Algebra 1 Semester 2 Review

Multiple Choice

Solve the following quadratic equation: $$x^2-6x-7=0$$  

• $$x=7\ \ \ \&\ \ \ x=-1$$  

• $$x=1\ \ \ \&\ \ \ x=-7$$  

• $$x=0$$  

• $$x=\frac{-7}{5}$$  

Multiple Choice

Factor 6x²-27x

• (6x+1)(x+3)
• 3x(2x-9)
• 6x(x-9)
• (3x-9)(2x+3)

Multiple Choice

What are the zeros of the function $$f\left(x\right)=3x\left(x-4\right)\left(x+5\right)$$  ?

• $$-4,\ 0,\ 5$$  

• $$-4,\ 3,\ 5$$  

• $$-5,\ -3,\ 4$$  

• $$-5,\ 0,\ 4$$  

Multiple Choice

What information can I find from this form of the equation?

f(x ) = x² + 8x + 11

• x-intercepts: (8, 0)(11, 0)

• y-intercept: (0, 11)

• vertex: (8, 11)

Multiple Choice

What information can I find from this form of the equation?

f(x ) = (x - 5)² + 8

• x-intercepts: (5, 0)(8, 0)

• y-intercept: (0, 5)

• vertex: (5, 8)

Multiple Choice

What information can I find from this form of the equation?

f(x ) = (x - 9)(x - 10)

• x-intercepts: (9, 0)(10,0)

• y-intercept: (0, 19)

• vertex: (9, 10)

Multiple Choice

Identify the form of the quadratic function:

f(x ) = 2(x - 9)² - 13

• Standard

• Factored

• Vertex

Multiple Choice

Find the roots of the equation:

$$\left(2x+5\right)\left(x-3\right)=0$$

• $$\left(-\frac{5}{2},0\right)\ \left(3,0\right)$$

• $$\left(\frac{5}{2},0\right)\ \left(3,0\right)$$

• $$\left(-\frac{5}{2},0\right)\ \left(-3,0\right)$$

• $$\left(\frac{5}{2},0\right)\ \left(-3,0\right)$$

Multiple Choice

Which equation matches the graph?

• $$y=\left(x-1\right)\left(x+5\right)$$

• $$y=\left(x+1\right)\left(x-5\right)$$

• $$y=\left(x-2\right)\left(x-9\right)$$

• $$y=\left(x+2\right)\left(x+9\right)$$

Multiple Choice

Solve using the Quadratic Formula:
$$x^2-7x+10=0$$

• $$x=2\ or\ x=5$$  

• $$x=-2\ or\ x=-5$$  

• $$x=4\ or\ x=10$$  

• No real solutions

Multiple Choice

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

• (2, 3); minimum

• (2, 5); maximum

• (2, 3); maximum

• (2, -3); minimum

• (2, -3); maximum

Multiple Choice

Find the Vertex: y= -5x² -20x - 26

• (-2, -6)

• (2, 6)

• (6,2)

• (3, 6)

Multiple Choice

Solve:  $$x^2+8=28$$  

• No solution

• $$x=\pm4\sqrt{5}$$  

• $$x=\pm6$$  

• $$x=\pm2\sqrt{5}$$  

Multiple Choice

Solve by taking square roots:
5b² - 4 = 41

• b = 9, b = -9
• b = 3, b = -3
• b = 8, b = -8
• no solution

Multiple Choice

Solve for x.

5(x - 3)² + 1 = 81

• x = -1, 7

• x = -7, 1

• x = ± 9

• x = 3, 10

Multiple Choice

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

• Set the equation equal to zero
• Divide 10 by 2 and add the result to both sides
• Add a² and 10a together
• Subtract the 21

Multiple Choice

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

• 4
• 2
• 8
• 20

Multiple Choice

Complete the Square
x² + 6x = 5

• (x + 3)² = 5
• (x + 6)² = 9
• (x + 3)² = 14
• (x + 6)² = 14

Multiple Choice

Identify a, b and c in the quadratic equation: $$2x^2-3x-5=0$$  

• a = 2 , b = 3, c = -5

• a = 2, b = -3, c = 5

• a = 2, b = -3, c = -5

• a = -2, b = 3, c = 5

Multiple Choice

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember:  b² - 4ac

• 400

  2 real roots

• 0

  1 real root

• -400

  2 imaginary roots

• -3

  no real roots

Multiple Choice

What should you do first in solving this equation if using the quadratic formula?
x² + 6x - 13 = 3

• Get factored form
• Write down: a=1, b=6, c=-13
• Make it equal 0 by subtracting 3 on each side
• Type it all in a calculator.

Multiple Choice

The discriminant is

• aX²  + bX  +  c
• b - 4ac
• b² - 4ac
• b² + 4ac

Multiple Choice

A function has a discriminant of 25.

How many solutions does it have?

• 0
• 1
• 2
• 5

Multiple Choice

For the function above, is the discriminant positive, negative, or zero?

• Positive
• Negative
• Zero

Multiple Choice

Solve

$$2y^2+2=9y$$  

• $$\frac{-9\pm\sqrt{65}}{2}$$  

• $$\frac{9\pm5\sqrt{13}}{4}$$  

• $$\frac{9\pm\sqrt{65}}{4}$$  

• $$\frac{-9\pm\sqrt{-97}}{4}$$  

Multiple Choice

Given $$y=x^2$$  . 

Find the equation of the parabola that has moved...

5 units to the right

• $$y=x^2+5$$

• $$y=x^2-5$$

• $$y=\left(x+5\right)^2$$

• $$y=\left(x-5\right)^2$$

Multiple Choice

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down

Multiple Choice

Identify the vertex of f(x) = 5(x+6)² - 7

• (5,6)

• (0,0)

• (6,-7)

• (-6,-7)

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

How did we transform from the parent function?
y = x² + 2

• horizontal shift up
• vertical shift up
• horizontal shift down
• vertical shift down

Multiple Choice

Which list orders the quadratic functions from narrowest to widest?

• y = x² 
  y = 4x² 
  y = 2x² - 2  
  y = 0.5 x²
• y = 0.5 x²  
   y = x² 
  y = 2x² - 2 
  y = 4x²
• y = 4x² 
  y = 2x² - 2
   y = x² 
  y = 0.5 x²  
•  y = 2x² - 2
   y = 4x²
   y = 0.5x²
   y = x²

Multiple Choice

How do the graphs of the functions
f(x) = x² + 9 and
g(x) = x² – 11 relate to each other?

• The graph of f(x) is 2 units above the graph of g(x).
• The graph of f(x) is 20 units above the graph of g(x).
• The graph of f(x) is 2 units to the right the graph of g(x).
• The graph of f(x) is 20 units to the right the graph of g(x).

Multiple Choice

Which of the following transformations are present?
-2f(x - 1) + 2

• Shift 1 unit down
• Shift 1 unit up
• Shift 1 unit left
• Shift 1 unit right

Multiple Choice

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

• f(x + 3) - 4
• f(x - 4) + 3
• f(x + 4) + 3
• f(x + 3) + 4

Multiple Choice

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

• f(x - 3)
• f(x + 3)
• f(x) + 3
• f(x) - 3

Multiple Choice

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

• 2 ft

• 80 ft

• 144 ft

• 64 ft

Multiple Choice

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

• 8 seconds

• 1 second

• 1.5 seconds

• 1/4 second

Multiple Choice

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

When would you reach 16 feet above the water?

• 8 seconds

• 1 second

• 1/2 second

• 1/4 second

Multiple Choice

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s.

Use the formula: h(t) = −16 t² + 8t + 24

How high is the platform?

• .25 ft

• 24 ft

• 25 ft

• 8 ft

Multiple Choice

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

• $6060

• $20

• $600

• $10,250

Multiple Choice

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function :

h(t) = -16t² + 40t + 10

How many seconds does it take the ball to reach its maximum height?

• 1.25 seconds

• 1.4 seconds

• 2.5 seconds

• 2 seconds

Multiple Choice

Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds.

h = -16t2 + 288t + 8

How many seconds will it take for the rocket to reach a height of 1,304 feet?

• 9.0 seconds

• 9.6 seconds

• 81.0 seconds

• 82.0 seconds

Multiple Choice

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t² + 45

When is the ball at ground level?

• only at t = 0 seconds

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds

Multiple Choice

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

• 1 foot

• 5 feet

• 7 feet

• 8 feet

• 12 feet

Multiple Choice

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

Multiple Choice

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions
• 1 solution
• 2 solutions
• 3 solutions

Multiple Choice

Find the solution:
y = x² - 4x + 6
y = x + 2

• (3, 1) and (6, 4)
• (-1, 1) and (4, 2)
• (1, 3) and (4, 6)
• (1, 4) and (3, 6)

Multiple Choice

Two equations were graphed on the set of axes below.  Which point is a solution to the system of equations ?

• (0,3)
• (5,0)
• (2,-3)
• (8,9)

Multiple Choice

Write the equation in standard form of the parabola passing through the points (1, -1), (2, -5), (3, -7).

• $$y=x^2-7x+5$$

• $$y=-x^2+4x-7$$

• $$y=x^2-5x-2$$

• $$y=-x^2+3x-8$$

Multiple Choice

Write the equation in standard form of the parabola passing through the points (2, -8), (3, -8), (6, 4).

• $$y=x^2-7x+5$$

• $$y=-x^2+4x-7$$

• $$y=x^2-5x-2$$

• $$y=-x^2+3x-8$$

Multiple Choice

Write the equation in standard form of the parabola passing through the points (1, -4), (2, -3), (3, -4).

• $$y=x^2-7x+5$$

• $$y=-x^2+4x-7$$

• $$y=x^2-5x-2$$

• $$y=-x^2+3x-8$$

Multiple Choice

Write the equation in standard form of the parabola passing through the points in the given table.

• $$y=x^2-x+5$$

• $$y=-x^2+2x+1$$

• $$y=x^2+5x-2$$

• $$y=2x^2-9$$

Multiple Choice

Determine if the following sequence is arithmetic or geometric.

4, 9, 14, 19, 24, ...

• Arithmetic

• Geometric

Multiple Choice

Determine if the following sequence is arithmetic or geometric.

15, 13, 11, 9, 7, ...

• Arithmetic

• Geometric

Multiple Choice

Determine if the following sequence is arithmetic or geometric.

6, 12, 24, 48, 96, ...

• Arithmetic

• Geometric

Multiple Choice

What is the recursive rule for the sequence:
-2, 12, -72, 432, ...

• a_n = -2(-6)^n-1
  a₁=-2
• a_n =a_n-1 + 10
  a₁=-2
• a_n = -6⋅a_n-1 a₁=-2

• a_n = a_(n-1) - 6 a₁=-2

Multiple Choice

Given the recursive formula, find the explicit form
a_n = a_n-1 - 5
a₁ = 22

• a_n = 22 + (n-1)(-5)
• a_n = 22 + (n-1)(5)
• a_n = -5 + (n-1)(22)
• a_n = -16 + (n-1)(-5)

Multiple Choice

Write the explicit formula for the sequence.

9, 5, 1, -3, ...

• $$a_n=9+5\left(n-1\right)$$

• $$a_n=9-4\left(n-1\right)$$

• $$a_n=4+9\left(n-1\right)$$

• $$a_n=9\cdot4^{\left(n-1\right)}$$

Multiple Choice

Write the explicit formula for the sequence.

216, 72, 24, 8, ...

• $$a_n=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$$

• $$a_n=8\cdot3^{\left(n-1\right)}$$

• $$a_n=216-144\left(n-1\right)$$

• $$a_n=216\cdot3^{\left(n-1\right)}$$

Multiple Choice

Use the explicit formula to find the 7th term of the sequence.
$$a_n=22-3\left(n-1\right)$$  

• 4

• 1

• 18

• 114

Multiple Choice

Use the explicit formula to find the 5th term of the sequence.
$$a_n=3\cdot2^{\left(n-1\right)}$$  

• 24

• 7,776

• 48

• 96

Multiple Choice

Write the explicit formula for the sequence.

7, 28, 112, 448, ...

• $$a_n=7+4\left(n-1\right)$$

• $$a_n=7\cdot4^{\left(n-1\right)}$$

• $$a_n=\frac{448}{4n}$$

• $$a_n=28+84\left(n-1\right)$$

Multiple Choice

Write the explicit formula for the sequence.

10, -2, -14, -26, ...

• $$a_n=10\cdot\left(-\frac{1}{5}\right)^{\left(n-1\right)}$$

• $$a_n=-2\cdot7^{\left(n-1\right)}$$

• $$a_n=10-8\left(n-1\right)$$

• $$a_n=10-12\left(n-1\right)$$

Multiple Choice

Which sequence is an arithmetic sequence?

• 3, 6, 2, 7, ...

• 3, 6, 12, 24, ...

• 3, 6, 10, 15, ...

• 3, 7, 11, 15, ...

Multiple Choice

What is the domain of the function shown?

• $$x>1$$  

• $$y>1$$  

• $$x>-2$$  

• $$y>-2$$  

Multiple Choice

What is the range of the function shown?

• $$x>1$$  

• $$y>1$$  

• $$x>-2$$  

• $$y>-2$$  

Fill in the Blank

Consider the given function that represents the balance in a bank account.

$$b\left(x\right)=850\left(1.025\right)^x$$  

What is the initial balance in the account?

Fill in the Blank

Consider the given function that represents the balance in a bank account.

$$b\left(x\right)=850\left(1.025\right)^x$$  

Is the balance increasing or decreasing?

Fill in the Blank

Consider the given function that represents the population of town.

$$f\left(x\right)=22000\left(0.94\right)^x$$  

Is the population of the town increasing or decreasing?

Multiple Choice

A small private school with a graduating class of 40 students in the year 2019 predicts that its graduating class will increase by 5% each year.

What function best represents this situation?

• $$f\left(x\right)=40\left(0.95\right)^x$$  

• $$f\left(x\right)=40\left(1.05\right)^x$$  

• $$f\left(x\right)=5\left(0.60\right)^x$$  

• $$f\left(x\right)=5\left(1.40\right)^x$$  

Multiple Choice

The value of a new video game is $40. The value is expected to decrease by 5% each year.

What function best represents this situation?

• $$f\left(x\right)=40\left(0.95\right)^x$$  

• $$f\left(x\right)=40\left(1.05\right)^x$$  

• $$f\left(x\right)=5\left(0.60\right)^x$$  

• $$f\left(x\right)=5\left(1.40\right)^x$$  

Multiple Choice

Which function models this table?

• $$f\left(x\right)=2\cdot4^x$$

• $$f\left(x\right)=4^x$$

• $$f\left(x\right)=4\cdot2^x$$

• $$f\left(x\right)=8^x$$

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

• The number of elephants was 1,015 in 1975.
• The number of elephants increases by 1.5% each year.
• The number of elephants increases by 101.5% each year.
• The number of elephants is multiplied by 1.015 each year.

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

• The predicted increase in number of elephants in the refuge each year.
• The predicted decrease in number of elephants in the refuge each year.
• The number of years it will take for the elephant population to stop increasing.
• The initial amount of elephants in the park.

Multiple Choice

A tennis tournament begins with 128 players. At the end of round one, there will be 64 players. There are 32 players at the end of round 2 and 16 players remaining after round 3. Write the equation that best models this situation.

• y = -64x + 128

• y = 0.5x + 128

• y = 128(0.5)^x

• y = 128(2)^x

Multiple Choice

Write an exponential function to model the situation. Solve.
2) The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. What will the cost be after 4 years?

• C(t) = 12000(1.06)^t ; $3149.72
• C(t) = 12000(.06)^t ; $3149.72
• C(t) = 12000(.06)^t ; $1472.95
• C(t) = 12000(1.06)^t ; $15149.72

Multiple Choice

Use the function $$m\left(t\right)=.05\left(2\right)^t$$  where M is the amount of money you have after t days.

How much money will you have after 14 days?

• $ 819.20

• $ 1.4

• $ 140

Multiple Choice

In an exponential function, what does the 'a' represent?

• Input

• Rate of change

• Y-intercept/Initial value

• Output

Multiple Choice

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

• f(x)=400(.97)^x
• f(x)=400(1-0.03)^x
• f(x)=400(1.03)^x
• f(x)=400(0.03)^x

Multiple Choice

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

• y=8(15,000)^x
• y=15,000(1.08)^x
• y=15,000(0.92)^x
• y=15,000(0.08)^x

Multiple Choice

What is a, the initial amount, for the function: f(x) = 300(1.16)^x?

• 300
• 1.16
• .16
• x

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 180 pages. 

• 12 chapters
• 15 chapters
• 18 chapters
• 21 chapters

Multiple Choice

Which of the following could be a possible line of best fit for the data?

• y = -5/2x + 20
• y = -x + 19
• y = x + 20
• y = 2/3x + 15 

Multiple Choice

What is the correlation?

• Negative correlation
• No correlation
• Positive correlation
• All of the above

Multiple Choice

Describe the correlation in the graph shown.

• Strong Negative
• Strong Positive
• Weak Negative
• Weak Positive

Multiple Choice

Describe the correlation in the graph shown.

• Weak Negative
• Weak Positive
• Strong Negative
• Strong Positive

Multiple Choice

Describe a correlation with a coefficient of r=-0.89

• Strong positive

• Weak positive

• Strong negative

• Weak negative

Multiple Choice

Describe a correlation with a coefficient of r=0.3

• Strong positive

• Weak positive

• Strong negative

• Weak negative

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Multiple Choice

Describe a correlation with a coefficient of $$r=.92$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = 1.2

• B) r = 0.89

• C)r = 0

• D) r = -0.89

Multiple Choice

Determine the Correlation Coefficient and decide whether it is weak, moderate, or strong.

• -0.19 weak
• -0.19 moderate
• 0.04 weak
• 0.04 strong

Multiple Choice

Find the equation of the line of best fit for this table.

• y = -0.18x + 6.47
• y = 6.47x - 0.18
• y = 0.04x - 0.19
• y = -0.18x - 0.19

Multiple Choice

Find the equation of the line of best fit for this table.

• y = -2.28x + 51.08
• y = 51.08x - 2.28
• y = 0.06x - 0.26
• y = -2.28x - 0.26

Multiple Choice

What is the line of best fit?

• f(x)= 5x+1.82
• cannot be determined
• f(x)= 1.82x + 5.02
• f(x)= 1.1x + 4.2

Multiple Choice

Rewrite in Vertex Form: $$f\left(x\right)=x^2-8x+17$$  

• $$f\left(x\right)=\left(x-4\right)^2-1$$  

• $$f\left(x\right)=\left(x-8\right)^2-1$$  

• $$f\left(x\right)=\left(x-4\right)^2+17$$  

• $$f\left(x\right)=\left(x-4\right)^2+1$$  

Multiple Choice

Solve using the Quadratic Formula:    $$x^2+12x+4=0$$  

• $$x\ =\ 6\pm8\sqrt{2}$$  

• $$x=-12\pm8\sqrt{2}$$  

• $$x=-6\pm4\sqrt{2}$$  

• $$x=-12\pm2\sqrt{8}$$  

Multiple Select

What score are you trying to make on the Algebra 1 LEAP test?

Choose the 2 BEST answers!

• Approaching Basic

• Basic

• Mastery

• Advanced