Linear Legends Worksheet Regents Raid
Sheet 1: Linear Legends
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Date:
Instructions: Answer all 10 multiple-choice questions. For each question, choose the best response. These questions are modeled after NYS Algebra I Regents standards and focus on Linear Equations, Inequalities, and Systems.
1
Which value of \(x\) is the solution to the equation \(3(x - 4) + 2x = 8x - 3\)?
1 \(-3\)
2 \(-5\)
3 \(3\)
4 \(5\)
2
Given the inequality \(2x + 5 < 5x - 4\), which is the smallest integer in the solution set?
1 \(2\)
2 \(3\)
3 \(4\)
4 \(5\)
3
What is the slope of the line that passes through the points \((2, -3)\) and \((-1, 6)\)?
1 \(3\)
2 \(-3\)
3 \(\frac{1}{3}\)
4 \(-\frac{1}{3}\)
4
The equation \(V = \frac{1}{3}\pi r^2 h\) represents the volume of a cone. Which equation correctly solves for \(h\) in terms of \(V\), \(\pi\), and \(r\)?
1 \(h = \frac{3V}{\pi r^2}\)
2 \(h = \frac{V}{3\pi r^2}\)
3 \(h = 3V - \pi r^2\)
4 \(h = \frac{\pi r^2}{3V}\)
5
A system of equations is shown below. What is the value of \(y\) in the solution to the system? \[x + y = 10\] \[2x - y = 8\]
1 \(6\)
2 \(4\)
3 \(2\)
4 \(18\)
6
Which table represents a linear function?
(1)
(2)
(3)
(4)
7
The cost of a car rental is \(C = 0.25m + 40\), where \(m\) is the number of miles driven and \(40\) is the daily fee. What does the \(0.25\) represent?
1 The total cost of the rental
2 The fixed daily fee
3 The cost per mile driven
4 The number of miles driven
8
Which graph represents the solution to the inequality \(y < 2x - 3\)?
(1) Dotted line, shaded above
(2) Solid line, shaded above
(3) Dotted line, shaded below
(4) Solid line, shaded below
9
If \(f(x) = 2x + 1\), what is the range for the domain \(\{-2, 0, 2\}\)?
1 \(\{-3, 1, 5\}\)
2 \(\{-5, 1, 5\}\)
3 \(\{-3, 0, 5\}\)
4 \(\{-4, 0, 4\}\)
10
The sequence \(5, 8, 11, 14, ...\) can be represented by which explicit formula?
1 \(a_n = 3n + 5\)
2 \(a_n = 3n + 2\)
3 \(a_n = 5n + 3\)
4 \(a_n = 3n - 2\)
Quadratic Quest Worksheet Regents Raid
Sheet 2: Quadratic Quest
Name:
Date:
Instructions: Answer all 10 multiple-choice questions. For each question, choose the best response. These questions focus on Quadratic Functions, Factoring, and Parabolas.
1
What are the zeroes of the function \(f(x) = x^2 - 7x + 10\)?
1 \(2\) and \(5\)
2 \(-2\) and \(-5\)
3 \(2\) and \(-5\)
4 \(-2\) and \(5\)
2
Which equation represents a parabola that has a vertex at \((3, -4)\)?
1 \(y = (x + 3)^2 - 4\)
2 \(y = (x - 3)^2 - 4\)
3 \(y = (x - 3)^2 + 4\)
4 \(y = (x + 3)^2 + 4\)
3
The height of a rocket is modeled by \(h(t) = -16t^2 + 64t + 80\). At what time, in seconds, does the rocket reach its maximum height?
1 \(2\)
2 \(4\)
3 \(5\)
4 \(144\)
4
What are the solutions to the equation \(x^2 + 6x = 10\)?
1 \(-3 \pm \sqrt{19}\)
2 \(3 \pm \sqrt{19}\)
3 \(-3 \pm \sqrt{1}\)
4 \(-6 \pm \sqrt{10}\)
5
Which expression is equivalent to \(2x^2 - 50\)?
1 \(2(x - 5)(x - 5)\)
2 \(2(x - 5)(x + 5)\)
3 \(2(x - 25)(x + 25)\)
4 \((2x - 10)(x + 5)\)
6
The function \(g(x)\) is defined as \(g(x) = (x - 2)^2 - 3\). If \(f(x) = x^2\), which transformation describes how \(g(x)\) is obtained from \(f(x)\)?
1 Left 2, down 3
2 Right 2, down 3
3 Left 2, up 3
4 Right 2, up 3
7
Which value is the constant term needed to complete the square for \(x^2 + 12x + \dots\)?
1 \(6\)
2 \(12\)
3 \(36\)
4 \(144\)
8
A quadratic function has zeroes at \(-3\) and \(5\). Which could be the equation for the axis of symmetry?
1 \(x = 1\)
2 \(x = 2\)
3 \(x = 4\)
4 \(x = -1\)
9
What is the average rate of change for the function \(f(x) = x^2 - 2x\) over the interval \([1, 4]\)?
1 \(3\)
2 \(9\)
3 \(-3\)
4 \(5\)
10
How many real solutions does the equation \(2x^2 + 3x + 5 = 0\) have?
1 None
2 One
Exponential Escape Worksheet Regents Raid
Sheet 3: Exponential Escape
Name:
Date:
Instructions: Answer all 10 multiple-choice questions. choose the best response. These questions cover Exponentials, Growth and Decay, and Geometric Sequences.
1
Which function represents exponential decay?
1 \(f(x) = 5(1.2)^x\)
2 \(f(x) = 1.2(5)^x\)
3 \(f(x) = 100(0.9)^x\)
4 \(f(x) = 0.9(100)^x\)
2
The population of a town is 5,000 and is increasing at a rate of 3% per year. Which equation can be used to find the population after \(t\) years?
1 \(P = 5000(1.3)^t\)
2 \(P = 5000(1.03)^t\)
3 \(P = 5000(0.97)^t\)
4 \(P = 5000(0.03)^t\)
3
What is the common ratio for the geometric sequence \(81, 27, 9, 3, ...\)?
1 \(3\)
2 \(-3\)
3 \(\frac{1}{3}\)
4 \(-\frac{1}{3}\)
4
The expression \(2000(1.05)^t\) represents the value of an investment. What is the annual interest rate?
1 \(1.05\%\)
2 \(5\%\)
3 \(0.05\%\)
4 \(50\%\)
5
If \(a_1 = 4\) and \(a_n = 3 \cdot a_{n-1}\), what is the value of \(a_3\)?
1 \(12\)
2 \(36\)
3 \(108\)
4 \(7\)
6
Which table shows exponential growth?
(1)
(2)
(3)
(4)
Function Frenzy Worksheet Regents Raid
Sheet 4: Function Frenzy
Name:
Date:
Instructions: Answer all 10 multiple-choice questions. choose the best response. These questions cover transformations, absolute value, square roots, and piecewise functions.
1
If \(f(x) = |x|\), which equation represents \(f(x)\) shifted 4 units down and 2 units to the right?
1 \(y = |x - 2| - 4\)
2 \(y = |x + 2| - 4\)
3 \(y = |x - 4| + 2\)
4 \(y = |x - 2| + 4\)
2
What is the domain of the function \(g(x) = \sqrt{x - 5}\)?
1 \(x \geq 0\)
2 \(x \leq 5\)
3 \(x \geq 5\)
4 All real numbers
3
The piecewise function \(f(x)\) is defined as: \[f(x) = \begin{cases} 2x + 1 & x < 3 \\ x^2 - 4 & x \geq 3 \end{cases}\] What is the value of \(f(3)\)?
1 \(7\)
2 \(5\)
3 \(13\)
4 \(0\)
4
Which graph represents the function \(y = |x + 3|\)?
(1) V-shape vertex at (3, 0)
(2) V-shape vertex at (-3, 0)
(3) V-shape vertex at (0, 3)
(4) V-shape vertex at (0, -3)
5
If \(h(x) = \sqrt[3]{x}\), which is true about its domain?
1 Only positive numbers
2 Only non-negative numbers
3 All real numbers
4 Numbers greater than or equal to 1
6
The function \(f(x)\) is shown in the table. Which equation represents \(g(x) = f(x) + 2\)?
1 \(g(1) = 7, g(2) = 10, g(3) = 13\)
2 \(g(3) = 5, g(4) = 8, g(5) = 11\)
3 \(g(1) = 3, g(2) = 6, g(3) = 9\)
4 \(g(1) = 10, g(2) = 16, g(3) = 22\)
7
Which type of function is \(y = 3^x + 5\)?
1 Linear
2 Quadratic
3 Exponential
4 Absolute Value
8
A step function represents the cost of parking. If it costs $5 for up to 1 hour, and $2 for each additional hour, how much does it cost to park for 2.5 hours?
1 $7
2 $9
3 $11
4 $8
9
The zeroes of a function are \(-2, 0,\) and \(4\). Which could be the factors of the function?
Statistical Showdown Worksheet Regents Raid
Sheet 5: Statistical Showdown
Name:
Date:
Instructions: Answer all 10 multiple-choice questions. choose the best response. These questions cover Statistics, Data Plots, Correlation, and Residuals.
1
In a box plot, which feature represents the median of the data?
1 The left edge of the box
2 The right edge of the box
3 The line inside the box
4 The whiskers
2
Which correlation coefficient indicates the strongest relationship between two variables?
1 \(0.85\)
2 \(-0.92\)
3 \(0.10\)
4 \(-0.15\)
3
A residual plot shows points randomly scattered above and below the x-axis. What does this suggest about the linear model?
1 A linear model is appropriate.
2 A linear model is NOT appropriate.
3 The data is exponential.
4 The correlation is exactly 1.
4
A set of test scores is \(\{70, 75, 80, 85, 90\}\). If a score of \(20\) is added to the set, which statistic will change the most?
1 Mean
2 Median
3 Mode
4 The statistics stay the same.
5
Which scenario describes a causal relationship?
1 The number of ice cream cones sold and the number of shark attacks.
2 The hours spent studying and the score on a test.
3 The amount of exercise and the amount of calories burned.
4 The height of a child and the size of their shoes.
6
The Interquartile Range (IQR) of a data set is calculated by:
1 Maximum - Minimum
2 \(Q3 - Q1\)
3 Mean - Median
4 \(Q2 - Q1\)
7
A frequency table for favorite pets is shown. What is the joint frequency for "Boys" who like "Dogs"?
Dogs Cats Total Boys 15 5 20 Girls 10 20 30
1 \(15\)
2 \(20\)
3 \(5\)
4 \(25\)
8
The line of best fit for a data set is \(y = -2.5x + 100\). What does the slope represent?
1 The starting value of y is 100.
Regents Raid Answer Key Regents Raid
Master Answer Key
Sheet 1: Linear Legends
1. Choice (1)-3
2. Choice (3)4
3. Choice (2)-3
4. Choice (1)h = 3V/πr²
5. Choice (2)4
6. Choice (2)Table 2
7. Choice (3)Cost/mile
8. Choice (3)Dotted, Below
9. Choice (1){-3, 1, 5}
10. Choice (2)an = 3n + 2
Sheet 2: Quadratic Quest
1. Choice (1)2 and 5
2. Choice (2)y = (x-3)² - 4
3. Choice (1)2
4. Choice (1)-3 ± √19
5. Choice (2)2(x-5)(x+5)
6. Choice (2)Right 2, Down 3
7. Choice (3)36
8. Choice (1)x = 1
9. Choice (1)3
10. Choice (1)None
Sheet 3: Exponential Escape
1. Choice (3)f(x) = 100(0.9)ˣ
2. Choice (2)5000(1.03)ᵗ
3. Choice (3)1/3
4. Choice (2)5%
5. Choice (2)36
6. Choice (2)Table 2
7. Choice (3)7
8. Choice (2)80
9. Choice (3)x > 3
10. Choice (2)100(0.5)^(d/10)
Sheet 4: Function Frenzy
1. Choice (1)|x-2|-4
2. Choice (3)x ≥ 5
3. Choice (2)5
4. Choice (2)Vertex (-3,0)
5. Choice (3)All real
6. Choice (1){7, 10, 13}
7. Choice (3)Exponential
8. Choice (2)$9
9. Choice (2)(x+2)x(x-4)
10. Choice (1)Reflection (x)
Sheet 5: Statistical Showdown
1. Choice (3)Median Line
2. Choice (2)-0.92
3. Choice (1)Appropriate
4. Choice (1)Mean
5. Choice (3)Ex/Calorie
6. Choice (2)Q3 - Q1
7. Choice (1)15
8. Choice (3)y decreases
9. Choice (1)Range
10. Choice (1)B more spread
