ACT Math Practice Questions

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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?

14.5

The solution set of which of the following equations is the set of real numbers that are 5 units from −3?

|x + 5| = 3

|x - 5| = 3

|x + 3| = 5 (correct)

|x + 5| = -3

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?

65 Signup and view all the answers

What is the formula for the Quadratic Formula?

x = -b ± √(b² - 4ac)/2a Signup and view all the answers

What is the surface area of a cylinder?

2πrh + 2πr² Signup and view all the answers

What is the volume of a cylinder?

V = πr²h Signup and view all the answers

What is the surface area of a sphere?

4πr² Signup and view all the answers

What is the volume of a sphere?

4/3πr³ Signup and view all the answers

What is the Discriminant in a quadratic equation?

b² - 4ac Signup and view all the answers

In nCr, order does matter.

False Signup and view all the answers

In nPr, order does not matter.

False Signup and view all the answers

What is the equation of a circle?

(x-h)² + (y-k)² = r² Signup and view all the answers

What is the equation of an ellipse?

(x-h)²/a² + (y-k)²/b² = 1 Signup and view all the answers

What is sin²x + cos²x equal to?

1 Signup and view all the answers

What is the value of the sin graph at 0?

0 Signup and view all the answers

What does the cos graph start at?

1 Signup and view all the answers

What is the tangent graph described as?

ALOHA Signup and view all the answers

What are log rules abbreviated as?

MA DS PM Signup and view all the answers

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?

1 1/2 Signup and view all the answers

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?

69 Signup and view all the answers

According to recent estimates, the Milky Way galaxy contains about 400 billion stars. Which of the following is 400 billion expressed in scientific notation?

4 x 10^11 Signup and view all the answers

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?

5th Signup and view all the answers

How many distinct real roots (solutions) does the equation x⁴ - x = 0 have?

2 Signup and view all the answers

A movie was shown 6 times every day from November 24 through December 19. How many times was the movie shown in total?

156 Signup and view all the answers

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?

(5,3) Signup and view all the answers

For any x and y, sin(x + y) = (sin x)(cos y) + (cos x)(sin y). What does sin(π/2 + a) equal?

cos a Signup and view all the answers

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?

73% Signup and view all the answers

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?

+46 Signup and view all the answers

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?

Sunday at 7am Signup and view all the answers

If g(n) = -3/(n+2) and h(n) = -n, for what real value of x is g(x) = h(x)?

1 and -3 only Signup and view all the answers

A teacher uses a 40 inch long roll of string to form a border. What is the maximum area she can reserve?

100 Signup and view all the answers

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?

3.00 Signup and view all the answers

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.