University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2019
Views:

429

Pages:

6
Author:

Lamghari6kx

H. Geometry Summer Math Packet Due by the 1st week of school. These are all review topics of Algebra 1 and should be known at mastery level. These topics will be tested the first week of school. Simplify the following: 1. \(4\sqrt{7}+3\sqrt{5}+5\sqrt{7}\) 9√7 + 3√5 2. \(5\sqrt{10}-3\sqrt{5}+4\sqrt{10}\) 9√10 - 3√5 3. \(4\sqrt{10}\cdot\sqrt{10}\) 4√100 = 4 * 10 = 40 4. \(\sqrt{6}(-2\sqrt{2}-\sqrt{3})\) -2√12 - √18 -2√4√3 - √9√2 -4√3 - 3√2 5. \(\sqrt[3]{48p^2q^3r^4}\) ∛(3⋅2⋅2⋅2⋅2p²q³r⁴) 2qr³∛6p²r 6. \(\sqrt{x^6y}\bullet\sqrt{x^5y^4}\) √(x¹¹y⁵) x⁵y²√xy 7. \(\sqrt{10}(\sqrt{2}+4)\) √20 + 4√10 2√5 + 4√10 8. \(-3\sqrt{6p^2}\bullet4\sqrt{12p}\) -12√72p³ -12√9⋅4⋅2p³ = -12⋅3⋅2p√2p -72p√2p 9. \(5\sqrt{3x}(2\sqrt{x}-3\sqrt{3x^3})\) 10√3x² - 15√9x⁴ 10x√3 - 45x² 10. \(\frac{\sqrt{32}}{\sqrt{2}}\) √(32/2) = √16 = 4 11. √(15/10) = √(3/2) = √3/√2 12. 2√5/√3 = (2√5/√3)(√3/√3) = 2√15/3 13. \(\frac{-2\sqrt{3}}{2\sqrt{3}}\) = \(\frac{-\sqrt{3}}{3}\) 14. \(-2x \cdot -4x^4y^3\) 8x⁵y³ 15. \(3x^4 \cdot 4u^2\) 12x⁴u² 16. \(-3x^2y^3 \cdot -3x^4 \cdot -3x^4\) -27x¹¹y³ 17. \(3x^2 \cdot -2u^2\) -6u²x² 18. \((-2)^2\) 4 19. \((4^3)^4\) 4¹² 20. \((2^1)^3\) 2³ 21. \((-2x^3)^2\) (-2)²(x³) = 4x⁶ 22. \((-x)^3\) -x³ 23. \((-2n)^2\) 4n² 24. \((3b^5)^4\) 81b²⁰ 25. \((-3y)^4v^8\) 81y⁴v⁸ 26. \((-4x^4y^4)^4\) 256x¹⁶y¹⁶ 27. \((-4x^4y^3)^4\) -64x¹⁶y¹² 28. \((-5y^6)^2\) 25y¹² 43. 5x² + 15x - 20 5(x² + 3x - 4) 5(x + 4)(x - 1) 44. 25x² - 49y² (5x - 7y)(5x + 7y) 45. 6x² + 11x + 15 3(2x² + 3x + 5) Nothing multiplies to 5 and adds to 3. So this is prime. 46. 3x² + 9x - 15 3(x² + 3x - 5) Nothing multiplies to -5 and adds to 3. So this is prime. 47. 10p² - 55p + 60 5(2p² - 11p + 12) 5(2p - 3)(p - 4) 48. Is (2, -4) a solution to the following system? 2x - 2y = 8 x + y = 4 2(2) - 2(-4) = 8 4 + 8 = 8 12 ≠ 8 Not a solution 49. Is (2, 1) a solution to the following system? 4x + y = 9 3x + 14y = 20 4(2) + 1 = 9 8 + 1 = 9 9 = 9 3(2) + 14(1) = 20 6 + 14 = 20 20 = 20 Yes 50. Find the equation of the line that is parallel to y = -½x + 4 and passes through (2, 8). y - y₁ = m(x - x₁) y - 8 = -½(x - 2) y - 8 = -½x + 1 y = -½x + 7 51. Find the equation of the line that is parallel to 2x + 3y = 6 and passes through (4, 1). 2x + 3y = 6 3y = -2x + 6 y = -⅔x + 2 The line will have m = -⅔ y - 1 = -⅔(x - 4) y - 1 = -⅔x + 8/3 y = -⅔x + 11/3