Mel Friedman - Praxis II Middle School Mathematics (0069)
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- Book:Praxis II Middle School Mathematics (0069)
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- Year:2013
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REAs PRAXIS II Middle School Mathematics (0069) Test Prep Gets You Certified and in the Classroom!
Our popular PRAXIS II test prep is designed to help you master the information on the Middle School Mathematics exam. Its perfect for college students, teachers, and career-changing professionals who are seeking certification as Middle School Mathematics teachers.
Written by mathematics experts, this comprehensive review guides you through all the mathematics categories tested on the exam: arithmetic and basic algebra, geometry and measurement, functions and graphs, data probability and statistical concepts, discrete math, and mathematical reasoning.
Three full-length practice tests simulate the actual PRAXIS exam. Each practice test is balanced to include every type of question, subject area, and skill tested on the exam. Every practice test comes with detailed feedback on every question. We dont just say which answers are rightwe explain why the other answer choices are wrongso youll be prepared on test day. This complete test prep package comes with a customized study schedule and REAs test-taking strategies and tips.
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We would like to thank Pam Weston, Vice President, Publishing, for setting the quality standards for production integrity and managing the publication to completion; Larry Kling, Vice President, Editorial, for his editorial direction; Kathleen Casey, Senior Editor, for project management and preflight editorial review; Christine Saul, Senior Graphic Artist, for cover design; and Maureen Mulligan, Graphic Artist, for post-production file mapping.
We also gratefully acknowledge the team at Transcend Creative Services (TCS) for typesetting the manuscript.
Mel H. Friedman, M.S., is REAs Lead Mathematics Editor. He has a diversified background in mathematics and has developed test items for Educational Testing Service. His teaching experience is at both the high school and college levels.
Practice Test 1
| ( a, b ) | { x: a < x < b } |
| [a, b ) | { x: a x < b } |
| (a, b ] | { x: a < x < b } |
| [a, b ] | { x: a x b } |
| gcd ( m, n ) | greatest common divisor of two integers m and n |
| lcm ( m, n ) | least common multiple of two integers m and n |
| [x] | greatest integer m such that m x |
| m k(mod n ) | m and k are congruent modulo n ( m and k have the same remainder when divided by n, or equivalently, m k is a multiple of n ) |
| f 1 | inverse of an invertible function f ( not the same as  ) |
 | right-hand limit of f (x); limit of f (x) as x approaches a from the right |
 | left-hand limit of f( x); limit of f (x) as x approaches a from the left |
| the empty set | |
| x S | x is an element of set S |
| S T | set S is a proper subset of set T |
| S T | either set S is a proper subset of set T or S = T |
| S U T | union of sets S and T |
| S T | intersection of sets S and T |
Discrete Mathematics
A relation on a set S is reflexive if x x for all x S symmetric if x y y x for all x, y S transitive if (x y and y z ) x z for all x, y, z S antisymmetric if (x y and y x) x = y for all x, y S
An equivalence relation is a reflexive, symmetric, and transitive relation.
Sum
Half-angle (sign depends on the quadrant of 
)
Range of Inverse Trigonometric Functions
Law of Sines
Law of Cosines
c = a + b 2ab (cos C )
DeMoivres Theorem
(cos + i sin ) k = cos( k ) + i sin ( k )
Coordinate Transformation
Rectangular ( x, y ) to polar (r, ) : r = x + y ; tan 
if x 0 x
Polar ( r , )to rectangular ( x, y ): x = r cos ; y = r sin
Distance from point ( x 1 y 1) to line Ax + By + C = 0
Volume
| Sphere with radius r: |  |
| Right circular cone with height h and base of radius r: |  |
| Right circular cylinder with height h and base of radius r: | V = r 2 h |
| Pyramid with height h and base of area B: |  |
| Right prism with height h and base of area B: | V = Bh |
Surface Area
| Sphere with radius r: | A = 4 r |
| Right circular cone with radius r and slant height s : | A = rs + r 2 |
Differentiation
Integration by Parts
u dv = uv vdu
TIME: 2 hours 40 Multiple-choice questions (Part A) 3 Short constructed-response questions (Part B)
Directions: Read each item and select the best response.
- The fraction
may be expressed more simply as 2a
- (A)
. - (B)
. - (C)
. - (D)
.
- (A)
- If there exist positive integers a and b such that 8 a + 12 b = c, then c must be divisible by
- (A) 3.
- (B) 4.
- (C) 18.
- (D) 24.
- For rectangle PQRS, point P is located at (1, 0) and point Q is located at (8, 3). What is the slope of
- (A)
- (B)
- (C)
- (A)
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