Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
, BA-Mathematics
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Get ready to ace your Algebra 1 EOC with our comprehensive practice test! Designed to sharpen your algebraic skills, this practice test features a range of thought-provoking questions and in-depth answers to ensure you're fully prepared for the real exam.
Covering essential topics from linear equations and inequalities to functions and polynomials, this quiz is the ultimate tool for assessing your algebraic prowess. Delve into a series of challenging problems that mirror the complexity and format of the actual Algebra 1 EOC exam.
Whether you're a student striving for excellence or an educator looking for effective test preparation resources, this Read morepractice test offers an invaluable learning experience. Strengthen your understanding of fundamental algebraic concepts, master problem-solving strategies, and gain the confidence needed to excel on exam day.
Navigate through the intricacies of expressions, equations, and graphing with precision, all while honing your time management skills. Each question is accompanied by detailed explanations of the solutions, allowing you to not only gauge your performance but also grasp the underlying principles. Don't leave your Algebra 1 EOC success to chance – practice, refine, and conquer the test with our meticulously crafted practice questions and comprehensive answers.
Algebra 1 EOC Practice Test Questions and Answers
1.
Daniel made a box-and-whisker plot of the ages of his cousins.
What is the median age of his cousins?
A.
24
B.
25
C.
27
D.
28
Correct Answer B. 25
Explanation The correct answer is 25 because the median age is the middle value when the ages are arranged in ascending order. Since there are four ages given, the median would be the average of the two middle values, which are 24 and 27. Adding them together and dividing by 2 gives us 25.
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2.
If the first Now = -9, which equation represents this sequence?
-9, -4, 1, 6, 11, ...
A.
Next = Now âˆ’ 5
B.
Next = Now + 5
C.
Next = 5 âˆ™ Now âˆ’ 1
D.
Next = 5 âˆ™ Now + 1
Correct Answer B. Next = Now + 5
Explanation The correct answer is Next = Now + 5. This equation represents the sequence because it shows that each subsequent term is obtained by adding 5 to the previous term. Starting with -9 and adding 5 repeatedly gives us the sequence -9, -4, 1, 6, 11, ...
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3.
What is the solution to the equation 3x + 5 = 2(x - 1) + 9?
A.
x = 2
B.
X = 3
C.
X = 4
D.
X = 5
Correct Answer B. X = 3
Explanation To solve the equation, first expand and simplify both sides: 3x + 5 = 2x - 2 + 9 => 3x + 5 = 2x + 7
Then, isolate the variable x on one side: => 3x - 2x = 7 - 5 => x = 2
It appears there was a mistake in my initial setup. The correct steps are: 3x + 5 = 2(x - 1) + 9 => 3x + 5 = 2x - 2 + 9 => 3x + 5 = 2x + 7 => 3x - 2x = 7 - 5 => x = 2
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4.
Given y=x^{2}, how would the graph of y=x^{2} -2 differ?
A.
It shifts 2 units up.
B.
It shifts 2 units down.
C.
It shifts 2 units left.
D.
It shifts 2 units right.
Correct Answer B. It shifts 2 units down.
Explanation The graph of y=x^2 - 2 would differ from y=x^2 by shifting 2 units down. This means that every point on the graph of y=x^2 - 2 would be 2 units lower than the corresponding point on the graph of y=x^2.
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5.
Given the following fractions:
Which group below has the fractions in order from least to greatest?
A.
3/5, 24/39, 18/29, 12/18, 3/4
B.
3/4, 3/5, 18/29, 24/39, 12/18
C.
3/5, 12/18, 24/39, 3/4, 18/29
D.
3/4, 3/5, 12/18, 18/29, 24/39
Correct Answer A. 3/5, 24/39, 18/29, 12/18, 3/4
Explanation The fractions are arranged in order from least to greatest based on their decimal equivalents. When converting the fractions to decimals, we get 0.6, 0.615, 0.621, 0.667, and 0.75. Therefore, the correct order from least to greatest is 3/5, 24/39, 18/29, 12/18, 3/4.
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6.
The automobile repair shop uses the following chart to determine the labor costs for each job.
Which function should the automobile repair shop use to determine the labor cost C for a job that takes h hours? Provided that the fixed amount is $15 per hour, and the additional cost is shown in the table.
A.
C = 15h
B.
C = 15+25(h-1)
C.
C = 15+20(h-1)
D.
C = 15+10(h-1)
Correct Answer B. C = 15+25(h-1)
7.
A survey was administered to 500 high school students to determine the type of music they preferred. The survey indicated that 22%prefer rock, 26% prefer hip hop, 29% prefer pop, and 23% selected “other.” Which representation best illustrates the number of students preferring each type of music?
A.
A
B.
B
C.
C
D.
D
Correct Answer B. B
Explanation Answer B best illustrates the number of students preferring each type of music. The pie chart in Answer B shows the percentage of students who prefer each type of music, with each section representing a different genre. This visual representation allows for a quick and clear understanding of the distribution of music preferences among the surveyed high school students.
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8.
What is the value of the numerical expression below?
A.
4
B.
6
C.
8
D.
10
Correct Answer A. 4
Explanation √16 = √42 = 4
24/3=8
Therefore, √16-23/8+23=4
In other words, the square root of 16 is 4. 2 to the power of 3 is 8. Then you will add and subtract from left to right. Thus, 4+8-8 = 4.
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9.
Aaron listed the ages of all of his family members as shown below.
10, 10, 10, 10, 10, 12, 14, 14, 15, 16, 50, 50, 51, 53, 80
What is the mean age of his family members?
A.
10
B.
14
C.
27
D.
70
Correct Answer C. 27
Explanation The mean age is calculated by summing up all the ages and dividing it by the total number of family members. In this case, the sum of all the ages is 10+10+10+10+10+12+14+14+15+16+50+50+51+53+80 =405. There are 15 family members listed. So, the mean age is 405/15 =27.
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10.
What is the product of the following expression?
2x(x^{2}+x-5)
A.
2x^{3}+x-5
B.
2x^{3}+2x-10
C.
2x^{3}+4x-5x
D.
2x^{3}+2x^{2}-10x
Correct Answer D. 2x^{3}+2x^{2}-10x
Explanation The product of the given expression can be found by multiplying the coefficients of the terms with the same degree of x. In this case, the expression is 2x3 + 2x - 10x. The product of this expression is D.
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11.
Beth and Jacob are graphing two equations on a coordinate grid. Beth has graphed the equation y = x^{2} + 1.
If Jacob graphs y = x^{2} + 3, where will his graph be in relation to the graph Beth made?
A.
2 units up
B.
3 units up
C.
2 units to the left
D.
3 units to the right
Correct Answer A. 2 units up
Explanation When comparing the equations y=x2+1 and y=x2+3, we can observe that both equations represent parabolas because they have the form y=ax2+c, where a represents the coefficient of the quadratic term and c represents the constant term.
The equation y=x2+1 represents a parabola that opens upwards and has its vertex at the point (0, 1) on the coordinate grid. This means that Beth's graph is shifted upward by 1 unit compared to the standard parabola 2y=x2.
Now, when Jacob graphs y=x2+3, the constant term in the equation is 3 instead of 1. This indicates that his graph will be vertically shifted upward by an additional 2 units compared to Beth's graph. Therefore, Jacob's graph will have its vertex at the point (0, 3) on the coordinate grid, 2 units higher than Beth's graph.
In summary, Jacob's graph y=x2+3 will be positioned above Beth's graph y=x2+1 at every point on the coordinate grid due to the vertical shift of 2 units upward.
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12.
A survey was taken asking participants their age and the number of minutes they exercise per week. The results of the survey are shown in the scatterplot below.
The data for people who are 30 to 39 years of age are not displayed. Based on the scatterplot, how many minutes would a 30- to 39-year-old person be expected to exercise?
A.
40-60 minutes
B.
60-80 minutes
C.
80-100 minutes
D.
100-120 minutes
Correct Answer C. 80-100 minutes
Explanation Based on the scatterplot, we can observe a general trend that as age increases, the number of minutes exercised per week tends to decrease. Since the data for people who are 30 to 39 years old are not displayed, we can estimate their expected exercise time by looking at the trend. The scatterplot shows that individuals in their 40s tend to exercise around 80-100 minutes per week. Therefore, it is reasonable to expect that a 30- to 39-year-old person would also exercise in a similar range, leading to the answer of 80-100 minutes.
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13.
Ben bought 8 notebooks for $24.50. Some of the notebooks were $2.50 each, and the others were $3.25 each. If X represents the number of least expensive notebooks, which equation can be used to find the number of least expensive notebooks purchased?
A.
$5.75(8 − x) = $24.50
B.
$2.50(x − 8) + $3.25x = $24.50
C.
$2.50x + $3.25(8 − x) = $24.50
D.
$2.50x + $3.25(x − 8) = $24.50
Correct Answer C. $2.50x + $3.25(8 − x) = $24.50
Explanation Let's use X to represent the number of least expensive notebooks (which cost $2.50 each).
The total cost of the $2.50 notebooks can be represented as 2.50X.
The total cost of the $3.25 notebooks (since there are 8 notebooks in total) can be represented as 3.25(8 - X) because the remaining notebooks are the more expensive ones.
Now, you know that the total cost of all the notebooks is $24.50. Therefore, you can set up the equation:
2.50X + 3.25(8 - X) = 24.50
This equation can be used to find the number of least expensive notebooks (X) purchased, as it represents the total cost of the notebooks.
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14.
The number 18 is 24% of which number?
A.
4.32
B.
75
C.
133 1/3
D.
432
Correct Answer B. 75
Explanation To find the number for which 18 is 24% of, you can set up an equation and solve for the unknown. Let's use N as the unknown number.
According to the question:
24% of N = 18
0.24 * N = 18
To solve for N, divide both sides by 0.24:
N = 18 / 0.24
N = 75
So, the number 18 is 24% of 75.
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15.
The graph of y = 2x - 4 is shown below.
If the slope of the line is doubled, the new equation is y = 4x -4. Which of these is a correct comparison?
A.
The x-intercept and y-intercept change.
B.
The x-intercept and y-intercept stay the same.
C.
The x-intercept changes, and the y-intercept is the same.
D.
The x-intercept is the same, and the y-intercept changes.
Correct Answer C. The x-intercept changes, and the y-intercept is the same.
Explanation When the slope of the line is doubled, the equation becomes y = 4x - 4. The x-intercept is the value of x when y is equal to zero. In the original equation y = 2x - 4, the x-intercept is x = 2. However, in the new equation y = 4x - 4, the x-intercept is x = 1. Therefore, the x-intercept changes. On the other hand, the y-intercept is the value of y when x is equal to zero. In both the original and new equations, the y-intercept remains the same at y = -4. Therefore, the correct comparison is that the x-intercept changes, and the y-intercept is the same.
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16.
The following line graph shows the test scores for 10 students on a unit exam.
Which shape most accurately describes these data?
A.
The data are skewed to the left.
B.
The data are skewed to the right.
C.
A bimodal or “U”-shaped curve
D.
A normal or “bell”-shaped curve
Correct Answer D. A normal or “bell”-shaped curve
Explanation The correct answer is a normal or "bell"-shaped curve. This is because a normal distribution is characterized by a symmetrical shape, with the majority of the data clustered around the mean and tapering off towards the tails. In a bell-shaped curve, the data is evenly distributed on both sides of the mean, indicating a balanced distribution of test scores among the students.
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17.
Mary would like to plant grass in her backyard. Her backyard is a rectangle that measures 10 yds by 8 yds. In the middle of her backyard is a circular swimming pool that has a diameter of 5 yds. What is the area to be planted with grass to the nearest tenth of a square yard?
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
Explanation The area to be planted with grass can be found by subtracting the area of the circular swimming pool from the total area of the rectangle. The area of the rectangle is calculated by multiplying the length and width, which gives us 10 yds * 8 yds = 80 yd2. The area of the circular swimming pool is calculated by using the formula for the area of a circle, which is π * (radius)2. The radius of the circular swimming pool is half of the diameter, so it is 5 yds / 2 = 2.5 yds. Plugging this into the formula, we get π * (2.5 yds)2 = 19.63 yd2. Subtracting this from the total area of the rectangle, we get 80 yd2 - 19.63 yd2 = 60.37 yd2. Rounding to the nearest tenth, the area to be planted with grass is approximately 60.4 yd2. Therefore, the correct answer is C.
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18.
What is the solution to the equation 3x - 7 = 20?
A.
X = 5
B.
X = 9
C.
X = 7
D.
X = 27
Correct Answer B. X = 9
Explanation To solve for x, add 7 to both sides of the equation:
3x - 7 + 7 = 20 + 7 3x = 27
Now, divide both sides by 3 to isolate x:
3x / 3 = 27 / 3 x = 9
So, the solution to the equation is x = 9.
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19.
What is the solution to the equation?
A.
-27
B.
-24
C.
-12
D.
-9
Correct Answer A. -27
Explanation The solution to the equation is -27. The solution to the equation is -27. This can be determined by solving the equation and finding the value that satisfies it. You will subtract 6 on both sides of the equation then multiply (3/2) (this is the reciprocal of 2/3) on both sides of the equation to get -27.
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20.
What is the mode of the data set displayed below?
A.
14
B.
48
C.
4 and 8
D.
14 and 48
Correct Answer D. 14 and 48
Explanation The mode of a data set is the value(s) that appear most frequently. In this case, the numbers 14 and 48 both appear five times, which is more than any other number in the data set. Therefore, the mode of the data set is 14 and 48.
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21.
Which number line below shows the set of numbers graphed correctly?
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
22.
What is true about the slope and y-intercept of the two equations below?
4x + 3y = 12
-8x + 6y = 6
A.
Same slope, same y-intercept
B.
Same slope, different y-intercept
C.
Different slope, same y-intercept
D.
Different slope, different y-intercept
Correct Answer D. Different slope, different y-intercept
Explanation The two equations have different slopes because the coefficients of x (-8 and 4) are different. They also have different y-intercepts because the constants on the right side of the equations (6 and 12) are different. Therefore, the correct answer is different slope, different y-intercept.
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23.
The diagram shows the outcomes of flipping a coin and rolling a die.
Which statement regarding the diagram is false?
A.
The probability of obtaining “H6” is 2 out of 12
B.
There are 12 possible outcomes in the sample space.
C.
The chance of flipping “heads” and rolling a “5” is 1 in 12.
D.
Flipping “tails” and rolling a “2” represents about 8% of the possible outcomes of the sample space.
Correct Answer A. The probability of obtaining “H6” is 2 out of 12
Explanation The probability of obtaining "H6" is not 2 out of 12. In the diagram, there are 2 possible outcomes for flipping a coin (H or T) and 6 possible outcomes for rolling a die (1, 2, 3, 4, 5, or 6). Therefore, the total number of possible outcomes is 2 * 6 = 12. However, "H6" is only one specific outcome out of these 12 possibilities, so the probability of obtaining "H6" is 1 out of 12, not 2 out of 12.
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24.
The population of a type of bacteria triples every minute. The chart below represents the population of bacteria after tminutes.
Which type of function represents the data?
A.
Linear
B.
Quadratic
C.
Exponential
D.
Absolute value
Correct Answer C. Exponential
Explanation The given information states that the population of bacteria triples every minute. This indicates exponential growth, as the population is increasing at an exponential rate. Exponential functions have a constant ratio of change, and in this case, the population is tripling every minute, which is a consistent rate of growth. Therefore, the correct answer is exponential.
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25.
What are the slope, m, and the y-intercept, b, of a line that passes through the points (âˆ’3, 1) and (7, âˆ’5)?
A.
A
B.
B
C.
C
D.
D
Correct Answer A. A
Explanation The slope, m, of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. In this case, the coordinates of the two points are (-3, 1) and (7, -5). Plugging these values into the formula, we get (1 - (-5)) / (-3 - 7) = 6 / (-10) = -3/5. Therefore, the slope, m, is -3/5. The y-intercept, b, can be found by substituting the slope, m, and the coordinates of one of the points into the equation y = mx + b. Using the point (-3, 1), we have 1 = (-3/5)(-3) + b. Simplifying this equation, we get 1 = 9/5 + b. Solving for b, we find b = -4/5. Therefore, the slope, m, is -3/5 and the y-intercept, b, is -4/5.
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26.
A.
A
B.
B
C.
C
D.
D
Correct Answer B. B
Explanation Set B is in order from least to greatest because the numbers are arranged in ascending order.
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27.
Which of these shows the following expression factored completely?
A.
(2x − 3) (x + 4)
B.
(6x + 9) (x − 4)
C.
3(2x − 3) (x + 4)
D.
3(2x + 3) (x − 4)
Correct Answer C. 3(2x − 3) (x + 4)
Explanation The expression 3(2x − 3) (x + 4) is the factored form of the given expression. It is factored completely because all the factors within the expression cannot be further simplified or factored.
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28.
A scatterplot is shown on the graph below.
Which of these could be a line of best fit?
A.
Y = x + 100
B.
Y = x − 100
C.
X = 100
D.
Y = 100
Correct Answer D. Y = 100
Explanation The line of best fit represents the trend or relationship between the variables in a scatterplot. In this case, the line y = 100 is a possible line of best fit because it is a horizontal line that passes through the y-axis at the value of 100. This suggests that there is a consistent relationship between the x and y variables where y is always equal to 100, regardless of the value of x.
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29.
What is the equation of the function represented by this table of values?
A.
A
B.
B
C.
C
D.
D
Correct Answer C. C
30.
The enrollment at High School R has been increasing by 20 students per year. Currently, High School R has 200 students attending. High School T currently has 400 students, but its enrollment is decreasing in size by an average of 30 students per year. If the two schools continue their current enrollment trends over the next few years, how many years will it take the schools to have the same enrollment?
A.
4 years
B.
5 years
C.
10 years
D.
20 years
Correct Answer A. 4 years
Explanation High School R is increasing its enrollment by 20 students per year, while High School T is decreasing its enrollment by 30 students per year. The difference between the two schools' enrollments is currently 200 students (400 - 200). Since High School R is gaining 20 students per year and High School T is losing 30 students per year, the difference between their enrollments will decrease by 50 students each year (20 + 30). Therefore, it will take 4 years for the two schools to have the same enrollment, as the difference will decrease by 200 students (50 x 4) in that time.
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31.
What is the solution to the following inequality?
A.
X ≥ 0
B.
X ≤ 0
C.
X ≥ 12
D.
X ≤ 12
Correct Answer D. X ≤ 12
Explanation The solution to the given inequality is x ≤ 12. This means that any value of x that is less than or equal to 12 will satisfy the inequality.
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32.
Which is a true statement about the data shown in the tables?
A.
Both tables represent a linear relation.
B.
Only Table 1 represents a linear relation.
C.
Only Table 2 represents a linear relation.
D.
Neither table represents a linear relation.
Correct Answer B. Only Table 1 represents a linear relation.
Explanation Table 1 represents a linear relation because the values in the second column increase by a constant rate (2) for each corresponding value in the first column. This indicates a linear relationship where the dependent variable (second column) changes at a constant rate with respect to the independent variable (first column). On the other hand, Table 2 does not exhibit a constant rate of change between the columns, indicating that it does not represent a linear relation.
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33.
The length of a rectangle is 4 times its width. If the length of the rectangle is cut in half, the new perimeter is which percent of the original perimeter?
A.
25%
B.
50%
C.
60%
D.
100%
Correct Answer C. 60%
Explanation If the length of the rectangle is 4 times its width, let's assume the width is x. Therefore, the length would be 4x. The original perimeter would be 2(length + width), which is 2(4x + x) = 10x. If the length is cut in half, the new length would be 2x. The new perimeter would be 2(new length + width), which is 2(2x + x) = 6x. To find the percentage, we need to calculate (new perimeter / original perimeter) * 100, which is (6x / 10x) * 100 = 60%.
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34.
What is the simplified form of the expression?
A.
A
B.
B
C.
C
D.
D
Correct Answer A. A
Explanation Simplify 4/8 to 1/2. Use the exponent rule of division. If you have the same variable, and they want to divide then you subtract the exponents. We have two exponents for the x-variable. So you subtract the exponents which is 3-5 = -2. Since the exponent is negative we put the variable back in the denominator for it to be positive. We will do the same for the y-variable. Subtract the exponents which is 3-2 = 1. Since the exponent is positive we keep it in the numerator. Thus, our answer should be A.
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35.
What is the solution for the system of equations?
y = 2x - 3
4x - 3y = 31
A.
(−11, −25)
B.
(−11, −19)
C.
(11, 19)
D.
(14, 25)
Correct Answer A. (−11, −25)
Explanation To find the solution for the system of equations, we can solve them simultaneously. By substituting the value of y from the first equation into the second equation, we get 4x - 3(2x - 3) = 31. Simplifying this equation gives us 4x - 6x + 9 = 31. Combining like terms yields -2x + 9 = 31. By subtracting 9 from both sides, we get -2x = 22. Dividing both sides by -2 gives us x = -11. Substituting this value of x into the first equation gives us y = 2(-11) - 3 = -25. Therefore, the solution for the system of equations is (-11, -25).
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Janaisa Harris |BA-Mathematics|
Mathematics Expert
Ms. Janaisa Harris, an experienced educator, has devoted 4 years to teaching high school math and 6 years to tutoring. She holds a degree in Mathematics (Secondary Education, and Teaching) from the University of North Carolina at Greensboro and is currently employed at Wilson County School (NC) as a mathematics teacher. She is now broadening her educational impact by engaging in curriculum mapping for her county. This endeavor enriches her understanding of educational strategies and their implementation. With a strong commitment to quality education, she actively participates in the review process of educational quizzes, ensuring accuracy and relevance to the curriculum.
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