M A T H T U T O R I N G
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is a national college admissions examination that consists of subject area tests in:
The ACT Plus Writing includes the four subject area tests plus a 30-minute Writing Test.
ACT results are accepted by all 4-year colleges and universities in the U.S.
The ACT includes 215 multiple-choice questions and takes approximately 3 hours and 30 minutes to complete,
including a short break (or just over four hours if you are taking the ACT Plus Writing).
Actual testing time is 2 hours and 55 minutes (plus 30 minutes if you are taking the ACT Plus Writing).
The ACT is administered on six test dates within the 50 United States and District of Columbia-in September,
October, December, February, April, and June. In other locations, the ACT is administered on five test
dates-all of the above dates except September.
In the Mathematics Test, three subscores are based on six content areas:
The ACT Mathematics Test is a 60-question, 60-minute test designed to measure the mathematical skills
students have typically acquired in courses taken by the end of 11th grade.
.The test presents multiple-choice questions that require you to use reasoning skills to solve practical
problems in mathematics.
You need knowledge of basic formulas and computational skills to answer the problems, but you aren't
required to know complex formulas and perform extensive computation.
" Pre-Algebra (23%). Questions in this content area are based on basic operations
using whole numbers, decimals, fractions, and integers; place value; square roots and
approximations; the concept of exponents; scientific notation; factors; ratio, proportion,
and percent; linear equations in one variable; absolute value and ordering numbers by value;
elementary counting techniques and simple probability; data collection, representation,
and interpretation; and understanding simple descriptive statistics.
" Elementary Algebra (17%). Questions in this content area are based on properties of
exponents and square roots, evaluation of algebraic expressions through substitution,
using variables to express functional relationships, understanding algebraic operations,
and the solution of quadratic equations by factoring.
" Intermediate Algebra (15%). Questions in this content area are based on an understanding
of the quadratic formula, rational and radical expressions, absolute value equations and inequalities,
sequences and patterns, systems of equations, quadratic inequalities, functions, modeling, matrices,
roots of polynomials, and complex numbers.
" Coordinate Geometry (15%). Questions in this content area are based on graphing and the
relations between equations and graphs, including points, lines, polynomials, circles,
and other curves; graphing inequalities; slope; parallel and perpendicular lines; distance; midpoints; and conics.
" Plane Geometry (23%). Questions in this content area are based on the properties and relations
of plane figures, including angles and relations among perpendicular and parallel lines;
properties of circles, triangles, rectangles, parallelograms, and trapezoids; transformations;
the concept of proof and proof techniques; volume; and applications of geometry to three dimensions.
" Trigonometry (7%). Questions in this content area are based on understanding trigonometric
relations in right triangles; values and properties of trigonometric functions; graphing
trigonometric functions; modeling using trigonometric functions; use of trigonometric
identities; and solving trigonometric equations.
|SAMPLE MATHEMATICS TEST QUESTIONS
|An actual ACT Mathematics Test
contains 60 questions to be answered in 60 minutes
|1. A car averages 27 miles per gallon. If gas costs $4.04 per gallon,
which of the following is closest to how much the gas would cost for
this car to travel 2,727 typical miles?
|2.When x = 3 and y = 5, by how much does the value of 3x2 - 2y exceed the value of 2x2 - 3y ?
|3.What is the value of x when 2x + 3 = 3x - 4 ?
|4.What is the greatest common factor of 42, 126, and 210 ?
|5.Sales for a business were 3 million dollars more the second
year than the first, and sales for the third year were double
the sales for the second year. If sales for the third year were
38 million dollars, what were sales, in millions of dollars,
for the first year?
|6.The length, in inches, of a box is 3 inches less than twice
its width, in inches. Which of the following gives the length, L inches, in
terms of the width, w inches, of the box?
||F.L = 1/2 w + 3
G.L = w + 3
H.L = w - 3
J.L = 2w + 3
K.L = 2w - 3
|7.How many irrational numbers are there between 1 and 6 ?
K. Infinitely many
|8.A typical high school student consumes 67.5 pounds of
sugar per year. As part of a new nutrition plan, each member of a track team
plans to lower the sugar he or she consumes by at least 20% for the coming year.
Assuming each track member had consumed sugar at the level of a typical high
school student and will adhere to this plan for the coming year, what is the
maximum number of pounds of sugar to be consumed by each track team member
in the coming year?
|9.Which of the following is an equation of the circle with
its center at (0,0) that passes through (3,4) in the standard (x,y) coordinate plane?
||F.x - y = 1
G.x + y = 25
H.x^2 + y = 25
J.x^2 + y^2 = 5
K.x^2 + y^2 = 25
|10.Taher plans to cut the 3 pieces of lumber for the flower bed border
from a single piece of lumber. Each cut takes inch of wood off the length of the piece
of lumber. Among the following lengths, in inches, of pieces of lumber, which is the
shortest piece that he can use to cut the pieces for the flower bed border?