3rd Nine Weeks Math Benchmark

3rd Nine Weeks Math Benchmark

Practice for the upcoming benchmark.

Reminders:

A line has 180º.

A triangle also has 180º.

Unit Rate

• Unit rate is over one

• Ex: The unit rate represents the cost per 1 pound.

Can you write the equation?

• Can you find the slope?

• Find the slope by using rise over run.

• Can you find the y-intercept?

• The y-intercept is not given, so you can use the slope to extend the line until it touches the y-axis.

What are the Types of Solutions?

• No Solution

• One Solution

• Infinitely Many Solutions

Plugging in

• If a question gives you an equation and a number, plug the number in.

• Remember: if you plug in, you must use parentheses.

System of Equations

The solution to a system of equations MUST make BOTH statements TRUE.

Multiple Choice

Consider the system of equations.

$$y=-4x+7$$  

$$y=-\frac{2}{3}x+2$$  

What is the solution to the system of equations?

• $$\left(1,\ \frac{3}{2}\right)$$  

• $$\left(1,3\right)$$  

• $$\left(\frac{3}{2},\ 1\right)$$  

• $$\left(3,0\right)$$  

Multiple Choice

Which graph represents the linear equation $$y=-\frac{1}{2}x+8$$  ?

• A

• B

• C

• D

Multiple Choice

The distance around the Earth at the equator is approximately 40,075,000 km. What is this estimated distance in scientific notation?

• $$4.01\times10^{-8}km$$  

• $$4.01\times10^{-7}km$$  

• $$4.01\times10^8km$$  

• $$4.01\times10^7km$$  

Multiple Choice

The graph of the linear function passes through points $$\left(2,-5\right)\ and\ \left(3,7\right)$$  . What is the rate of change of the function?

• -12

• $$-\frac{12}{19}$$  

• $$\frac{12}{19}$$  

• 12

Multiple Choice

Which fraction is equivalent to $$0.91\overline{6}$$  

• $$\frac{11}{12}$$  

• $$\frac{17}{19}$$  

• $$\frac{13}{19}$$  

• $$\frac{12}{17}$$  

Multiple Select

Which two equations are true?

$$A.\ \left(6\times10^2\right)\cdot\left(1.5\times10^{-4}\right)=9\times10^{-8}$$  

$$B.\ \left(6\times10^2\right)\div\left(1.5\times10^{-4}\right)=4\times10^6$$  

$$C.\ \left(6\times10^{-2}\right)\cdot\left(1.5\times10^4\right)=9\times10^2$$

$$D.\ \left(6\times10^{-2}\right)\div\left(1.5\times10^4\right)=4\times10^2$$  

$$E.\ \left(6\times10^{-2}\right)\cdot\left(1.5\times10^4\right)=4\times10^6$$   

• A

• B

• C

• D

• E

Multiple Choice

A convenience store sells 30 small bottles and 45 large bottles of soda. The store sells 22 bottles of grape soda, 30 bottles of orange soda, and 23 bottles of lemon-lime soda.

Which two-way frequency table represents the data?

Multiple Choice

Which function is linear?

• A

• B

• C

• D

Multiple Choice

Consider the line on the graph.

Which equation represents the linear relationship shown by the graph?

• $$y=-3x+5$$  

• $$y=-\frac{1}{3}x+5$$  

• $$y=3x+5$$  

• $$y=\frac{1}{3}x+5$$  

Multiple Choice

The equation v=3.2t+8 represents the velocity, v, of an object under a constant acceleration after a certain number of seconds, t. What is the meaning of the v-intercept?

***What letters could you change v and t to instead?

• The acceleration at t=0

• the initial velocity at t=0

• the time t

• the velocity at time t

Multiple Choice

What is the value of $$\frac{2\cdot4^0\cdot6^2}{2^4\cdot4^{-1}\cdot6^1}$$   when simplified?

• $$\frac{1}{3}$$  

• 2

• $$\frac{8}{3}$$  

• 3

Multiple Choice

What is the solution to the equation $$\frac{3}{4}\left(8x-4\right)=7x+2$$  

• -6

• -5

• -2

• -1

Multiple Choice

Which equation represents a nonlinear function?

• $$y=+2\left(x-1\right)^2+6$$  

• $$y=-\frac{3}{2}\left(x+3\right)-4$$  

• $$y=\frac{4}{5}x-11$$  

• $$4y-8x=16$$  

Multiple Choice

Consider the scatter plot?

Which best describes the linear function that is a line-of-best fit for the data in the scatter plot?

• The line goes through the first and last points.

• The line goes through ever single point.

• The line is above all points in the scatter plot.

• The line minimizes the distance to each point.

Multiple Choice

Consider the graph.

Which equation represents a proportional relationship with the same slope as the graph?

• $$y=\frac{1}{10}x$$  

• $$y=\frac{1}{10}+x$$  

• $$y=10x$$  

• $$y=10+x$$  

Multiple Choice

A student graphs points on the coordinate plane.

$$\left(7,-9\right),\left(-4,10\right),\left(13,0\right),\left(6,10\right),\left(-9,0\right),\left(-4,1\right)$$  

• $$\left(-4,10\right)$$  

• $$\left(7,-9\right)$$  

• $$\left(13,0\right)$$  

• $$\left(-9,0\right)$$  

Multiple Choice

Consider the system of equations.

What is the solution of the system of equations?

• $$\left(-5,-3\right)$$  

• $$\left(-5,3\right)$$  

• $$\left(-3,-5\right)$$  

• $$\left(-3,5\right)$$  

Multiple Choice

Which statement best describes the equation

$$-2\left(2x-4\right)=16-4\left(3+x\right)$$  

• The equation has infinitely many solutions.

• The equation has no solution.

• The equation has one solution at $$x=0$$  .

• The equation has one solution at $$x=-4$$  .

Multiple Choice

Which expression is equivalent to $$5^{-3}$$  

• $$\frac{1}{25}$$  

• $$\frac{1}{15}$$  

• $$5\cdot5\cdot5^{-5}$$  

• $$-5\cdot-5\cdot-5$$  

Multiple Select

Consider the equations.

For which two equations is $$x=4$$  a solution?

• Equation 1

• Equation 2

• Equation 3

• Equation 4

• Equation 5

Multiple Choice

The height of a 7-inch candle decreases by 2 inches every hour after being lit.

• The graph is linear and decreasing.

• The graph is linear and increasing.

• The graph is nonlinear and decreasing.

• The graph is nonlinear and increasing.

Multiple Choice

Pizzeria 1 and Pizzeria 2 each charge a bas fee for a cheeses pizza plus an additional charge per topping. The equation $$C=0.75t+5.99$$  represents the cost, C for t toppings at Pizzeria 1. The tables shows the costs of pizzas with different amounts of toppings at Pizzeria 2.

Which pizzeria charges more for a 5-topping pizza and by how much?

• Pizzeria 1 charges more than Pizzeria 2 by $0.15.

• Pizzeria 1 charges more than Pizzeria 2 by $0.65.

• Pizzeria 2 charges more than Pizzeria 1 by $0.15.

• Pizzeria 2 charges more than Pizzeria 1 by $0.65.

Multiple Choice

The table shows the number of students who wear green on St. Patrick's Day.

Approximately what percentage of students do not wear green?

• 35% 

• 55% 

• 65%

• 74%

Multiple Select

Consider the values.

$$\left(2+\pi\right),\ 2\pi,\ 3\sqrt[]{2},\ 3\pi,\ \sqrt[]{40}$$   

Which two values are between 6 and 7 on a number?

• $$\left(2+\pi\right)$$  

•   $$2\pi$$  

• $$3\sqrt[]{2}$$  

• $$3\pi$$  

• $$\sqrt[]{40}$$