ONLINE Pre-Algebra TUTORING TOPICS
ONLINE MATH TUTORING TOPICS
Prealgebra 1 includes a thorough exploration of the fundamentals of arithmetic, including fractions, exponents, and decimals. We introduce beginning topics in number theory and algebra, including common divisors and multiples, primes and prime factorizations, basic equations and inequalities, and ratios.
Art of Problem Solving: PRE ALGEBRA tutoring text
PRE ALGEBRA ONLINE TUTORING
Numbers and Operations:
1. Add and Subtract Rational Numbers
2. Multiply and Divide Rational Numbers *Multiply and Divide Monomials
3. Powers of Monomials *Negative Exponents *Scientific Notation *Roots
4. Estimate Roots *Compare Real Numbers
5. Solve Equations with Rational Coefficients. Solve Addition and Subtraction Equations. Solve Multiplication and Division Equations
6. Solve Two-Step Equations. The Distributive Property. Solve Equations with Variables on Each Side. Solve Multi-Step Equations
7. Ordered Pairs and Relations
Tables and graphs
8. Two-Way Tables. Analyze Tables. Analyze Graphs.Translate Tables and Graphs into Equations. Functions
Lines and Linear Relationships
9. Linear Functions. Nonlinear Functions. Linear and nonlinear Associations
Functions and their properties
10. Graph Quadratic Functions
11. Families of Nonlinear Functions
Rate of Change/ Slope
12. Constant Rate of Change. Construct Functions. Slope
13. Investigating Linear Equations
14. Proportional and Non- proportional Relationships. Direct Variation. Slope-Intercept Form. Compare Properties of Functions
15. Graph Functions Using Intercepts
16. Model Linear Behavior. Qualitative Graphs. Systems of Equations
17. Use Logical Reasoning.
Lines and Triangles
Shapes and Polygons
Similar Polygons. Similar Triangles. Right Triangle Relationships
The Pythagorean Theorem
Distance on the Coordinate Plane Slope Triangles Special Right Triangles Translations Reflections Congruence and Transformations Rotational Symmetry Rotations
Dilations Similarity and Transformations Compositions of Transformations
Lines of Best Fit Select an Appropriate Display
Geometric Probability Act it Out Strategy Collect Data
Make a Model Strategy Volume of Prisms and Cylinders
Volume of Pyramids, Cones, and Spheres
Pre-Algebra Essential Skills
1. Write and evaluate variable expressions.
2. Use the order of operations.
3. Add, subtract, multiply and divide integers.
4. Write rules for patterns.
5. Graph points in the coordinate plane.
6. Identify and use properties of addition and multiplication and the Distributive Property. 7. Simplify expressions.
8. Solve one-step equations and inequalities.
9. Round decimals.
10. Find mean, median and mode of a set of data.
11. Substitute into formulas.
12. Convert metric and customary units.
13. Use divisibility tests.
14. Find the prime factorization of a number.
15. Find the greatest common factor and least common multiple.
16. Write fractions in simplest form.
17. Simplify expressions with integer exponents.
18. Write and evaluate numbers in scientific notation.
19. Write fractions as decimals and write terminating and repeating decimals as fractions. 20. Add, subtract, multiply and divide fractions and mixed numbers.
22. Solve proportions.
23. Find probability and odds.
24. Write percents as fractions and decimals and write decimals and fractions as percents. 25. Find a part of a whole, a percent and a whole amount
25.evaluate order of operations with absolute value;
26. distribute and combine like terms;
27. evaluate algebraic expressions;
28.solve linear equations (simple, dual side variables, infinite or no solution, and rational coefficients);
29. solve linear absolute value equations (simple and dual side);
30.solve algebraic formulas with several variables for one of the variables; and
solve applications of linear equations (age, integers, and triangles).
Art of problemsolving : course prealgebra1
Pre Algebra is the foundation for learning further mathematics. These important topics are the building blocks of all future courses in High School and College Mathematics.
With more hours of online pre-algebra tutoring you increase your chances of expanding your mathematical knowledge and gaining the necessary skills for your success in high school. Knowing all these pre-algebra principles will give you an advantage over your peers in getting a better high school average and a better chance of college acceptance.
Learn topics from integers and ratios to polynomials and functions, so that you can expand your career opportunities and get through your next math exam with ease.
- August 29, 2019Math Tutoring / Online Statistics Tutoring / Tutoring Algebra 2 / Tutoring StatisticsAlgebra II Regents Tutoring Topics SECTION: Statistics EXAMPLE 1: To answer this question you need to know what is the “variability of data” in this context? Standard deviation, sigma tells us how deviated the data is from the mean. The higher the standard deviation is the more spread out the data is. How come this is true? Imagine a bar graph with each bar representing one standard deviation. In the middle of the bar graph is the mean, or the average. The higher the number of each bar the wider each bar is (farther away from the center) and more wider bars will result in a spread out graph. What does it mean to have more variability? Variability is the extent to which data points in a statistical distribution or data set diverge from the average, or mean, value as well as the extent to which these data points differ from each other. There are four commonly used measures of variability: range, mean, variance and standard deviation. If the standard deviation is higher for the second data set that means the variability is greater for that data set. Choice (2) EXAMPLE 2: What are independent events? Independent events are independent of each other. One event has not bearing on the other. The probabilities of those events have no effect on each other. The outcome of one event is not effected by the outcome of the other event. -Mutually exclusive events are not the same as independent events. -Disjoint events are the same as mutually exclusive. mutually exclusive events(disjoint events) – events that can not happen at the same time. disjoint events – if one event occurs the other one can not. independent events – each event has not effect on the other’s probability. -Event intersection is zero for mutually exclusive events. (Because those events cannot occur together P(A and B) =0) If two events are disjoint they are dependent, because if one event occurs the other one can not has an impact on the other event. Therefore the fact that one event cannot occur because of the other means that one event has an effect on the other and therefore is dependent on the other not occuring. What is the formula for P(A and B)? Eliminate Choices (1) (3) (4). The multiplication of P(A)*P(B) does not yield 0.4 Choice (2). How many students will be enrolled in a tutoring program? The number of students who score less then one standard deviation above the mean will be enrolled. REMINDER: One standard deviation above the mean means one bar(interval) to the right from the mean. Each bar represents one standard deviation in a normally distributed distribution (check out the graph below !>). 68 – MEAN One S.D. = 7.2 – the equivalent of ONE INTERVAL How many students are below one standard deviation? Well based on the graph 50 % of the students are below the mean, and 50 % of the students are above the mean. Which means 50% + 34.1% = 84.1% of the students are below one standard deviation. How much is 84.1% out of all the students? 750 * 0.841 = 630.75. Choice (1) . Basic conditional probability question. NOTE: If the question contains the word probability “given” some other probability. It is a conditional probability question. GIVENS: P(O) = 0.8 P(F | O)= 0.85 P( O and F) =? P (F | O ) = P(F and O) / P(O) 0.85 = P (F and O) / 0.8 multiply both sides by 0.8 0.68 = P ( F and O ) QUESTION: Is P (F and O ) = P (O and F). Another words is the intersection of F and O the same as the intersection of O and F. Yes it is. QUESTION: In your conditional probability formula can A and B be switched? What do I need to remember when remembering to use the formula? THINGS TO REMEMBER: P(A | B) – -> always reads P of A given B this can not be switched. P(A | B) * P (B) = P (the intersection of A and B) The conditional Probability is multiplied by the second Probability to give P (intersection). This order cannot be switched. The simulation graph shows the average (mean = 29.101). Interval containing middle 95 % of the data is two standard deviations below the mean + two standard deviations above the mean. Based on the simulation picture the majority of the data (95 %) falls between 27.0 and 31.0 on the graph. Let’s calculate it using the values provided rounding to the nearest hundredth. If you add two standard deviations to the mean 29.101 + 2(0.934) = 27.23 If you subtract two standard deviations from the mean you get the left bound. 29.101 – 2(0.934) = 27.23 (27.23, 30.97)—The 95 % confidence interval, means that there is a 95% chance that the mean will fall within this range. Therefore it is possible that the mean is 30. Advertisements...
- March 26, 2019Math Tutoring / Online Math Tutors / Online Statistics Tutoring / Online STEM tutoring / Tutoring Algebra 2 / Tutoring Algebra 2 / Tutoring StatisticsStatistics Tutoring Ex. Linear Regression Regents Do you know how to calculate linear regression by heart? If you do not, this post will help you enter this data in a calculator and successfully produce the correct linear regression equation. START: Hit STAT — > EDIT– > EDIT You should See lists. Enter the data for the x values into the first list, and the data for the y values for the second list. Hit STAT — > CALC — > Scroll down to choice 4. LinReg(ax+b) and hit enter. This produces a Linear Regression equation with a=1.9 b= 29.79, r^2 =0.113 R = 0.337 Y= 1.917 X + 29.79 —– Linear Regression Equation Y= 1.9X + 29.8 —– Linear Regression Equation rounded to the nearest tenth What do the R and R^2 values mean in statistics? R squared – the STRENGTH of Association. R- how LINEAR the association is and DIRECTION. Exactly –A perfect downhill (negative) linear relationship –70. A strong downhill (negative) linear relationship –50. A moderate downhill (negative) relationship –30. A weak downhill (negative) linear relationship No linear relationship +0.30.A weak uphill (positive) linear relationship +0.50.A moderate uphill (positive) relationship +0.70.A strong uphill (positive) linear relationship Exactly +1.A perfect uphill (positive) linear relationship Ref:s https://www.dummies.com/education/math/statistics/how-to-interpret-a-correlation-coefficient-r/ Advertisements...
- March 26, 2019Math Tutoring / Tutoring Algebra 2 / Tutoring TrigonometryTutoring Algebra 2 Regents Review Trigonometry Functions START: To start this problem we must know what The angle 13pi/20 represents, what is 13pi/20? What is pi? Pi=3.18 if you said this you have no idea what the question is asking, and you should continue reading. Pi in this case means 180 degrees; the angle in the question is in radians and contains the symbol pi. RULE: If the angle (theta) contains the symbol pi it is represented in radians. If the angle (theta) contains numbers only it is represented in degrees. How many degrees is 13pi/20? Do know we must convert this angle (represented in radians) to an angle represented in degrees. Only then we can locate this angle on the coordinate plane. To convert an angle represented in radians: Substitute pi=180 for the symbol pi. In which quadrant is 117 degrees located? Quadrant II. All of the choices have the image of the terminal side of the angle located in QII. So which of the choices is correct? To eliminate choices you need to know the definition of the terminal angle. RULE: Reference angle- positive angle created from the x-axis. It is always less then 90 degrees. Eliminate choices 1) and 2) they do not show the reference angle created from the x-axis. Eliminate choice 3) it shows the angle in question as negative. Choice (4). Amplitude – height of the given trigonometric sine graph. What is the height from the middle of the graph, break the graph horizontally in half. For the first two choices Technique: To break a trigonometric graph count the number of graph intervals from the bottom of the graph to the top. Choice 1) 4 total /2 ->2 amplitude Choice 2) 8 total /2 ->4 amplitude Choice 3) Amplitude is 3 | number in front of the trig function| – absolute number of the value in front of the trig function. In this case the number in front of the function sine is 3, it is positive. Amplitude – always positive. Choice 4) Amplitude is 5 Negative number has to do with reflection of the graph across the x axis( all the y values are negated) and has no effect on the value of the amplitude. Choice (4). START: The question is asking for the number of hours y. The equation models the number of hours in days x. Let’s count how many days x will pass till Feb 14 2013 from January 1, 2013? 44 days . Substitute 44 for the number of days –x. Choice (4) START: Where is the terminal side of the angle located? In other words, where is the angle located? The x value is negative and the y value is negative. Which means that it has to be in QUADRANT III. Let us sketch some angles. Reminder: Unit Circle is a circle centered in the origin with radius =1. Every point on the unit circle has the (x value = cosine of the angle, y value = sine of the angle). The angle is not the reference angle but actual angle in question. -1/3 is the actual value of cos (angle in question) -sqrt (8)/3 is the actual value of sin (angle in question). sec(109.47)=-3. Choice (1). SHORT CUT: If you noticed that You would see the answer right away. If cos (theta) = -1/3 Sec (theta) would be 1 over that, or a flipped fraction. 1/ (-1/3) = 3 Choice (1) The question is asking for the smallest minimum value, for all the y values. In the second example this can be easily seen with the smallest q(x) value -8. What is the smallest y value for the first function 2sin(3x)+1. This is a sine function with the amplitude 2 translated up 1 unit and period 2pi/3. So the graph 2sin(3x) is a sine graph with the height of 2, from y value of -2 to +2. graph 2sin(3x)+1 is a sine graph translated one unit up so the range of the y values will be from -1 to +3, and the minimum y value for the graph is -1. Check this by graphing this function on a graphing calculator. **Before graphing a trig function on a graphing calculator à Change mode to radian: MODEà Radian** Advertisements...
- March 18, 2019Math Tutoring / Online Math Tutors / Online STEM tutoring / Tutoring Algebra 2 / Tutoring Algebra 2 / Tutoring TrigonometryTutoring Algebra 2 Regents Review SECTION 2: Logarithms Exponentials Absolute Value Problems EXAMPLE 1: All the answer choices have ln (natural log) in them. This means we will use natural log to solve this problem. The givens in the problem : a – is a number >0 , b- is a number>0, c- is any number>0, t- is a variable. E- base of the logarithm in this case natural logarithm, it is a specific number 2.718 Take the log of both sides Choice (3) EXAMPLE 2: The question is asking for which value of x, out of the choices given. OPTION 1) Substituting into the choices. OPTION 2) Graph both functions to see where they are equal on the graph. Using the change of base formula it is easy to rewrite the into logx/log3. To enter absolute value into the calculator hit MATH-> NUM ->abs( To calculate hit 2nd Calc choose Intersect. First curve? Hit the first curve, move the mouse x symbol closer to the intersection. Hit enter. Second curve? Move the mouse of the x on the second curve closer to the intersection. Hit enter. Guess? Hit enter. Since there are TWO intersections the same procedure can be applied to finding the second intersection. Choice (1). EXAMPLE 3: What is the question asking? The average decreasing rate of change per year. What is the average decreasing rate of change? It is the slope from T – 2012 to T- 2014. Formula of the slope = Y1- Y2/ X1-X2 (The difference in Y values over the difference in X values) What are the Y values in this case? Greg purchased the can in June 2011 which means by June 2012. The value of the car after ONE year would be t =1. The value of the car after one year is 13600. The value of the car after THREE years would be t =3. Y1 = 13600 Y2 = 8704 X1 =1 years X2= 3 years (Y1- Y2) /(X1- X2) = average rate of change (decrease from 3 years to 1 year). Choice (3). EXAMPLE 4: This question has a lot of information, and the important thing is what is the question asking? The number of grams A of Iridium 192 present after t days is Given in the question. But then the question asks what is the number of Iridim -192 present after t days? So the question is asking already what is given in the question itself. This could only mean that there is a different way of expressing A- the number of grams of Iridium present after t days. Choice (3) EXAMPLE 5: What are rational Exponents? Rational – means involving a ratio ( fraction) one number divided by another 2) fraction can be expressed as a decimal. What are the properties of rational exponents? The Definition of : , this says that if the exponent is a fraction, then the problem can be rewritten using radicals. Notice that the denominator of the fraction becomes the index of the radical. The Definition of : , this says that if the exponent is a fraction, then the problem can be rewritten using radicals. Notice that the denominator of the fraction becomes the index of the radical and the numerator becomes the power inside the radical. 3 is the denominator of the rational exponent and it becomes the index in the radical. 4 is the numerator of the rational exponent and it becomes the power the radical is taken to. Simplifying the radical and (-2) ^4 = 16. Exponents can be integers, positive, negative and zero as well as fractions. Ref: More Examples of fractional exponents: http://www.mesacc.edu/~scotz47781/mat120/notes/exponents/rational/rational_exponents.html Advertisements...
- March 9, 2019Math TutoringTutoring-Online Tutor Responsibilities Online Tutoring responsibilities are: Online Tutors act as Facilitators. Online learning climate is open and non-threatening but nonetheless rigorous. All students should be comfortable enough to identify their difficulties openly, to challenge themselves, their tutor and be able to admit if they “don’t know”. Online Tutors set learning goals. Be familiar with the learning objectives of both the Tutoring Topic at hand and the course to which the tutoring topic belongs. Be professional in speech and demeanor. Be knowledgeable about the school standards and curriculum offered at the school the student attends and at least have a general idea of what level the topic is being taught. Be forward thinking and prepare your students for future learning, act as a guide for progressive learning. Online Tutors extend and go beyond the basics. Student learning continues after the tutoring session is over. For this reason online tutors should encourage critical thinking and ensure that the students’ knowledge is challenged and probed during the tutoring session and after. Online Tutors ensure that an objective, rigorous but evidence based evaluation occurs in the tutoring session. Evaluating students based on routine questioning before the start of each online session and after. Online Tutors assist students to become independent and collaborative learners. Online Tutors assist and train students in developing appropriate study skillsin order to succeed in future learning endeavors. (guidance on reading and note-taking, skills on using the Internet, computer assisted learning programmes, etc) in order for them to complete their courses effectively. Marking Commenting Checking Assisting Students with Student Assignments. Students are required to submit any tutoring documents to a tutor at least one day prior to a tutoring session. Tutors are to check the accuracy of all completed assignments, assist and facilitate students on completing those assignment, mark and save notes (as well as video footage) on all the tutoring sessions. Student Progress Online tutors will use the tutorial and assignment systems to monitor fully the progress of individual students, by the maintenance of proper records of completed assignments, grades, attendance at laboratory sessions, etc. Provide constant feedback to the student. Online Tutoring Skills include: Facilitatory teaching through: – asking non-directive, stimulating questions, challenging students as appropriate – presenting consequences of student conclusions, opposing views, cues as necessary – indicating when additional external information is required – referring students to resources Promoting group problem solving and critical thinking by helping students: -to examine a range of phenomena, from the molecular level to the family and community level – to critically assess/appraise evidence supporting hypotheses – to define issues and synthesize information Promoting individual learning by: -helping students to develop a study plan, considering students goals and programme goals – helping students improve study methods including the selection of appropriate learning resources Evaluation through: – helping students define personal objectives – helping students select appropriate evaluation methods – reviewing demonstrated learning achievement and ensuring that the student gets feedback – reporting on individual student learning progress to parents Tutor.com Tutor Responsibilities Ref:s https://myjobsearch.com/careers/online-tutor.html Online Instructor – Degree Requirements, Job and Salary Info https://www.jobisjob.com/tutor/job-description Advertisements...
- March 7, 2019Math Tutoring / Online Math Tutors / Online STEM tutoring / Tutoring Algebra 2 / Tutoring Algebra 2 / Tutoring TrigonometryAlgebra 2 Regents Review Topics (Introduction.) TEST TAKING TIPS Most Common Challenging Concepts Students TIP 1: Examine the question. TIP 2: Examine the answers. TIP 3: Use a calculator whenever possible to check and solve. In these algebra 2 review sessions we will be exploring strategies, important techniques and approaches to solving algebra 2 regents questions more efficiently. SECTION 1: Exponential Questions/ Interest Rate Problems EXAMPLE 1: The equation in question has an exponent which is negative (-0.10x) and is an exponential equation. START: Question is asking which is not equivalent, which mean we need to examine if the answers are same as the question. The obvious choice is (1) but that can be checked with a calculator. Simplest solution: Using graphing calculator enter each of the choices and the given question into the options so check which are the same. MODE is set to funct. 2. Wrong way to enter this exponential function: Notice if you enter this choice as it is written in the question it is not correct: Right way to enter this exponential function choice: Choice (1) and the question yield the same graph. But the question is asking which of the following is not equivalent. Choice (2) Multiply exponents. Choice (3) Negative exponent rules say that one over a base to a positive power can be turned into a negative power. Choice (4) Adding exponents because the base is the same. Ex 2^3 * 2^4 = 2^7. Ans choice 4 is not equivalent. EXAMPLE 2: Interest rate problems involve interest rate formula. On the last pages of the regents exam you can find the formula sheet. “The exponential e is used when modeling continuous growth that occurs naturally such as populations, bacteria, radioactive decay, etc. You can think of e like a universal constant representing how fast you could possibly grow using a continuous process.” Converting the percent to decimal. A0 – initial amount = 5000 A – final amount = 9110 K= rate of change t – time 30 years 9110=5000*e^(k(30) +B0 Formal solution : divide both sides by 5000 take the natural log of both sides bring forward the exponent (rules of logs) lne = 1 0.599 =30r divide by 30 both sides r= 0.5999/30 =0.019997 ~0.02 = 2% Now suppose you did not know how to use natural logs and solve this problem. Shortest solution Substituting Answers \ EXAMPLE 3: If you have no idea what this equation represents and missed or intentionally slept through classes with rate, growth and exponential problems. Look at the choices and try to use any math that you already know. START: Choice 1. Every hour, the amount of pain reliever remaining is cut in half. Hour = t time. One hour = t =1 substitute t into the formula. If every hour the amount would be half the answer would be half of 220= 110 this equation is not going to produce that. The reason is that it is already halved by the fraction but there is an extra fraction in the exponent. Lets check with the calculator entering and using proper parenthesis. 207 is not half of 220. Choice 2. In 12 hours, t=12 substitute into the function to find how many milligrams will be remaining. Reducing 12/12=1 there will be 110 mg remaining. This is choice 4. Choice 3. In 24 hours= t, there will be 55 mg remaining not zero. Ans choice 4. EXAMPLE 4: If the test day is the first time you have seen exponential problems do not panic. Using a calculator you can solve these problems with ease. START: Graph this function. Pick a number for a, b, since the first choice says that a >0 and b>1 lets pick a=1 b=2. Graph this function. We can see from the graph that the function is going up which means it is increasing on the domain of the function( -inf, +inf). Choice 2. The y intercept is (0,a) we choose a to be 1 in our example. Y intercept is where the graph hits (intercepts) the y axis. The y intercept is (0,1) is this true? Lets find it on the graph. To find the exact value hit 2ndCalc and type x=0 hit enter, this finds the exact value of the function at (0=x, 1). If you wanted to check algebraically substitute x =0 into the function 1 * 2^0 = 1 =y. Choice 3. The asymptote is y=0. Asymptote is the value a function comes close to but never reaches. Where is y=0, in this case it is not just a point, it is a line. Where is this line located? It is a line where all the y values are zeros which is the x axis. This is the line exponential function never reaches. You can check this by hitting the TRACE FUNCTION and using the left arrow scroll as left as possible. You will notice that the values of the function approach zero but never get to it. Y= 0.0089 . Y = 0.0045… This statement is true. Choice 4. The x intercept is (b,0) we choose b =2. The x intercept (2,0) is this true? X intercept is where the graph hits (intercepts) the X axis. Does this graph hit the x axis at (2,0)? No. So this statement is false. Ans choice 4. Ref:s https://www.nysmathregentsprep.com/uploads/6/2/3/2/62326735/1._algebra_ii_[common_core]_january_2018_regents_exam.pdf https://www.cemetech.net/projects/jstified/ Advertisements...