Mathematics High School Entry Test Review

Sep 4, 2024

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Mathematics Entry Test Practice

Introduction

  • Topic: Practice for the high school mathematics entry test
  • Objective: Review of necessary mathematical knowledge for high school entry
  • Applicable to: scientific secondary school, professional institute, etc.

Exercise 1: Proportions

  • Problem: 8 workers take 5 hours to build a wall; how many workers are needed to complete it in 2 hours?
  • Proportion: 8 : x = 2 : 5
  • Solution:
    • Solution: x = (8 * 5) / 2 = 20 workers

Exercise 2: Discount on a Jacket

  • Problem: 150€ jacket with a 30% discount
  • Discount Calculation:
    • Discount: 150 * 30/100 = 45€
    • Final Price: 150 - 45 = 105€

Exercise 3: Calculations with Expressions

  • Problem: Subtract 20 from the difference between four times 80 and twice 50
  • Calculations:
    • Four times 80: 320
    • Twice 50: 100
    • Difference: 320 - 100 = 220
    • Final Result: 220 - 20 = 200

Exercise 4: GCD and LCM

  • Numbers: 360 and 50
  • Prime Factorization:
    • 360 = 2^3 * 3^2 * 5
    • 50 = 2 * 5^2
  • GCD: 2 * 5 = 10
  • LCM: 2^3 * 3^2 * 5^2 = 1800

Exercise 5: Expressions with Relative Numbers

  • Expression: (6 - 6[10 - 2×3 + 2 - 3(-2)]) / -3
  • Calculations and Simplifications:
    • Final Result: 30

Exercise 6: Fractions

  • Expression: (9/3 + 2/3) × 2/1 - (7/3 × 11/3 - 10/9)
  • Calculations:
    • Final Result: -1/9

Exercise 7: Properties of Powers

  • Problem: (2^5 / 3)^4 / 2^17
  • Final Result: 1/8

Geometry: Angles

  • Identification of acute and obtuse angles:
    • Acute: α, β, γ
    • Obtuse: δ
  • Pairs of consecutive and adjacent angles:
    • Consecutive: α with β, β with γ
    • Adjacent: δ with γ

Exercise 8: Cube Problem

  • Problem: Calculate the volume of a cube with an edge equal to the hypotenuse of a right triangle with legs 3 and 4
  • Hypotenuse Calculation:
    • Hypotenuse: √(3^2 + 4^2) = 5
  • Volume of the cube: 5^3 = 125

Exercise 9: First-Degree Equations

  • Problem: Solve 4x + 8 - 10 = x
  • Solution:
    • x = 2/3

Fundamental Review Topics

  • Proportions
  • Percentages
  • Expressions with relative numbers
  • GCD and LCM
  • Properties of powers
  • Geometry of angles
  • Pythagorean Theorem
  • Solving first-degree equations

Conclusion

  • Importance of knowing these topics to face the high school entry test
  • Invitation to comment and discuss in the video's comments