ALU2

Which pair of complex numbers has a real-number product? (1 + 3i)(6i) (1 + 3i)(2 - 3i) (1 + 3i)(1 - 3i) (1 + 3i)(3i)

(1 + 3i)(1 - 3i)

Which equation is an example of the commutative property of multiplication? (4 + 2i) = (2i + 4) (4 + 2i)(3 - 5i) = (3 - 5i)(4 + 2i) (4 + 2i)(3 - 5i) = (4 + 2i)(3 - 5i)(1) (4 + 2i) = (4 + 2i + 0)

(4 + 2i)(3 - 5i) = (3 - 5i)(4 + 2i)

Which equation demonstrates the additive identity property?

(7+4i) + 0 = 7+4i

Which equation illustrates the identity property of multiplication? (a + bi) × c = (ac + bci) (a + bi) × 0 = 0 (a + bi) × (c + di) = (c + di) × (a + bi) (a + bi) × 1 = (a + bi)

(a + bi) × 1 = (a + bi)

Which complex number has an absolute value of 5? -3 + 4i 2 + 3i 7 - 2i 9 + 4i

-3 + 4i

What is the first step when rewriting y = -4x2 + 2x - 7 in the form y = a(x - h)2 + k? 2 must be factored from 2x - 7 -4 must be factored from -4x2 + 2x x must be factored from -4x2 + 2x -4 must be factored from -4x2 - 7

-4 must be factored from -4x2 + 2x

What is the square root of -16? -8i -4i 4i 8i

-4i

What is the value of (-7 + 3i) - (2 - 6i)? -9 + 9i -9 - 3i -5 - 3i -5 + 9i

-9 + 9i

If , i = sqrt -1 what is the value of i 3? -1 i 1 -i

-i

Which of the following is equivalent to ? 5i 18 - 5i 18 + 5i 23

18 - 5i

rectangular pan has a length that is the width. The total area of the pan is 432 in.2. What is the width of the cake pan? A = lw

18in

If the complex number x = 3 + bi and |x|2 = 13, which is a possible value of b? 2 4 9 10

2

If f(x) = x3 - 2x^2, which expression is equivalent to f(i)? -2 + i -2 - i 2 + i 2 - i

2 - i

Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3? 2 units left and 3 units up 2 units left and 3 units down 2 units right and 3 units up 2 units right and 3 units down

2 units right and 3 units up

An egg is dropped from a height of 90 ft. If acceleration due to gravity is -16 ft/s2 and initial velocity is 0 ft/s, approximately how long will it take for the egg to reach the ground?h(t) = at2 + vt + h0 1.9 s 2.4 s 9.7 s 40.7 s

2.4 s

A projectile is launched straight up from the ground with an initial velocity of 120 ft/s. If acceleration due to gravity is -16 ft/s2, after about how many seconds will the object reach a height of 200 ft?h(t) = at2 + vt + h0 1.0 s 1.7 s 2.5 s 8.0 s

2.5s

The total area of two square windows is 1,025 in.2. Each side of the larger window is 5 in. longer than the sides of the smaller window. How long are the sides of the smaller window?A = s2 13.5 in. 20 in. 25 in. 31.6 in.

20 in

A firework is launched into the air from ground level with an initial velocity of 128 ft/s. If acceleration due to gravity is -16 ft/s2, what is the maximum height reached by the firework?h(t) = at2 + vt + h0 256 ft 448 ft 512 ft 1,024 ft

256 ft

What is the discriminant of 9x2 + 2 = 10x? -356 -172 28 72

28

Evaluate (2-5i)(p+q) when p=2 and q=5i

29i

Which complex number is represented by the point graphed on the complex plane below? -4 + 3i 3 + 4i 3 - 4i 4 + 3i

3 - 4i

What is the first step when rewriting y = 3x2 + 9x - 18 in the form y = a(x - h)2 + k? 3 must be factored from 3x2 + 9x x must be factored from 3x2 + 9x 9 must be factored from 9x - 18 3 must be factored from 3x2 - 18

3 must be factored from 3x2 + 9x

Which complex number has a distance of from the origin on the complex plane? 2 + 15i 17 + i 20 - 3i 4 - i

4 - i

What is the sum of sqrt -2 and sqrt -18

4 sqrt 2i

Which value must be added to the expression x2 + 16x to make it a perfect-square trinomial? 8 32 64 256

64

The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 - i, what is the voltage of the circuit? 4 - i 4 + i 8 + i 8 + 7i

8 + i

Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of 5 - 4i and Tomas has a score of 3 + 2i, what is their total score? 8 - 6i 8 + 6i 8 - 2i 8 + 2i

8 - 2i

What is the additive inverse of the complex number -8 + 3i? -8 - 3i -8 + 3i 8 - 3i 8 + 3i

8 - 3i

What is the sum of 12 - 5i and -3 + 4i? -16 + 63i 9 - i 9 - 9i 15 - 9i

9 - i

A skydiver jumps from an airplane at an altitude of 2,500 ft. He falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. Approximately how long does the jumper fall before he opens his chute?For this quadratic model we will let the y-axis be the axis of symmetry.h(t) = -16t2 + vt + h0 2.4 s 9.7 s 12.5 s 14.8 s

9.7s

If x = -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation? The discriminant is negative. The discriminant is -3. The discriminant is 0. The discriminant is positive.

The discriminant is 0.

A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is -16 ft/s2.

a

Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?

b

solve for x in the equation x^2 + 2x + 1 = 17

b. x = -1 +- sqrt 17

Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?

c

solve for x in the equation x^2 -12x +59 = 0

c. x= 6 +- sqrt 23i

Which property of addition is shown below?a + bi + c + di = a + c + bi + di identity property associative property commutative property inverse property

commutative property

A baseball is thrown into the air from a height of 5 feet. The ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. Which equation models the height of the baseball? Assume that acceleration due to gravity is -16 ft/s2. h(t) = 16t2 + 49.64t + 5 h(t) = -16t2 + 5t + 49.64 h(t) = -16t2 + 49.64t + 5 h(t) = 16t2 + 5t + 49.64

h(t) = -16t2 + 49.64t + 5

A softball pitcher throws a softball to a catcher behind home plate. The softball is 3 feet above the ground when it leaves the pitcher's hand at a velocity of 50 feet per second. If the softball's acceleration is -16 ft/s2, which quadratic equation models the situation correctly?h(t) = at2 + vt + h0 h(t) = 50t2 - 16t + 3 h(t) = -16t2 + 50t + 3 3 = -16t2 + 50t + h0 3 = 50t2 - 16t + h0

h(t) = -16t2 + 50t + 3

What is the square root of -1? -i i -1 1

i

Which property of addition is shown in the equation below?a + bi + 0 + 0i = a + bi commutative property inverse property identity property associative property

identity property

Which property of addition is shown below?If x = a + bi and y = -a - bi, x + y = 0. commutative property identity property associative property inverse property

inverse property

The main cable of a suspension bridge forms a parabola modeled by the equation y = a(x - h)2 + k where y is the height in feet of the cable above the road, x is the horizontal distance in feet from the right bridge support, a is a constant, and (h, k) is the parabola's vertex. What is the maximum and minimum height of the bridge modeled by the equation y = 0.005(x - 60)2 + 8? maximum height = 100 feet and minimum height = 26 feet maximum height = 100 feet and minimum height = 8 feet maximum height = 60 feet and minimum height = 26 feet maximum height = 26 feet and minimum height = 8 feet

maximum height = 26 feet and minimum height = 8 feet

Which point shows the location of 5 - 2i on the complex plane below? point A point B point C point D

point C

When using a quadratic equation in the form y = ax2 + bx + c to model the height of a projectile (y) over time (x), which of the following is always represented by the constant term? the initial height of the projectile the initial velocity of the projectile the time at which the projectile hits the ground the maximum height of the projectile

the initial height of the projectile

Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x - h)2 + k. Which of the following must be true? h and k cannot both equal zero k and c have the same value the value of a remains the same h is equal to one half -b

the value of a remains the same

Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y, of the rectangular garden that she creates if one side is x feet long?A = lw y = (60 - x)(x) y = (120 - x)(120 + x) y = (120 - x)(x) y = (60 - x)(60 + x)

y = (60 - x)(x)

Which equation has a graph that is a parabola with a vertex at (-2, 0)? y = -2x2 y = (x + 2)2 y = (x - 2)2 y = x2 - 2

y = (x + 2)2

Which equation could generate the curve in the graph below? y = -2x2 + 3x - 5 y = -2x2 - 4x - 2 y = -2x2 - 16x- 28 y = -2x2 +16x -28

y = -2x2 - 16x- 28

Which equation is y = -3x2 - 12x - 2 rewritten in vertex form? y = -3(x + 2)2 + 10 y = -3(x - 2)2 + 10 y = -3(x + 2)2 - 14 y = -3(x - 2)2 - 2

y = -3(x + 2)2 + 10

Which pair of equations generates graphs with the same vertex? y = -(x + 4)2 and y = (x - 4)2 y = -4x2 and y = 4x2 y = -x2 - 4 and y = x2 + 4 y = (x - 4)2 and y = x2 + 4

y = -4x2 and y = 4x2

Which equation is y = 2x2 - 8x + 9 rewritten in vertex form? y = 2(x - 2)2 + 9 y = 2(x - 2)2 + 5 y = 2(x - 2)2 + 1 y = 2(x - 2)2 + 17

y = 2(x - 2)2 + 1

Which equation could generate the curve in the graph below? y = 3x2 - 2x + 1 y = 3x2 - 6x + 3 y = 3x2 - 7x + 1 y = 3x2 - 4x - 2

y = 3x2 - 2x + 1

Which equation is y = 6x2 + 12x - 10 rewritten in vertex form? y = 6(x + 1)2 - 11 y = 6(x + 1)2 - 10 y = 6(x + 1)2 - 4 y = 6(x + 1)2 - 16

y = 6(x + 1)2 - 16