Questions and Answers
What is the result of $(−3+2i)(1−i^3)$?
-5-i
What is the result of $(5−7i+i^2)+(8i^3+12)$?
16
What is the result of $(3−i)^3$?
18−26i
What is $3/(2+i)$ simplified?
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What is the result of $−8(7i−3i^2)$?
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What is the system of equations to determine the number of pumpkins and squashes sold?
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Which graph shows the possible volumes of candy in cups a customer may have if each jar has a volume of 3 cups?
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Which graph shows the possible number of bases a player touches given the number of runs he gets?
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What is one possible combination of fence panels Priyanka could buy?
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What is the inequality that must be true for the number of beats counted by Li Qiang?
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What is the system of inequalities that represents the wear on Priyanka's car?
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What is a reasonable conclusion about the mean number of trials for Octopus vulgaris to learn to find food?
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What is the most plausible value for the mean heart rate of all astronauts?
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What is a reasonable claim about the average daily spending of adults in the U.S. based on the provided data?
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What percentage of households in the sampled county lived in the same residence as the previous year?
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Study Notes
Complex Numbers and Equations
- The product of (−3 + 2i) and (1 − i^3) simplifies to -5 - i.
- The expression (5−7i + i^2) + (8i^3 + 12) evaluates to 16.
- The cube of (3−i) results in 18 - 26i.
- Dividing 3 by (2 + i) gives the result of (6 - 3i)/5.
- The expression −8(7i − 3i^2) simplifies to −56i − 24.
Systems of Equations
- A vegetable stand sells pumpkins for $5 each and squashes for $3 each. The system of equations to model the sales is:
- (5p + 3s = 98)
- (p = s + 6)
Volume and Capacity in Context
- Each jar of candy has a volume of 3 cups and contains more than ( \frac{8}{3} ) cups of candy. The correct graph indicating possible volumes is graph B.
Patterns in Sports
- In baseball, a player touches 4 bases to score a run, but may get out from touching bases. The graph showing the relation of bases touched to runs scored is graph C.
Fence Panel Combinations
- Prachi needs between 240 and 260 feet of fencing. A suitable combination is 6 short (6-foot) panels and 26 long (8-foot) panels.
Music Symphony Beats
- A symphony features 2 movements with 3 and 4 beats per measure, respectively. The inequality relating counts in both movements to total measures is:
- ( \frac{x}{3} + \frac{b}{4} \leq 446 )
Vehicle Wear Metrics
- Priyanka's car efficiency is 35 miles per gallon. The wear on her vehicle can be represented with:
- ( w - g \geq \frac{15}{4}m )
- ( m \leq 35g )
Learning Trials in Octopus Study
- In a study of captive Octopus vulgaris, the average trials to learn to find food is 119 with a margin of error of 18. This suggests a range of 101 to 137 trials for all octopi.
Astronaut Heart Rate Study
- Mean heart rate for astronauts during exercise tests was found to be 155 beats per minute, with a 12 beats margin of error at a 90% confidence level, suggesting a plausible mean heart rate of 160 beats per minute.
Spending Habits Poll
- A poll of 14,697 adults showed an average daily spending of $95 in November last year, compared to $91 two years prior, with a margin of error of $4; this indicates consistent spending habits.
Residency Stability in County
- In a county, 84% of households remained in the same residence as the previous year, with a 1.5% margin of error at a 90% confidence level, suggesting stability in residence for 50,000 households.
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Test your skills with these SAT Math practice flashcards. Each card features different math problems involving complex numbers and algebraic expressions, designed to help you prepare for the SAT exam. Master these concepts to enhance your performance in the Math section of the quiz.
