x)(3) = 12x, so k = 12.

A car travels 180 miles at an average speed of 60 mph. How long does the trip take?

Answer: 3 hours

Time = distance ÷ speed = 180 ÷ 60 = 3 hours.