Shortcuts that replace a long multiplication with a single step.

• s1.1FOILing/LIOFing When Multiplying1000
• s1.2.1Multiplying by 11 Trick1000
• s1.2.2Multiplying by 101 Trick1000
• s1.2.3Multiplying by 25 Trick1000
• s1.2.5Multiplying by Any Fraction of 100, 1000, etc...1000
• s1.2.6Double and Half Trick1000
• s1.2.7Multiplying Two Numbers Near 1001000
• s1.2.8Squares Ending in 5 Trick1000
• s1.2.9Squares from 41-591000
• s1.2.10Multiplying Two Numbers Equidistant from a Third Number1000
• s1.2.11Multiplying Reverses1000
• s1.3.1Extending Foiling1000
• s1.3.2Factoring of Numerical Problems1000
• s1.3.3Sum of Consecutive Squares1000
• s1.3.4Sum of Squares: Factoring Method1000
• s1.3.5Sum of Squares: Special Case1000
• s1.3.6Difference of Squares1000
• s1.3.7Multiplying Two Numbers Ending in 51000
• s1.3.8Multiplying Mixed Numbers1000
• s1.3.9a x a/b Trick1000
• s1.3.10Combination of Tricks1000
• s1.4.1Finding a Remainder when Dividing by 4, 8, etc...1000
• s1.4.2Finding a Remainder when Dividing by 3, 9, etc...1000
• s1.4.3Finding a Remainder when Dividing by 111000
• s1.4.4Finding Remainders of Other Integers1000
• s1.4.5Remainders of Expressions1000
• s1.4.6Dividing by 9 Trick1000
• s1.4.7Converting a/40 and b/80, etc... to Decimals1000
• s1.5.1Subtracting Reverses1000
• s1.5.2Switching Numbers and Negating on Subtraction1000
• s1.5.3Sum of Fractions in a Series1000
• s1.5.4a/b + b/a Trick1000
• s1.5.5a/b - (na-1)/(nb+1)1000

The numbers and formulas you are expected to already know cold.

• s2.1.1Squares1000
• s2.1.2Cubes1000
• s2.1.3Powers of 2, 3, 51000
• s2.1.4Important Fractions1000
• s2.1.5Special Integers1000
• s2.1.6Roman Numerals1000
• s2.1.7Platonic Solids and Euler’s Formula1000
• s2.1.8π and e Approximations1000
• s2.1.9Distance and Velocity Conversions1000
• s2.1.10Conversion between Distance → Area, Volume1000
• s2.1.11Fluid and Weight Conversions1000
• s2.1.12Celsius to Fahrenheit Conversions1000
• s2.2.1Sum of Series1000
• s2.2.3Integral Divisors1000
• s2.2.4Number of Diagonals of a Polygon1000
• s2.2.5Exterior/Interior Angles1000
• s2.2.6Triangular, Pentagonal, etc... Numbers1000
• s2.2.7Finding Sides of a Triangle1000
• s2.2.8Equilateral Triangle Formulas1000
• s2.2.9Formulas of Solids1000
• s2.2.10Combinations and Permutations1000
• s2.2.11Trigonometric Values1000
• s2.2.12Trigonometric Formulas1000
• s2.2.13Graphs of Sines/Cosines1000
• s2.2.14Vertex of a Parabola1000
• s2.2.15Discriminant and Roots1000

Bases, remainders, logs and sets — the middle of the test.

• s3.1.1GCD and LCM1000
• s3.1.2Perfect, Abundant, and Deficient Numbers1000
• s3.1.3Sum and Product of Coefficients in Binomial Expansion1000
• s3.1.4Sum/Product of the Roots1000
• s3.1.5Finding Units Digit of x^n1000
• s3.1.6Exponent Rules1000
• s3.1.7Log Rules1000
• s3.1.8Square Root Problems1000
• s3.1.9Finding Approximations of Square Roots1000
• s3.1.10Complex Numbers1000
• s3.1.11Function Inverses1000
• s3.1.12Patterns1000
• s3.1.13Probability and Odds1000
• s3.1.14Sets1000
• s3.2.1Converting Integers1000
• s3.2.2Converting Decimals1000
• s3.2.3Performing Operations1000
• s3.2.4Changing Between Bases: Special Case1000
• s3.2.6Changing Bases: Miscellaneous Topics1000
• s3.3.2In the form: .ababa...1000
• s3.3.3In the form: .abbbb...1000
• s3.3.4In the form: .abcbcbc...1000
• s3.4Modular Arithmetic1000
• s3.5.11*1! + 2*2! + ... + n*n!1000
• s3.5.2a! ± b! / c!1000
• s3.5.3Wilson's Theorem1000
• s3.6.1Limits1000
• s3.6.2Derivatives1000
• s3.6.3Integration1000

The back forty: Fibonacci, phi, and the harder approximations.

• s4.1.1Multiplying Three-Digit Number by Two-Digit Number1000
• s4.1.2Multiplying Three-Digit Number by Three-Digit Number1000
• s4.1.3Multiplying Two Numbers Whose Units Add to 10 and the Rest is the Same1000
• s4.1.4Binomial Approximation1000
• s4.1.5Multiplying by Fraction Close to 11000
• s4.1.6n² + n = (n+1)² - (n+1)1000
• s4.2.1Conversions, Part 21000
• s4.2.2Exotic Definitions of Numbers1000
• s4.2.3Square Root of Small Integers1000
• s4.2.4Approximations Using Phi1000
• s4.2.5Standard Fibonacci Numbers1000
• s4.3.1Adding Consecutive Terms of Arbitrary Fibonacci Sequence, Method 11000
• s4.3.2Adding Consecutive Terms of Arbitrary Fibonacci Sequence, Method 21000
• s4.3.3Adding Odd or Even Terms of Arbitrary Fibonacci Sequence1000
• s4.3.4Sum of the Squares of Arbitrary Fibonacci Sequence1000
• s4.4.1Additional Formulas: a/b - (na-1)/(nb-1)1000
• s4.4.2Factorizations1000
• s4.4.3Sum of the Reciprocals of Triangular Numbers1000
• s4.4.4Geometric and Harmonic Means1000
• s4.4.5Distance Between a Point and a Line1000
• s4.4.6Distance Between Two Parallel Lines1000
• s4.5.1More on Sets1000
• s4.5.2Repeating Decimals in Reverse1000
• s4.5.3Repeating Decimals in Other Bases - Convert to Base 101000
• s4.5.4Repeating Decimals in Other Bases - Keeping Same Base1000
• s4.5.5Remainders with a/p, b/p, and ab/p1000
• s4.5.6Minimal and Maximum Value of Expressions1000

Types that appear on real papers but were missing from the book.

• s5.1.1Systems of Two Linear Equations1000
• s5.1.2Reflections, Midpoints and Distance1000
• s5.1.3Parabolas: Directrix, Focus and Vertex1000
• s5.1.4Vectors: Components and Magnitude1000
• s5.1.5Determinants of 2x2 and 3x3 Matrices1000
• s5.1.6Inverse Trigonometric Values1000
• s5.1.7Double Integrals over Rectangles1000
• s5.2.1Texas Land Units: Varas and Leagues1000
• s5.2.2Rate Conversions: ft/s, mph and km/h1000
• s5.2.3Relatively Prime Counts and Euler’s Totient1000
• s5.2.4Area and Perimeter under Dilation1000
• s5.2.5Mean, Median, Mode and Range1000
• s5.2.6Counting Problems with Digits1000