Grade: 9 Subject: Math (Algebra I) Unit: Introduction to Quadratics Lesson: 6 of 6 SAT: AdvancedMath ACT: Math

Unit Quiz

Instructions

This quiz covers all topics from the Introduction to Quadratics unit:

Try to complete all problems before checking your answers.

Question 1: Factor: x^2 - 8x + 15

Answer: (x - 3)(x - 5)

Solution: Find numbers that multiply to 15 and add to -8: -3 and -5.

Question 2: Solve: x^2 - 5x - 14 = 0

Answer: x = 7 or x = -2

Solution: Factor: (x - 7)(x + 2) = 0. Set each factor to zero.

Question 3: Use the quadratic formula to solve: x^2 + 3x - 10 = 0

Answer: x = 2 or x = -5

Solution: x = (-3 +/- sqrt(9 + 40))/2 = (-3 +/- 7)/2. So x = 2 or x = -5.

Question 4: Factor: x^2 - 25

Answer: (x + 5)(x - 5)

Solution: This is a difference of squares: a^2 - b^2 = (a+b)(a-b).

Question 5: Solve: 2x^2 + 5x - 3 = 0

Answer: x = 1/2 or x = -3

Solution: Factor: (2x - 1)(x + 3) = 0. 2x - 1 = 0 gives x = 1/2. x + 3 = 0 gives x = -3.

Question 6: Find the discriminant and number of solutions: x^2 - 4x + 4 = 0

Answer: Discriminant = 0, one real solution (double root)

Solution: b^2 - 4ac = 16 - 16 = 0. One solution: x = 2.

Question 7: The product of two consecutive even integers is 168. Find them.

Answer: 12 and 14 (or -14 and -12)

Solution: Let n = first even integer. n(n+2) = 168. n^2 + 2n - 168 = 0. (n-12)(n+14) = 0.

Question 8: Factor completely: 3x^2 - 27

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

Solution: Factor out GCF: 3(x^2 - 9). Then factor difference of squares: 3(x+3)(x-3).

Question 9: A ball's height is h = -16t^2 + 64t. Find the maximum height.

Answer: 64 feet

Solution: Maximum at t = -b/(2a) = -64/(2(-16)) = 2 seconds. h(2) = -16(4) + 64(2) = 64 feet.

Question 10: Solve: x^2 + 6x = 16

Answer: x = 2 or x = -8

Solution: Set equal to zero: x^2 + 6x - 16 = 0. Factor: (x - 2)(x + 8) = 0.