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Questions and Answers
What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?
What is the sum of the first 4 terms of the arithmetic sequence in which the 6th term is 8 and the 10th term is 13?
14.5
The solution set of which of the following equations is the set of real numbers that are 5 units from −3?
The solution set of which of the following equations is the set of real numbers that are 5 units from −3?
Which of the decimals −0.057, −0.57, −0.55, 0.073, 0.57 is the least?
Which of the decimals −0.057, −0.57, −0.55, 0.073, 0.57 is the least?
-0.57
For the fraction, assume that p is a prime number and q is not a multiple of p. For which of the following values of q will the decimal equivalent be a repeating decimal?
For the fraction, assume that p is a prime number and q is not a multiple of p. For which of the following values of q will the decimal equivalent be a repeating decimal?
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What is the formula for the Quadratic Formula?
What is the formula for the Quadratic Formula?
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What is the surface area of a cylinder?
What is the surface area of a cylinder?
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What is the volume of a cylinder?
What is the volume of a cylinder?
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What is the surface area of a sphere?
What is the surface area of a sphere?
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What is the volume of a sphere?
What is the volume of a sphere?
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What is the Discriminant in a quadratic equation?
What is the Discriminant in a quadratic equation?
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In nCr, order does matter.
In nCr, order does matter.
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In nPr, order does not matter.
In nPr, order does not matter.
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What is the equation of a circle?
What is the equation of a circle?
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What is the equation of an ellipse?
What is the equation of an ellipse?
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What is sin²x + cos²x equal to?
What is sin²x + cos²x equal to?
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What is the value of the sin graph at 0?
What is the value of the sin graph at 0?
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What does the cos graph start at?
What does the cos graph start at?
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What is the tangent graph described as?
What is the tangent graph described as?
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What are log rules abbreviated as?
What are log rules abbreviated as?
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A package of 25 baseball cards sells for $2.00, and a package of 100 cards sells for $6.50. The cards in the larger package sell for how many cents less per card than the cards in the smaller package?
A package of 25 baseball cards sells for $2.00, and a package of 100 cards sells for $6.50. The cards in the larger package sell for how many cents less per card than the cards in the smaller package?
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When 27 is divided by 6, the remainder is 3, and when 27 is divided by 7, the remainder is 6. What is the next greatest positive integer that has a remainder of 3 when divided by 6 and a remainder of 6 when divided by 7?
When 27 is divided by 6, the remainder is 3, and when 27 is divided by 7, the remainder is 6. What is the next greatest positive integer that has a remainder of 3 when divided by 6 and a remainder of 6 when divided by 7?
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According to recent estimates, the Milky Way galaxy contains about 400 billion stars. Which of the following is 400 billion expressed in scientific notation?
According to recent estimates, the Milky Way galaxy contains about 400 billion stars. Which of the following is 400 billion expressed in scientific notation?
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In a basketball passing drill, if 5 players stand evenly spaced around a circle, on what pass will the designated first passer be the receiver?
In a basketball passing drill, if 5 players stand evenly spaced around a circle, on what pass will the designated first passer be the receiver?
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How many distinct real roots (solutions) does the equation x⁴ - x = 0 have?
How many distinct real roots (solutions) does the equation x⁴ - x = 0 have?
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A movie was shown 6 times every day from November 24 through December 19. How many times was the movie shown in total?
A movie was shown 6 times every day from November 24 through December 19. How many times was the movie shown in total?
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If (3,5) is a point on the graph of the function f, which of the following points must be on the graph of the inverse function f⁻¹?
If (3,5) is a point on the graph of the function f, which of the following points must be on the graph of the inverse function f⁻¹?
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For any x and y, sin(x + y) = (sin x)(cos y) + (cos x)(sin y). What does sin(π/2 + a) equal?
For any x and y, sin(x + y) = (sin x)(cos y) + (cos x)(sin y). What does sin(π/2 + a) equal?
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A stock's price is expected to vary between $10 and $20 over the next 6 months. What is the theoretical probability that I will make money purchasing this stock?
A stock's price is expected to vary between $10 and $20 over the next 6 months. What is the theoretical probability that I will make money purchasing this stock?
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In 2015, total rainfall in central city was 13 inches less than in 2000. In 2016, it was 33 inches greater than in 2000. What was the difference in rainfall from 2015 to 2016?
In 2015, total rainfall in central city was 13 inches less than in 2000. In 2016, it was 33 inches greater than in 2000. What was the difference in rainfall from 2015 to 2016?
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A park ranger records the height of a river daily. If the river was 14 feet at 7 pm and fell at 1.5 feet per day, when will it first exceed 14 feet?
A park ranger records the height of a river daily. If the river was 14 feet at 7 pm and fell at 1.5 feet per day, when will it first exceed 14 feet?
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If g(n) = -3/(n+2) and h(n) = -n, for what real value of x is g(x) = h(x)?
If g(n) = -3/(n+2) and h(n) = -n, for what real value of x is g(x) = h(x)?
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A teacher uses a 40 inch long roll of string to form a border. What is the maximum area she can reserve?
A teacher uses a 40 inch long roll of string to form a border. What is the maximum area she can reserve?
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A house painting company has three employees. How many hours will it take the third employee to finish painting the remainder of the house by himself?
A house painting company has three employees. How many hours will it take the third employee to finish painting the remainder of the house by himself?
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Study Notes
Arithmetic Sequences
- The sum of the first 4 terms of an arithmetic sequence with the 6th term as 8 and the 10th term as 13 is 14.5.
Absolute Value Equations
- The equation |x + 3| = 5 represents values 5 units from -3.
Decimal Comparisons
- Among the decimals -0.057, -0.57, -0.55, 0.073, and 0.57, -0.57 is the least.
Repeating Decimals
- For a prime number p and a non-multiple q, q = 65 results in a repeating decimal with at least one nonzero repeating digit.
Quadratic Formula
- The quadratic formula is x = -b ± √(b² - 4ac)/2a, used to find roots of quadratic equations.
Cylinder Formulas
- Surface area of a cylinder: 2πrh + 2πr².
- Volume of a cylinder: V = πr²h.
Sphere Formulas
- Surface area of a sphere: 4πr².
- Volume of a sphere: 4/3πr³.
Discriminant
- The discriminant for a quadratic equation is defined as b² - 4ac, used to determine the nature of roots.
Combinatorics
- nCr calculates combinations where order does not matter.
- nPr calculates permutations where order does matter.
Geometry Equations
- Circle equation: (x - h)² + (y - k)² = r².
- Ellipse equation: (x - h)²/a² + (y - k)²/b² = 1.
Trigonometric Identities
- sin²x + cos²x = 1.
Graph Behavior
- The sine graph value is 0 at x = 0.
- The cosine graph starts at 1.
Tangent Graph Behavior
- The tangent graph is represented by the acronym ALOHA.
Logarithm Rules
- Key acronym for logarithm rules is MA DS PM.
Cost per Card Calculation
- A package of 100 baseball cards costs 6.50, equating to 1.5 cents less per card compared to a package of 25 costing 2.00.
Remainder Problems
- The next greatest positive integer with a remainder of 3 when divided by 6 and a remainder of 6 when divided by 7 is 69.
Scientific Notation
- 400 billion expressed in scientific notation is 4 x 10^11.
Basketball Passing Drill
- In a passing drill with restrictions, the designated player becomes a receiver for the first time on the 5th pass.
Real Roots of Equations
- The equation x⁴ - x = 0 has 2 distinct real roots.
Movie Showings
- A movie shown 6 times daily from November 24 to December 19 totals 156 showings.
Inverse Function Points
- If (3, 5) is a point on the graph of f, then (5, 3) must be on the graph of its inverse f⁻¹.
Trigonometric Sine Rule
- For sin(x + y), the identity is sin(x)cos(y) + cos(x)sin(y). Therefore, sin(π/2 + a) = cos(a).
Stock Probability
- The theoretical probability of making money on a stock priced between $10 and $20, currently at $12, is 73%.
Rainfall Comparison
- The difference in rainfall between 2015 (13 inches less) and 2016 (33 inches more) results in a difference of +46 inches.
River Height Calculation
- A river’s height, decreasing then increasing due to rain, first exceeds 14 feet on Sunday at 7 am.
Function Intersection
- For g(n) = -3/(n+2) and h(n) = -n, the real values of x where g(x) = h(x) are x = 1 and x = -3.
Maximum Area from Perimeter
- A 40-inch roll of string used as a perimeter can form a maximum rectangular area of 100 square inches.
Painting Task Completion
- It will take the third painter 3.00 hours to finish painting the remaining part of the house.
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Description
Test your knowledge with these ACT math practice questions. The quiz includes various concepts such as arithmetic sequences, equations, and real numbers. It's a great way to prepare for the math section of the ACT exam.
