
Explore natural numbers, integers, rational and irrational numbers, and real numbers, including primes, composites, and arithmetic properties like commutative, associative, distributive laws, identities, and inverses.
Apply divisibility by two and three to verify divisibility by six, and determine the least x so the number becomes 5522, which is divisible by two and three.
Convert decimals to standard form by shifting the decimal and writing the number as a digit before the decimal times ten to a negative power, such as 2.9 × 10^-1.
Apply the least common multiple of four, six, and seven to find the smallest number that leaves a remainder of two, yielding 86.
Find the largest container size that can measure both tanks by computing the greatest common factor of 504 and 735 using prime factorization, yielding 21 liters.
Learn square roots and cube roots, including radical notation and indices form, with division and factoring methods and examples like sqrt(196)=14 and 1331's cube root.
apply nested radical simplification by recalling the squares of the first 20 numbers, use sqrt(169) = 13, and simplify to obtain a final value of 16.
Explain how to compute a complex expression using multiplication, division, and powers, then simplify to 1.11108.
Master algebraic simplification of nested brackets, applying sign changes when a negative sits outside, to solve for x in a sat math multiple-choice problem.
This lecture guides you through simplifying expressions divided by another, calculating the LCM, combining terms, and identifying the correct option through fraction simplification.
Solve two equations in three unknowns by testing option values, then substitute candidates to verify which set satisfies both equations, saving time during the exam.
The lecture demonstrates cancellation in a long sequence of fractions, multiplying numerator and denominator and canceling terms to arrive at minus one.
Learn a quick trick for q.no.7: rationalize the denominator, set a minus b equal to a known value, square both sides, and substitute to avoid lengthy cubing.
Subtract x from 19 and 31 to make 1 to 4, solve by cross-multiplication, and find x equals 15 with verification.
The lecture shows how to calculate the percentage error when a number x is multiplied by 5/3 instead of 3/5, yielding a 64% error compared to the true value (5/3)x.
Solve a man and his son's age problem by applying the age ratio and total sum; derive each age to satisfy a 66-year combined total.
Determine the missing value x so the arithmetic mean of twelve numbers is 12 by summing to 127 and solving (127 + x)/12 = 12, giving x = 7.
Explains a two-number problem with numbers a and b, where one equals m; derive the second as two m minus m and identify option c as the solution.
Set the present age as x, express after 15 years as x+15 and five years back as x-5, then solve x+15 = 5(x-5) to find x = 10.
Solve for the present age x using the equation 1/(x−3) + 1/(x+5) = 1/3; derive and solve a quadratic, concluding the present age is 7.
Solve the fifth SAT math question where the denominator exceeds numerator by two and adding five to the numerator increases the fraction by one, confirming the fraction 3/5 (option d).
The lecture resolves two equations from the given conditions. It finds x=7 and y=8, so the fraction is 7/8.
Find a fraction whose numerator and denominator increase by two to yield 1/2 and by twelve to yield 3/4, using option checking and a system of equations to get 3/8.
Practice solving an exponent problem by applying power rules to deduce x, y, z are equal to one, with the correct option B.
Solve a sat math problem: simplify (x-1)/√x for x = 5+2√6 by showing √(5+2√6) = √2+√3, yielding 2√2+√3 and identifying option b.
Identify cyclic terms and apply exponent rules to rewrite each term. Cancel exponents across the cycle to show the expression simplifies to one.
Simplify the expression 16 x^{-3} y^2 × 8^{-1} x^3 y^{-2} using exponent rules. Cancel x^3 with x^{-3} and y^2 with y^{-2}, and use 8^{-1} to reduce 16 to 2.
Explore rewriting quadratic expressions using the identity a^2 + b^2 = (a+b)^2 − 2ab, applying it to x^2 − 2x + 4 and (3x+5)^2 to simplify.
If you find it difficult to remember various formulas of Math ? If you have a feeling of not being confident in Geometry ? If you facing difficulty in solving Trigonometry questions and feel that you need to strengthen your basics? Then you have come to the right place.
Here, this course covers the questions of following areas
Arithmetic
Algebra
Geometry
Trigonometry
I am sure that this course will be create a strong platform for students and those who are planning for appearing in competitive tests and studying higher Mathematics.
You will also get a good support in Q&A section . It is also planned that based on your feed back, new topics like Factorisation, Polynomials, Quadratic Equations, Inequations , Logarithm, Complex Numbers, Sequence and Series Arithmetic Progressions AP, Geometric Progressions, Some special series or more topics of geometry and Trigonometry or statistics or probability etc. will be added to the course. Hope the course will develop better understanding and boost the self confidence of the students.
Waiting for you inside the course!
Important Note: The course is intended for purchase by adults. Those under 18 years may use the services only if a parent or guardian opens their account, handles any enrollments, and manages their account usage.