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The Alexander Tutoring Blog

Tips and thoughts about math, physics, and the mysteries of our universe.

Comparison of ib physics sl and hl: 150 vs 240 teaching hours, paper 1 and paper 2 durations and marks, and the same 3,000-word scientific investigation worth 20 percent at both levels.

IB Physics Guide: SL vs HL, Topics, Data Booklet and IA (2026)
The college math readiness gap: uc berkeley students ready for calculus i fell from 71% to 44%, 1 in 8 uc san diego freshmen are below high school math level, and mission high had a 44. 7% berkeley admit rate while 6% of its 11th graders were proficient in math.

AI and the State of Education: Why College Math Readiness Is Slipping
Research summary of passion + purpose tutoring: 147 students in grades 7–12 and 266 nwea map growth test pairs, with growth 3. 4 rit above projection (95% ci 1. 7 to 5. 1) and 57% meeting or beating projected growth.

Passion + Purpose Tutoring and Math Growth: A Four-Year MAP Study (2022–2026)
Graphic with three reasons the sat still matters: it gives colleges a common scale, all eight ivy league schools have announced testing requirements again, and sat math signals readiness for college math.

Why Is the SAT Important? Top Student Struggles and Proven Tutoring Strategies
Graphic comparing four tutoring price tiers: worksheet programs like kumon, learning centers like mathnasium and sylvan, marketplace tutors at about $35 to $60 an hour, and specialist one-on-one tutors at around $150 an hour or a monthly program.

Kumon vs Mathnasium vs Sylvan: What You Get for the Price
Comparison of the psat/nmsqt and sat: score ranges of 320 to 1520 and 400 to 1600, both 2 hours 14 minutes with 98 questions; the psat is used for national merit and the sat by colleges.

PSAT vs. SAT: Format, Scoring and Key Differences
Graphic of the key 6th grade math skills: ratios and unit rates, fraction division and decimals, negative numbers on the number line, and the start of algebra with exponents, pemdas and one-variable equations.

6th Grade Math Essentials: Key Skills Students Need to Master This Year
Four key 5th grade math skills: adding fractions with unlike denominators such as one half plus one third equals five sixths, decimals to the thousandths, volume as length times width times height, and plotting points in the first quadrant of the coordinate plane.

5th Grade Math Guide: Essential Skills Students Learn Before Middle School
Pathway chart of senior-year math: algebra 2 leads to precalculus or ap precalculus and then ap calculus ab or bc for engineering, physics, computer science, pre-med and economics, or to ap statistics for psychology, biology, social science and business.

12th Grade Math: Senior Year Course Options and Key Skills
Checklist of skills to review before 11th grade algebra 2: factoring, exponent rules, linear equations and systems, function notation with domain and range, and right-triangle trigonometry.

11th Grade Math Essentials: What to Review Before Algebra 2
Two similar right triangles from the shadow problem: a 6-foot person with a 4-foot shadow and a tree of height h with an 18-foot shadow; the same sun angle makes them similar by aa, so h is 27 feet.

10th Grade Math Essentials: A Parent’s Guide to Geometry, Proofs, and Building Real Problem-Solving Skills
Graph of the lines y = 2x + 1 and y = −x + 7 crossing at the point (2, 5), the solution of the system of equations.

9th Grade Math Essentials: What Your Student Needs to Succeed in Algebra 1 (and Beyond)