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Hi parents and students! This is an introduction to what you’ll be needing to know by the end of the first Algebra 1 semester. My courses cover all of the common core requirements (the syllabus for semester 1 is here, and semester 2 is here!) and prepare my students to think critically. Not only do I want your student to know the material in my class, I want them to succeed in all future classes and opportunities. Please try out this sample test to see what your child will be learning this semester!

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1. What are the roots of x*(x-5)*(x+12) = 0
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2. Identify the inequality of [ 3 < -x + 4 < 15 ] on a number line.
Solve the inequality first!
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3. Identify the graph of the system of inequalities [ x – 2y ≥ 4 ] & [ 3y + x > 18 ]
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4. In a three lap race a driver wishes to have at least a 180 mph average. If his speed on the first lap was 165 mph and 181 mph on the second lap, what must his speed be on the third lap so that the desired average is reached?
Average
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5. Factor [ 4x² – 49 ]
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6. Expand [ 6x*(x – 8)*(2x + 5) ]
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7a. When using the quadratic formula to solve for [ x² = -11x – 30 ], what is the value for b?
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7b. Solve [ x² = -11x – 30] using the quadratic formula.
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8. Identify the graph of [ y = (5.2)^(x) – 3 ]
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9. Simplify [ -28p⁷q⁵/(2p⁴q⁶) ]
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10. Simplify [ (16a⁴b² – 8a²b² – 2a⁴b²) / 4 ]
Group, factor and cancel
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11. Simplify [ 42 / (2√7) ]
Remove the root from the denominator
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12. Factor [ -11v + 22v² – 121v³ ]
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13. Factor [ (-4x²b³)⁴ – (-2x⁴b²)³ ]
Distribute the exponents and find a GCF.
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14. Simplify [ (30c⁻⁵) / (12c⁻²) ]
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15. Factor [ -2x² – 14x + 36 ]
Box method for factoring
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16. Factor [ p² + 2p – 24 ]
Box method for factoring
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17. Factor [ w² – 12w + 36 ]
Box method for factoring
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18. Factor [ y² + 18y + 81 ]
Box method for factoring
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19. Find the zeros of [ 4x² + 35x – 9 = 0 ]
Factor and solve
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20. Which of the following equations has a minimum point of (0, -4)?
Think of the graph of a parabola!
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21. What are the roots of [ 2x² – 6x + 1 = 0 ]
Quadratic formula
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22. Identify the graphs of [ y = 4x² ] & [ y = -.1x² ] on the same coordinate plane.
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23. Simplify [ √24 – 8√54 ]
Can you make them the same root?
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24a. Identify the equation of the parabola with stretch factor, a = -2, and a maximum point of (0, -4).
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24b. Identify the graph of the equation.
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25. How many roots does [ y = .5x² – 2x – 7 ] have?
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26. A car purchased for $25,000 will depreciate by 6% per year. How much will it be worth in 4 years?
A(t) = A₀(1 – r)^t
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27a. A pile of nickels and quarters is worth $4.40. There are 32 coins in total. What is the system of equations used to solve this problem?
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27b. Solve the system. How many quarters are there?
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28. The lawn can be mowed by Bo in 45 minutes while it takes Larry a full hour to do the same lawn. If both work together, how long will it take them to mow the lawn?
Find the rate for each. Add them together and solve.
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29. Find the distance between (4.7, -2.8) and (3.02, 17)
d = √((x₁-x₂)² + (y₁-y₂)²)
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30. What is the midpoint of the line segment connecting (4, -1) and (2, 15)?
mp = ((x₁ + x₂)/2, (y₁+y₂)/2)
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