Welcome, Abhinav! - TJHSST & IAAT Prep Hub

Hey Abhinav, this is your cousin Sijan! I built this hub to help you prepare for the TJHSST admissions process and the IAAT exam. You've got this - let's work through it together. Stay consistent, practice daily, and don't hesitate to ask questions. Good luck!

TJHSST Admissions Overview

  • Minimum 3.5 unweighted GPA across 7th grade and the 1st quarter of 8th grade
  • Honors Algebra 1 completed by the end of 8th grade
  • Application timeline: start early - research in spring of 7th grade, prepare for the IAAT over the summer, finalize your application by the fall of 8th grade
  • Submit teacher recommendations, student essays, and report cards as part of the application
  • Fairfax County residents are eligible; out-of-county applicants have limited seats via a lottery

IAAT Test Structure

  • 60 questions in 40 minutes
  • 91st percentile benchmark: approximately 43-45 correct answers
  • Four sub-sections (15 questions each):
    • Pre-requisite Skills - basic arithmetic, fractions, decimals, percentages, order of operations
    • Basic Algebra and Representation - evaluating expressions, understanding variables, translating words to equations
    • Mathematical Interpretation - reading graphs, tables, charts, and interpreting data
    • Problem Solving - multi-step word problems requiring logical reasoning and algebra

Practice Problems

1. Solve for x: 3(x - 4) + 5 = 2x + 1
Answer: x = 8
Explanation: Distribute: 3x - 12 + 5 = 2x + 1 -> 3x - 7 = 2x + 1. Subtract 2x: x - 7 = 1. Add 7: x = 8.
2. Simplify: (2x^3 y^2)(3x y^5)
Answer: 6x^4 y^7
Explanation: Multiply coefficients: 2 * 3 = 6. Add exponents of like bases: x^3 * x = x^(3+1) = x^4, y^2 * y^5 = y^(2+5) = y^7. Result: 6x^4 y^7.
3. Factor completely: x^2 - 9x + 20
Answer: (x - 4)(x - 5)
Explanation: Find two numbers that multiply to 20 and add to -9: -4 and -5. Write as (x - 4)(x - 5).
4. Solve: 2/3 x + 1/2 = 5/6
Answer: x = 1/2
Explanation: Multiply both sides by 6: 4x + 3 = 5. Subtract 3: 4x = 2. Divide by 4: x = 2/4 = 1/2.
5. Graph the line: y = -2x + 3. What is the slope and the y-intercept?
Answer: Slope = -2, y-intercept = 3
Explanation: The equation is in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. So m = -2 and b = 3. The line crosses the y-axis at (0, 3) and goes down 2 units for every 1 unit right.
6. Solve: |2x - 5| = 9
Answer: x = 7 or x = -2
Explanation: Set up two equations: 2x - 5 = 9 or 2x - 5 = -9. First: 2x = 14, x = 7. Second: 2x = -4, x = -2.
7. Solve the system: 2x + y = 10 and x - y = 2
Answer: x = 4, y = 2
Explanation: Use elimination. Add the equations: (2x + y) + (x - y) = 10 + 2 -> 3x = 12 -> x = 4. Substitute: 4 - y = 2 -> y = 2.
8. Simplify: (3 + 2i)(4 - i)
Answer: 14 + 5i
Explanation: FOIL: 3*4 = 12, 3*(-i) = -3i, 2i*4 = 8i, 2i*(-i) = -2i^2. Since i^2 = -1, -2i^2 = 2. Combine: 12 + 2 = 14, -3i + 8i = 5i. Result: 14 + 5i.
9. What is the domain of f(x) = sqrt(x - 5)?
Answer: x >= 5, or [5, infinity)
Explanation: The expression under a square root must be >= 0. So x - 5 >= 0 -> x >= 5. In interval notation: [5, infinity).
10. Simplify: (x^2 - 16)/(x - 4)
Answer: x + 4, x != 4
Explanation: Factor numerator: x^2 - 16 = (x - 4)(x + 4). Cancel (x - 4) from numerator and denominator, leaving x + 4, with the restriction x != 4 since original denominator would be zero.
11. What is the vertex of the parabola y = x^2 - 6x + 11?
Answer: (3, 2)
Explanation: Complete the square: y = x^2 - 6x + 9 + 2 = (x - 3)^2 + 2. In vertex form y = (x - h)^2 + k, the vertex is (h, k) = (3, 2).
12. Find the x-intercept of the equation 3x - 4y = 12
Answer: x = 4
Explanation: Set y = 0: 3x - 4(0) = 12 -> 3x = 12 -> x = 4. The x-intercept is (4, 0).
13. Solve: 5^(2x+1) = 125
Answer: x = 1
Explanation: Rewrite 125 as 5^3: 5^(2x+1) = 5^3. Since bases are equal, set exponents equal: 2x + 1 = 3 -> 2x = 2 -> x = 1.
14. The sum of two numbers is 28 and their difference is 4. Find the numbers.
Answer: 16 and 12
Explanation: Let x and y be the numbers. x + y = 28 and x - y = 4. Add equations: 2x = 32 -> x = 16. Substitute: 16 + y = 28 -> y = 12.
15. Simplify: sqrt(50) + sqrt(18)
Answer: 8 sqrt(2)
Explanation: Simplify each: sqrt(50) = sqrt(25*2) = 5 sqrt(2). sqrt(18) = sqrt(9*2) = 3 sqrt(2). Add: 5 sqrt(2) + 3 sqrt(2) = 8 sqrt(2).

Essential Algebra Formula Sheet

  • Quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a
  • Slope-intercept: y = mx + b (m = slope, b = y-intercept)
  • Slope formula: m = (y2 - y1) / (x2 - x1)
  • Distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
  • Midpoint formula: ((x1 + x2)/2, (y1 + y2)/2)
  • Area of a circle: A = π r^2
  • Circumference: C = 2π r
  • Area of a triangle: A = (1/2) b h
  • Pythagorean theorem: a^2 + b^2 = c^2
  • Point-slope form: y - y1 = m(x - x1)
  • FOIL: (a + b)(c + d) = ac + ad + bc + bd
  • Difference of squares: a^2 - b^2 = (a - b)(a + b)
  • Perfect square trinomial: a^2 + 2ab + b^2 = (a + b)^2
  • Exponent rule: a^m * a^n = a^(m+n)
  • Exponent rule: (a^m)^n = a^(m*n)

Study Timer

Use the Pomodoro-style timer below to stay focused. A typical session is 25 minutes of study followed by a 5-minute break.

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