1. Class 1 Comprehensive Review

2. What is being tested on SAT Math? Total Math Content No. of Question s Section 1 Math 1 (25 minutes) 20 mcqs Section 2 Math 2 (25 minutes) 8 mcqs 10 grid-in Section 3 Math 3 (20 minutes) 16 mcqs Total 44 mcqs 10 grid-in Numbers and operations Algebra and functions Geometry and measurement 11-13 19-21 14-16 6-7 3. What is being tested on GRE Math? Total Math Content Same as SAT Approximate No. of Questions Section 1 Math 1 (35 minutes) 20 multiple choice and plug in questions Quantitative comparison Problem solving Data Interpretation 10 7 3 Section 2 Math 2 (35 minutes) 20 multiple choice and plug in questions Quantitative comparison Problem solving Data Interpretation 10 7 3 Total 40 questions 4. Math class, topic wise schedule: Math topics: Handouts: Duration: 1) Algebra: i. 1 variable ii. 2+ variables iii. Unknown variables iv. Function v. Quadratics vi. Factorization 1) Math Notes from SAT bible. 2) ETS Algebra Set Week 1 and 2 2) Arithmetic: i. Properties of Numbers ii. Computation iii. Percents iv. Ratios/Proportions v. Mean/Median/Mode vi. Exponents & Roots 3) ETS Arithmetic Set Week 3 5. Math class, topic wise schedule: 3) Geometry: Circles Lines and Angles Triangle Area/Perim/Pythag Third Side Rule/ Angle Side Rule Similar Triangles Rectangle Area/Perim Graphing Functions/Equations Coordinate Geometry Polygons Solids 4) ETS Geometry Set Weeks 4 & 5 4) Misc. Problems: Charts Stats/Probability Patterns/Sequences Counting Logic Visual/Spatial Groups 5) ETS Misc. Set Week 6 5) Advanced Math Questions Handouts: TBD Weeks 7 & 8 6. Math Notes: Handout 1 for home Discussion next week if needed 7. Strategies 1a) Picking Numbers Step 1. Pick Simple Numbers and substitute for variables. Step 2. Try Them Out Try out all the answer choices using the numbers you picked, eliminating those that gave you a different result. Step 3. Try Different Values If more than one answer choice works, use different values and start again 1b) Recognition by prolonged and multiple use of Picking Numbers 8. 1a) Picking Numbers 9. 1b) Recognition Use different and easy Number Picks to eliminate any possible integer answers. 10. 2) Back-solving Step 1: Estimate the answer. Step 2: Plug in an answer. Step 3: Keep plugging in till you find one that works. Step 4: Try out all answers. Q. If x is an integer and 2 is the remainder when 3x + 4 is divided by 5, then x could equal (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 11. 3) Elimination 12. Algebra: 1 variable What is a modulus or absolute value? Modulus and square root 13. Algebra: 1 variable Square root of a number 14. Algebra: 1 variable Create an equation. 15. Algebra: 1 variable Picking numbers: Try all 4 types of real numbers, positive integers, negative integers, positive fractions and negative fractions. 16. Algebra 1 variable: Practice From the relevant topic in ETS set, do as many questions as you can in ten minutes. 17. Algebra: 2+ variables For simultaneous equations, learn to recognize what will be faster, substitution or elimination. 18. Algebra: 2+ variables Make sure to solve for of j. 19. Which strategy would work best here? Algebra: 2 variables 20. Algebra: 2+ variables 21. Algebra: 2+ variables 22. Algebra: 2+ variables 23. Algebra 2+ variables: Practice From the relevant topic in ETS set, do as many questions as you can in ten minutes. 24. Algebra: Unknown variables 25. Algebra: Unknown variables 26. Algebra: Unknown variables 27. Algebra Unknown variables: Practice From the relevant topic in ETS set, do as many questions as you can in ten minutes. 28. Thats it for today! Complete as homework the remainder of the questions in the ETS Algebra Practice Set from topics of: 1 variable 2+ variables Unknown variable 29. Example 3: If x, y and z are positive integers such that x< y < z and x + y + z = 6, then what is the value of z? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 30. Practice Problem Set A Review Problem Set B Review 31. 2) Defined Function Example 1: If x* y represents the number of integers between x and y then (-2*8) + (2*-8) = (A) 0 (B) 9 (C) 10 (D) 18 (E) 20 32. Example 2: For any positive integer n, n! denotes the product of all the integers from 1 through n. what is the value of 3!(7 -2)! ? (A) 2! (B) 3! (C) 5! (D) 6! (E) 10! 33. Example 3: A function @ is defined on positive integers as @(a) = @(a-1) +1. if the value of @(1) is 1, then @(3) equals which one of the following? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 34. Practice Problem Set A Review Problem Set B Review 35. 3)Number Theory Example 1: The remainder is 57 when a number is divided by 10,000. What is the remainder when the same number is divided by 1,000? (A) 5 (B) 7 (C) 43 (D) 57 (E) 570 36. Example 2: If n is a positive integer and (n + 1)(n + 3) is odd, then (n + 2)(n + 4) must be a multiple of which one of the following? (A) 3 (B) 5 (C) 6 (D) 8 (E) 16 37. Example 3: The number of prime numbers divisible by 2 plus the number of prime numbers divisible by 3 is (A) 0 (B) 1 (C) 2 (D) 3 (E) 4 38. Example 4: If 15x + 16 = 0, then 15 x equals which one of the following? (A) 15 (B) 16x (C) 15x (D) 16 (E) 16x