Transcript Document

Introduction to the ACT MATH
Content Covered by the ACT
Mathematics Test
3 sub-scores are based on 6
areas: pre-algebra,
elementary algebra,
intermediate algebra,
coordinate geometry, plane
geometry, and trigonometry.
60 Questions
60 Minutes
If you correctly answer the first
40 and simply guess on the last
20 questions, your score is
roughly a 25.
Your PLAN score will give you an
idea of your predicted score.
Out of a 32… it will give you your
score and percentage correct in
both Algebra and Geometry
We review this with you during
your first Junior Meeting.
Pre-Algebra/Elementary Algebra (20-25%)
Basic operations:
whole numbers, decimals, fractions, and
integers; place value; square roots and
approximations; 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 (15-20%)
Questions 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 (15-20%)
Questions 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.
Plane Geometry (20-25%)
Questions 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.
Coordinate Geometry (15-20%)
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.
Trigonometry (5-10%)
Questions 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.
Example:
What fraction of 2 ⅓ is 1 ⅙?
(What if it said… what fraction of
4 is 2? What would you do?)
LET’S TRY USING THE CALCULATOR!
ALPHA F1
ARROW DOWN TO #2, PRESS ENTER
IN THE FIRST BOX, PUT 1
ARROW OVER TO THE FRACTION
IN THE NUMERATOR PUT 1, THEN ARROW DOWN
IN THE DENOMINATOR PUT 6
PRESS ENTER WHICH GIVES YOU 7/6
NOW PRESS DIVIDE
ANS/BLINKING CURSOR
ALPHA F1
ARROW DOWN TO #2, PRESS ENTER
IN THE FIRST BOX, PUT 2
ARROW OVER TO THE FRACTION
IN THE NUMERATOR PUT 1, THEN ARROW DOWN
IN THE DENOMINATOR PUT 3
ENTER
CLICK ON THE
ARROW NEXT
TO REPORTS
TESTS
LESSONS
HASKELL STRATEGIES
Tip #1: Make sure you answer what
the question is asking!
________________________________
Example: 5x + 40 ÷ 2x =
Solve for the measure of the smaller angle
(Reminder: Are you looking for x or 2x?):
a. 10
b. 20
c. 30
d. 40
Tip #2: Make sure you are using
common sense – that your answer
MAKES SENSE
_______________________________
Example:
Pair of skiis normally costs $800. They
are on sale for 30% off. What is the
new price?
The new price is 70% of the original.
.7 x 800
Tip #3: Pictures are almost always
drawn to scale. Make sure that your
figure also MAKES SENSE VISUALLY!
_______________________________
Example:
The angle < is NOT 90 degrees
Tip #4: Learn to recognize your
danger zones… where do you
normally make careless mistakes? If
you can recognize where you tend to
mess up, you can put the brakes on
and slow down on that problem.
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Example: Solve for x: -8 (x-5)
The careless mistake is to forget the
negative when distributing to the -5
Tip #5:
Balance SPEED with ACCURACY
When you are running out of
time, skim the later problems to
see if any of them are easier for
you to answer
Tip #6: Temptation on the
tough problems is to waste
time trying to figure it out.
First – Ask Yourself: Is this as
tough as they are making it
look? Give it a few seconds.
Tip #7: This strategy ONLY works if
you have a question with a lot of text
AND have a geometric diagram…
save yourself some time and
headache by just reading the last
sentence (80% of the time you don’t
need the information in the word
problem).
Before you guess,
try these techniques:
1) Plug in Answers
(pg. 420, #9)
2) Use your own numbers
3) Graph It (on your calculator)
For the MEDIUM problems,
stop and THINK. Really use
your head. Figure out what
math to do. (select the
proper tool)
(x+a) (x+b) = 0
x² + ab + bx + ab = 0 NO
On every section EXCEPT Math,
force your timing to stay on PACE:
English = 9 min/passage
Reading = 9 min/passage
Science = 5 min/passage*
(Hypothesis is 7 questions, typically you need more time)
Writing = 5 min to plan
5 min per paragraph
This is a DAMAGE CONTROL
Final Tip:
Keep things in perspective. Do your
best but know that your score is
not going to make or break your
future.