Quiz about Math 2 - Semester 1 Final Review (2024)

Question 1

Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.

$$8x-3x^2+10x^3-4$$

Accepted Answer

$$10x^3-3x^2+8x-4$$

cubic polynomial

Answer

$$10x^3+8x-3x^2-4$$

cubic polynomial

Answer

$$-3x^3+10x^2+8x-4$$

quadratic polynomial

Answer

$$-4+8x-3x^2+10x^3$$

cubic polynomial

Question 2

Simplify the difference: $$\left(6w^2-7w-8\right)-\left(2w^2+2w-7\right)$$

Accepted Answer

$$4w^2-9w-1$$

Answer

$$4w^2-5w-15$$

Answer

$$8w^2-5w-15$$

Answer

$$8w^2+9w+1$$

Question 3

Find the product: $$\left(4x-5\right)\left(2x-4\right)$$

Accepted Answer

$$8x^2-26x+20$$

Answer

$$8x^2+26x+20$$

Answer

$$8x^2-6x-20$$

Answer

$$8x^2+6x-20$$

Question 4

What is the factored form of the following expression? $$d^2+d-20$$

Accepted Answer

$$\left(d-4\right)\left(d+5\right)$$

Answer

$$\left(d-4\right)\left(d-5\right)$$

Answer

$$\left(d+4\right)\left(d+5\right)$$

Answer

$$\left(d+4\right)\left(d-5\right)$$

Question 5

What is the factored form of the expression? $$x^2-5xy-24y^2$$

Accepted Answer

$$\left(x-8y\right)\left(x+3y\right)$$

Answer

$$\left(x-8y\right)\left(x-3y\right)$$

Answer

not factorable

Answer

$$\left(x+2y\right)\left(x-12y\right)$$

Question 6

What is the factored form of the expression? $$6x^2+5x+1$$

Accepted Answer

$$\left(3x+1\right)\left(2x+1\right)$$

Answer

$$\left(3x-1\right)\left(2x-1\right)$$

Answer

$$\left(3x+1\right)\left(2x-1\right)$$

Answer

$$\left(3x-1\right)\left(2x+1\right)$$

Question 7

What is the expression in factored form? $$3x^2+24x+45$$

Accepted Answer

$$3\left(x+5\right)\left(x+3\right)$$

Answer

$$3\left(x-5\right)\left(x-3\right)$$

Answer

$$3\left(x+5\right)\left(x-3\right)$$

Answer

$$3\left(x-5\right)\left(x+3\right)$$

Question 8

What is the expression in factored form? $$49x^2-4$$

Accepted Answer

$$\left(7x+2\right)\left(7x-2\right)$$

Answer

$$\left(7x+2\right)\left(-7x-2\right)$$

Answer

$$\left(-7x+2\right)\left(7x-2\right)$$

Answer

$$\left(7x-2\right)^2$$

Question 9

What is the simpler form of the product? $$\left(4m+1\right)^2$$

Accepted Answer

$$16m^2+8m+1$$

Answer

$$16m^2-8m+1$$

Answer

$$16m^2+8m-1$$

Answer

$$16m^2+4m-1$$

Question 10

What are the coordinates of the vertex of the graph? Is it a maximum or minimum?

Accepted Answer

$$\left(-1,\ -1\right)$$ ; maximum

Answer

$$\left(-1,\ -1\right)$$ ; minimum

Answer

$$\left(-1,\ 0\right)$$ ; maximum

Answer

$$\left(-1,\ 0\right)$$ ; minimum

Question 11

What is the vertex and the axis of symmetry of the equation? $$y=2x^2+4x-18$$

Accepted Answer

vertex: $$\left(-1,-20\right)$$

axis of symmetry: $$x=-1$$

Answer

vertex: $$\left(1,-20\right)$$

axis of symmetry: $$x=-20$$

Answer

vertex: $$\left(-1,20\right)$$

axis of symmetry: $$y=-1$$

Answer

vertex: $$\left(-1,-20\right)$$

axis of symmetry: $$x=-20$$

Question 12

Identify the vertex and the axis of symmetry of the graph of the function $$y=-2\left(x+3\right)^2+4$$

Accepted Answer

vertex: $$\left(-3,4\right)$$

axis of symmetry: $$x=-3$$

Answer

vertex: $$\left(3,4\right)$$

axis of symmetry: $$x=3$$

Answer

vertex: $$\left(-3,-4\right)$$

axis of symmetry: $$x=-3$$

Answer

vertex: $$\left(3,-4\right)$$

axis of symmetry: $$x=3$$

Question 13

Suppose a parabola has vertex $$\left(-2,5\right)$$ and also passes through the point $$\left(-1,7\right)$$ . Write the equation of the parabola in vertex form.

Accepted Answer

$$y=2\left(x+2\right)^2+5$$

Answer

$$y=\left(x+2\right)^2+5$$

Answer

$$y=2\left(x+2\right)^2-5$$

Answer

$$y=2\left(x-2\right)^2+5$$

Question 14

What steps transform the graph of $$y=x^2$$ to $$y=-2\left(x+2\right)^2+3$$

Accepted Answer

opens down, translate 2 units to the left, translate up 3 units, stretch by the factor 2

Answer

translate 2 units to the right, translate down 3 units, stretch by the factor 2

Answer

translate 2 units to the left, translate up 3 units, stretch by the factor 2

Answer

opens down, translate 2 units to the right, translate down 3 units, stretch by the factor 2

Question 15

Use the vertex form to write the equation of the parabola.

Accepted Answer

$$y=3\left(x-2\right)^2+2$$

Answer

$$y=3\left(x+2\right)^2+2$$

Answer

$$y=3\left(x+2\right)^2-2$$

Answer

$$y=\left(x-2\right)^2+2$$

Question 16

What is the graph of the function? $$y=\frac{1}{2}x^2$$

Accepted Answer

Question 17

What is the vertex form of the equation?

$$y=x^2+16x+54$$

Accepted Answer

$$y=\left(x+8\right)^2-10$$

Answer

$$y=\left(x+8\right)^2+10$$

Answer

$$y=\left(x+16\right)^2+54$$

Answer

$$y=\left(x-8\right)^2-10$$

Question 18

The length of the rectangle is $$4x-5$$ inches. The width of the rectangle is $$x+1$$ inches. Find a quadratic function equation to model the area of the rectangle. Then evaluate the function for $$x=2$$

Accepted Answer

$$f\left(x\right)=4x^2-x-5$$ $$f\left(2\right)=9$$ square inches

Answer

$$f\left(x\right)=4x^2+4x-5$$

$$f\left(2\right)=197$$ square inches

Answer

$$f\left(x\right)=4x^2-5x+1$$ $$f\left(2\right)=7$$ square inches

Answer

$$f\left(x\right)=4x^2+x-4$$ $$f\left(2\right)=14$$ square inches

Question 19

A ball is thrown into the air with an upward velocity of 48 ft/s. Its heigh h in feet after t seconds is given by the function $$h=-16t^2+48t+8$$ . How long does it take the ball to reach its maximum height? What is the ball's maximum height? Round to the nearest hundredth, if necessary.

Accepted Answer

1.5 s; 44 ft

Answer

3 s; 8 ft

Answer

1.5 s; 116 ft

Answer

1.5 s; 56 ft

Question 20

Complete the following sentence:

You can verify the zeros of the function $$y=x^2+6x-7$$ by using a graph and finding where the graph _________.

Accepted Answer

crosses the x-axis

Answer

is at a maximum

Answer

is at a minimum

Answer

crosses the y-axis

Question 21

Use the table to find the solutions.

Accepted Answer

-1, 2

Answer

-1

Answer

-2

Answer

2

Question 22

What are the solutions of the equation?

$$16x^2+20x+6=0$$

Accepted Answer

$$-\frac{1}{2},-\frac{3}{4}$$

Answer

$$\frac{1}{2},-\frac{3}{4}$$

Answer

$$-\frac{1}{2},\frac{3}{4}$$

Answer

$$\frac{1}{2},\frac{3}{4}$$

Question 23

What are the solutions of the equation?

$$z^2-2z-24=0$$

Accepted Answer

6, -4

Answer

6, 4

Answer

-6, 4

Answer

-6. -4

Question 24

Fill in the blanks to complete the square.

$$x^2\ -\ 30x\ +$$ __________ $$=19\ +$$ ___________

Accepted Answer

225

Answer

-15

Answer

15

Answer

-225

Question 25

Simplify the radical expression completely.

$$\sqrt[]{44a^6b^4}$$

Accepted Answer

$$2a^3b^2\sqrt[]{11^{ }}$$

Answer

$$2\sqrt[]{11a^6b^4}$$

Answer

$$ab\sqrt[]{22}$$

Answer

$$4\sqrt[]{11a^6b^4}$$

Question 26

Simplify the radical expression completely.

$$\sqrt[]{72}$$

Accepted Answer

$$6\sqrt[]{2}$$

Answer

$$6\sqrt[]{4}$$

Answer

$$12$$

Answer

4

Question 27

Solve the equation using square roots.

$$4x^2-250=6$$

Accepted Answer

-8, 8

Answer

-64, 64

Answer

$$-\sqrt[]{8},\ \sqrt[]{8}$$

Answer

no real number solutiongs

Question 28

Solve the equation using square roots.

$$x^2-16=0$$

Accepted Answer

-4, 4

Answer

-16, 16

Answer

$$-\sqrt[]{4},\sqrt[]{4}$$

Answer

No real number solutions

Question 29

Solve the equation by completing the square.

$$x^2+16x+46=7$$

Accepted Answer

-3, -13

Answer

-5, -15

Answer

$$-9\pm6\sqrt[]{2}$$

Answer

-4, -14

Question 30

Solve the quadratic equation.

$$x^2+8x-25=0$$

Accepted Answer

$$-4\pm\sqrt[]{41}$$

Answer

$$-6\pm\sqrt[]{82}$$

Answer

$$7\pm\sqrt[]{26}$$

Answer

$$1\pm4\sqrt[]{2}$$

Question 31

Simplify the expression.

$$\left(2-i\right)-\left(-1-2i\right)$$

Accepted Answer

$$3+i$$

Answer

$$1-3i$$

Answer

$$4i$$

Answer

$$-3-i$$

Question 32

Simplify the expression.

$$\left(6-3i\right)\left(5+4i\right)$$

Accepted Answer

$$42+9i$$

Answer

$$18+9i$$

Answer

$$90+21i$$

Answer

$$30+21i$$

Question 33

Find the solutions of the equation.

$$x^2+10x+55=0$$

Accepted Answer

$$-5\pm i\ \sqrt[]{30}$$

Answer

13, 3

Answer

$$5\pm2i\sqrt[]{5}$$

Answer

$$5\pm\sqrt[]{70}$$

Question 34

Use the quadratic formula to solve the equation.

$$-3x^2-2x+85=0$$

Accepted Answer

$$-\frac{17}{3},\ 5$$

Answer

$$-\frac{1}{2},\ -5$$

Answer

-1, 1

Answer

$$\frac{17}{3},\ -5$$

Question 35

Use the quadratic formula to solve the equation.

$$-3x^2-3x+7=0$$

Accepted Answer

$$-\frac{3\pm\sqrt[]{93}}{6}$$

Answer

$$\frac{3\pm\sqrt[]{93}}{6}$$

Answer

$$-\frac{3\pm\sqrt[]{75}}{6}$$

Answer

$$-\frac{1\pm\sqrt[]{93}}{2}$$

Question 36

You roll a standard number cube. Find P(5).

Accepted Answer

$$\frac{1}{6}$$

Answer

$$\frac{1}{2}$$

Answer

$$\frac{5}{6}$$

Answer

$$\frac{2}{3}$$

Question 37

A drug trial is testing the effectiveness of two drugs. If 30 patients are given Drug A, 10 patients are given Drug B, and 75 patients are given the placebo, what is the probability that a patient will NOT be given a placebo?

Accepted Answer

$$\frac{8}{23}$$

Answer

$$\frac{15}{23}$$

Answer

$$\frac{2}{23}$$

Answer

$$\frac{6}{23}$$

Question 38

A local pizzeria offers 14 toppings for their pizzas and you can choose any 4 of them for a fixed price. How many different types of pizzas can you order with 4 toppings?

Accepted Answer

1,001

Answer

24,024

Answer

3,632,428,800

Answer

24

Question 39

A jar contains 4 blue cubes, 8 blue spheres, 3 purple cubes, and 9 purple spheres. If you select an object at random, what is the probability that the object is purple or a cube.

Accepted Answer

$$\frac{2}{3}$$

Answer

$$\frac{19}{24}$$

Answer

$$\frac{1}{8}$$

Answer

$$\frac{11}{12}$$

Question 40

You are dealt two cards successively without replacement from a standard deck of 52 cards. Find the probability that the first card is an eight and the second card is a two.

Accepted Answer

$$\frac{4}{663}$$

Answer

$$\frac{1}{169}$$

Answer

$$\frac{2}{663}$$

Answer

$$\frac{1}{2652}$$

Question 41

There are 7 red chips, 4 blue chips, and 9 white chips in a basket. Two chips are randomly selected. Find the probability that the first chip is blue, and the second chip is white assuming the first chip is replaced.

Accepted Answer

$$\frac{9}{100}$$

Answer

$$\frac{59}{95}$$

Answer

$$\frac{13}{20}$$

Answer

$$\frac{64}{95}$$

Question 42

1. On Valentine's Day, you took note of who was coming into your restaurant wearing red. The frequency table shows the results of your survey. What is the probability that a randomly chosen customer will be a male wearing red? Round to the nearest tenth.

Accepted Answer

$$\frac{18}{117}$$

Answer

$$\frac{45}{117}$$

Answer

$$\frac{2}{7}$$

Answer

$$\frac{9}{20}$$

Question 43

The table shows the results of a study examining social media company preferences between females and males. Find the probability that a person prefers watching Netflix, given that the person is a female.

Accepted Answer

$$\frac{16}{33}$$

Answer

$$\frac{49}{66}$$

Answer

$$\frac{7}{8}$$

Answer

$$\frac{32}{49}$$

Question 44

There are 10 students participating in a spelling bee. In how many ways can students who go first and second be chosen?

Accepted Answer

90

Answer

3,628,800

Answer

45

Answer

1

Question 45

A yogurt shop offers 3 different flavors of frozen yogurt and 10 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?

Accepted Answer

30

Answer

720

Answer

120

Answer

3,628,800

Math 2 - Semester 1 Final Review (2024)

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