Digital SAT Math Walkthrough

Jul 23, 2024

Digital SAT Math Walkthrough

Introduction

  • Perfect scores on back-to-back SAT Math sections
  • Walkthrough covers Digital SAT Practice Test 1 (Math Section 1 & 2)
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  • Starting with Section 1

Section 1 Walkthrough

  1. Question 1:

    • What is ten percent of 470?
    • Solution: 470 x 0.1 = 47
    • Answer: B

  2. Question 2:

    • Which equation has the same solution as the given equation?
    • Solution: Subtract 6 from both sides; 4X = 12
    • Answer: C

  3. Question 3:

    • Surfboard rental cost problem
    • Solution: 25 + 10T ≤ 75
    • Answer: D

  4. Question 4:

    • Function G(x) = x² + 9, find x when G(x) = 25
    • Solution: x² = 16; x = 4
    • Answer: A

  5. Question 5:

    • Probability of rolling a 2 on a 14-sided die
    • Solution: 1/14
    • Answer: A

  6. Question 6:

    • Conversion of posters per minute to posters per hour
    • Solution: 42 posters/minute x 60 minutes = 2520 posters/hour
    • Answer: 2520

  7. Question 7:

    • Find f(x) when x = 4 for f(x) = 7x + 2
    • Solution: f(4) = 30
    • Answer: 30

  8. Question 8:

    • Equation for assignment points
    • Solution: 1x + 3y = 70
    • Answer: D

  9. Question 9:

    • Similar triangles problem
    • Solution: Corresponding angles Q and M both measure 53°
    • Answer: B

  10. Question 10:

    • Solution for the system of equations, find x
    • Solution: Substitution method
    • Answer: C

  11. Question 11:

    • Linear model for data in scatter plot
    • Solution: Identify correct linear form
    • Answer: B

  12. Question 12:

    • Finding zero values in a cubic graph
    • Solution: 3 zeros
    • Answer: C

  13. Question 13:

    • Cost math problem with party hats and cupcakes
    • Solution: Solve for number of cupcakes using total cost
    • Answer: 41

  14. Question 14:

    • Factor the given quadratic equation
    • Solution: Possible roots are 2 and -12
    • Answer: 2

  15. Question 15:

    • Exponential growth problem with bacteria
    • Solution: Use exponential growth formula, 96 million cells after 15 hours
    • Answer: D

  16. Question 16:

    • Simplifying algebraic expressions
    • Solution: Factor out common terms
    • Answer: 6x²y²(2 + x⁶)

  17. Question 17:

    • Equation representing park and residential area trees
    • Solution: Average number of trees per hectare in the park
    • Answer: A

  18. Question 18:

    • Relationship between two stock shares in graph form
    • Solution: Identify the slope-intercept form
    • Answer: B

  19. Question 19:

    • Radius and area relationship in circles
    • Solution: Ratio of the areas based on radius, 1849
    • Answer: 1849

  20. Question 20:

    • Finding max data value in a frequency table
    • Solution: 14 is the max value
    • Answer: 14

  21. Question 21:

    • Circle with given endpoints
    • Solution: Calculate radius using endpoints
    • Answer: 5

  22. Question 22:

    • Angle measure conversions and calculations
    • Solution: Compute new angle in degrees
    • Answer: 195

  23. Question 23:

    • Area conversion from square miles to square yards
    • Solution: Multiply baseline value by 1760 squared
    • Answer: 1,350,5536

  24. Question 24:

    • Translation of line H to line K
    • Solution: Find new x-intercept
    • Answer: -17/6

  25. Question 25:

    • Quadratic and linear graph intersection points
    • Solution: Verify using Desmos for accurate plotting
    • Answer: -79.75

  26. Question 26:

    • Perpendicular line equations
    • Solution: Use coefficients to identify perpendicular lines
    • Answer: B

Section 2 Walkthrough

Starting Section 2

  1. Question 1:

    • Salary calculation problem
    • Solution: 39P
    • Answer: A

  2. Question 2:

    • Time calculation in a biking problem
    • Solution: 5.7X
    • Answer: D

  3. Question 3:

    • Value of y in the given system of equations
    • Solution: Add equations; Y equals 6
    • Answer: B

  4. Question 4:

    • Speed after a certain time
    • Solution: Plug in 5 for t
    • Answer: 55

  5. Question 5:

    • Pythagorean theorem for right triangle
    • Solution: Calculate C using 4² + 5²
    • Answer: √41

  6. Question 6:

    • Solve given algebraic equation
    • Solution: X equals 40
    • Answer: 40

  7. Question 7:

    • X-intercept identification
    • Solution: Where Y equals zero
    • Answer: 7

  8. Question 8:

    • Y-intercept of defined function
    • Solution: Plug in X equals 0
    • Answer: -2

  9. Question 9:

    • Transformation of functions
    • Solution: Y equals 7X³ - 2
    • Answer: D

  10. Question 10:

    • Solve system of equations for given ordered pair
    • Solution: Substitute X equals 7 for solving
    • Answer: A

  11. Question 11:

    • Simplifying algebraic expressions
    • Solution: Combine like terms
    • Answer: X³ + 10X

  12. Question 12:

    • Solve for N in polynomial function
    • Solution: Using given conditions
    • Answer: 2

  13. Question 13:

    • Angle relationships in intersecting lines
    • Solution: Calculate unknown angles
    • Answer: 70

  14. Question 14:

    • Mean value calculation
    • Solution: Sum of values divided by count
    • Answer: 10

  15. Question 15:

    • Growth factor interpretation in functions
    • Solution: Identify coefficient for initial value
    • Answer: A

  16. Question 16:

    • Minimum value of a quadratic function
    • Solution: Minimum value is 55
    • Answer: 55

  17. Question 17:

    • Linear vs exponential growths
    • Solution: Identify growth pattern
    • Answer: Increasing exponentially

  18. Question 18:

    • Population increase problem
    • Solution: Calculate K to reflect 7% growth
    • Answer: 1.07

  19. Question 19:

    • Equivalent expressions
    • Solution: Simplify using given conditions
    • Answer: B

  20. Question 20:

    • Total attendees without exceeding budget
    • Solution: Solve for maximum A
    • Answer: 16

  21. Question 21:

    • Absolute value problem
    • Solution: Consider absolute value properties
    • Answer: 28

  22. Question 22:

    • Volume difference between cube and sphere
    • Solution: Calculate using volume formulas
    • Answer: 149796

  23. Question 23:

    • Diameter of a given circle equation
    • Solution: Calculate using circle properties
    • Answer: 8

  24. Question 24:

    • Identify correct function for given exponential model
    • Solution: Analyze given formulas
    • Answer: C

  25. Question 25:

    • Population of squirrels model
    • Solution: Analyze yearly increase model
    • Answer: B

  26. Question 26:

    • Identifying perpendicular lines in a given set
    • Solution: Analyze given equations
    • Answer: B

  27. Question 27:

    • Equation with no real solutions
    • Solution: Use discriminant method
    • Answer: 289

Conclusion

  • Covered Section 1 and 2 of Digital SAT Practice Test 1 Math
  • Key topics include algebra, functions, geometry, and exponential growth
  • Emphasis on transformation, simplification, and discriminant methods
  • Tips: use Desmos for complex graphs, always set up equations correctly to avoid mistakes