SAT Desmos calculator strategies flashcards

Graph a linear function in Desmos.

Enter the equation in the format y = mx + b. E.g., y = 2x + 3.

True or False: Desmos can graph complex functions.

True - It can handle polynomials, rationals, and more!

Identify the vertex of y = (x - 2)^2 - 5.

Vertex: (2, -5). This is a parabola opening upwards.

Fill in the blank: The ____ of a function is where it crosses the y-axis.

y-intercept

Example of a quadratic function.

y = x^2 - 4x + 4. This factors to (x-2)^2.

Graphing y = |x| in Desmos results in a ____ shape.

V-shape. It reflects across the y-axis.

Find the x-intercepts of y = x^2 - 4.

Set y = 0: x^2 - 4 = 0. Roots: x = 2 and x = -2.

True or False: You can adjust graph settings in Desmos.

True - Adjust axes, colors, and labels easily.

Compare: Linear vs. Quadratic functions.

Linear: Straight line, form y = mx + b. Quadratic: Parabola, form y = ax^2 + bx + c.

Graphing y = 3x + 1, what is the slope?

Slope: 3. Rise over run is 3/1.

Desmos allows you to add ____ for better graph analysis.

Tables of values to view points.

Find the range of y = -x^2 + 4.

Range: y ≤ 4. Maximum value at vertex (0, 4).

What does the 'zoom' feature in Desmos do?

Adjusts the view of the graph to fit all plotted points.

Identify the type of function: y = x^3 - 3x.

Cubic function - has one inflection point.

How to graph y = sin(x) in Desmos?

Just enter y = sin(x) and observe the wave pattern.

Example of transformation: y = (x - 2)^2 + 3.

Shifted 2 units right, 3 units up.

What is the significance of asymptotes?

Lines that the graph approaches but never touches.

Fill in the blank: The ____ of a function indicates its steepness.

Slope

Graph y = -2|x| + 5. What is its maximum?

Maximum value: 5 at x = 0.

What does it mean for a function to be increasing?

As x increases, y also increases over an interval.

Equation solving technique using Desmos?

Use the 'y=' feature to enter equations, find intersections, and visualize solutions.

True or False: Desmos can solve equations automatically.

False. Desmos visualizes, but manual analysis is often needed to interpret solutions.

Fill in the blank: To solve for x, isolate x on one side of the equation, e.g., $\displaystyle x + 5 = 12$ leads to \displaystyle x = ____.

7

What do you do with $\displaystyle 2x + 3 = 11$?

Subtract 3: $\displaystyle 2x = 8$, then divide by 2: $\displaystyle x = 4$.

Comparison: Graphing $\displaystyle y = 3x + 2$ vs. $\displaystyle y = 5$.

First graph is a line; second is horizontal. Intersection shows solution.

Solve: $\displaystyle 3(x - 1) = 6$.

Distribute: $\displaystyle 3x - 3 = 6$. Add 3: $\displaystyle 3x = 9$. Divide: $\displaystyle x = 3$.

Inequality example: Solve and graph $\displaystyle x - 4 < 2$.

Add 4: $\displaystyle x < 6$. Shade left of 6 on the number line.

What does Desmos show for $\displaystyle x^2 - 4 = 0$?

It helps find roots at $\displaystyle x = -2$ and $\displaystyle x = 2$ through intersection points.

Solve for y: $\displaystyle 2y + 3 = 11$.

Subtract 3: $\displaystyle 2y = 8$. Divide by 2: $\displaystyle y = 4$.

Cause → Effect: Why simplify before solving?

It makes equations easier to manipulate. Less complexity leads to quicker solutions.

True or False: An equation has at most one solution.

False. Equations can have zero, one, or infinite solutions depending on their form.

Example: Solve $\displaystyle x^2 = 16$.

Find roots: $\displaystyle x = 4$ or $\displaystyle x = -4$. Use Desmos for visual verification.

Find x: $\displaystyle 5x + 10 = 0$.

Subtract 10: $\displaystyle 5x = -10$. Divide by 5: $\displaystyle x = -2$.

Graphing $\displaystyle y = 2x + 1$ and $\displaystyle y = 5$ shows?

Intersection at $\displaystyle x = 2$; solution is $\displaystyle (2, 5)$.

Solve $\displaystyle 4(x - 2) = 8$.

Distribute: $\displaystyle 4x - 8 = 8$. Add 8: $\displaystyle 4x = 16$. Divide: $\displaystyle x = 4$.

What does $\displaystyle 3x + 4 < 10$ simplify to?

Subtract 4: $\displaystyle 3x < 6$. Divide by 3: $\displaystyle x < 2$.

Fill in the blank: For $\displaystyle 2(x + 3) = 12$, $\displaystyle x$ equals ____.

3

Solve: $\displaystyle x^2 - 5x + 6 = 0$.

Factor: $\displaystyle (x-2)(x-3) = 0$. Solutions: $\displaystyle x = 2$, $\displaystyle x = 3$.

What happens if $\displaystyle x + 2 = 5$?

Subtract 2: $\displaystyle x = 3$. Verify with Desmos by checking intersection.

Use Desmos to check solutions: $\displaystyle x + 3 = 10$?

Input $\displaystyle x + 3 = 10$ into Desmos. The graph shows where the line intersects the x-axis. The solution is $\displaystyle x = 7$. This verifies your answer visually.

Mean vs. Median: What's the difference?

Mean is the average of all values. Median is the middle value when sorted. If a dataset has outliers, mean can be skewed while median remains stable.

Calculate the mean: 5, 10, 15, 20.

Mean = (5 + 10 + 15 + 20) / 4 = 12.5.

True or False: Median is affected by outliers.

False. Median remains unaffected by extreme values, making it a better measure of central tendency in skewed distributions.

Standard deviation: Define it.

Standard deviation measures the dispersion of data points from the mean. A low standard deviation indicates data points are close to the mean.

Fill in the blank: The ___ is the value that separates the higher half from the lower half.

Median.

Use Desmos to find the median of: 3, 7, 8, 12, 14.

Input data into Desmos. The median is 8, as it is the middle number in the sorted list.

Calculate the standard deviation for: 2, 4, 4, 4, 5, 5, 7, 9.

Mean = 5; Variance = 4; Standard deviation = 2. Use Desmos to visualize this.

True or False: The mean is always greater than the median.

False. In a skewed left dataset, mean can be less than median.

What is the interquartile range (IQR)?

IQR is the difference between the first (Q1) and third quartiles (Q3). It measures the middle 50% of data, reducing the influence of outliers.

Real-life example: Analyzing test scores.

Scores: 70, 75, 80, 85, 90. Mean = 80, Median = 80. Use Desmos to visualize the distribution.

Calculate Q1 and Q3 for: 1, 3, 5, 7, 9.

Q1 = 3, Q3 = 7. Q1 is the median of the lower half, Q3 of the upper half.

Data set: 5, 7, 8, 12, 15. What is the mode?

Mode = 5, 7, 8, 12, 15. All values occur once, thus no mode.

Effect of outliers on mean.

Outliers can significantly raise or lower the mean, making it unrepresentative of the dataset. Use median for skewed data.

What does a standard deviation of 0 mean?

A standard deviation of 0 indicates all values in the dataset are identical and equal to the mean.

Use Desmos: Find the mean of 10, 20, 30, 40.

Mean = (10 + 20 + 30 + 40) / 4 = 25.

Identify the outlier in: 1, 2, 2, 3, 100.

Outlier = 100. It significantly deviates from the other values.

Variance vs. Standard Deviation: Explain.

Variance is the average of squared differences from the mean. Standard deviation is the square root of variance.

What do you use to analyze data trends?

Desmos can plot data and help visualize trends, including means and standard deviations.

Five-number summary: What does it include?

Minimum, Q1, Median, Q3, Maximum. Provides a quick overview of the distribution of a dataset.

Calculate the median for: 2, 3, 9, 10, 12.

Median = 9, the middle value when sorted.

John buys 5 shirts for $20 each. Total cost?

Total cost = $\displaystyle 20 × 5 =$100.

True or False: Desmos can solve systems of equations.

True - You can input equations and use the intersection point.

A car travels 60 miles at 30 miles/hour. Time taken?

Time = Distance ÷ Speed = 60 ÷ 30 = 2 hours.

Fill in the blank: The slope of a line represents _____.

The rate of change.

Comparison: Direct Variation vs. Inverse Variation.

Direct: $\displaystyle y = kx$. Inverse: $\displaystyle y = \frac{k}{x}$.

A store has a sale: $\displaystyle 30 off$150. New price?

New price = $\displaystyle 150 -$30 = $120.

True or False: Desmos can create tables for data.

True - You can input data points and visualize them.

Samantha saves $200 monthly. How much in 6 months?

$\displaystyle 200 × 6 =$1200 saved.

Solve: 3x + 5 = 20. What is x?

x = (20 - 5) ÷ 3 = 5.

A recipe requires 2 cups of sugar for 4 servings. For 10 servings?

Sugar needed = $\displaystyle \frac{2}{4} imes 10 = 5$ cups.

Calculate the average speed: 120 miles in 2 hours.

Average speed = Distance ÷ Time = 120 ÷ 2 = 60 mph.

If rent is $1200 yearly, monthly rent?

Monthly rent = $\displaystyle \frac{1200}{12} = 100$.

True or False: You can use Desmos to find the max of a function.

True - Use the 'maximum' feature in Desmos.

A phone plan costs $\displaystyle 50/month plus$0.10/min. Cost for 200 min?

Total cost = $\displaystyle 50 + (200 × 0.10) =$70.

True or False: The y-intercept is where x = 0.

True - This is where the line crosses the y-axis.

A train travels at 80 mph for 3 hours. Distance covered?

Distance = Speed × Time = 80 × 3 = 240 miles.

A pizza costs $\displaystyle 15 plus$2 for each topping. Cost for 3 toppings?

Total cost = $\displaystyle 15 + (3 ×$2) = $21.

How to input a polynomial in Desmos?

Use format: $\displaystyle f(x) = ax^2 + bx + c$.

Fill in the blank: The break-even point occurs when _____.

Total revenue = Total cost.

Maria buys x books at $12 each. Total cost?

Use Desmos: Enter y = 12x. - Input x for number of books. - Evaluate y for total cost. Example: For 4 books, y = 12(4) = $48.