Reflects AKS/TEKS objectives Practice Workbook

73 Pages·2004·0.43 MB·English

PRENTICE HALL MATH
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AKS TAKS/vised
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Practice
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Correlations of Lesson-specific references in
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◆◆ TAKS Sample Test
◆◆ Practice Sets aligned to TAKS/TEKS
objective-by-objective
◆◆ Mixed Practice Test Items
TAKS Practice Workbook
Table of Contents
TAKS Correlation to Prentice Hall Algebra and Prentice Hall Geometry . . . . . . . v
Formula Chart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
TAKS Practice Items
Objective 1:The student will describe functional relationships
in a variety of ways.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Objective 2:The student will demonstrate an understanding
of the properties and attributes of functions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Objective 3:The student will demonstrate an understanding
of linear functions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Objective 4:The student will formulate and use linear equations
and inequalities.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Objective 5:The student will demonstrate an understanding
of quadratic and other nonlinear functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Objective 6:The student will demonstrate an understanding
of geometric relationships and spatial reasoning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Objective 7:The student will demonstrate an understanding
of two- and three-dimensional representations of geometric
relationships and shapes.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Objective 8:The student will demonstrate an understanding
of the concepts and uses of measurement and similarity.. . . . . . . . . . . . . . . . . . . . . . 28
Objective 9:The student will demonstrate an understanding of
percents,proportional relationships,probability,and statistics
in application problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Objective 10:The student will demonstrate an understanding
of the mathematical processes and tools used in problem solving. . . . . . . . . . . . . . . 36
TAKS Mixed Practice Items. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
TAKS Sample Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Answer Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
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Copyright by Pearson Education,Inc.,publishing as Prentice-Hall,Inc.,Upper Saddle River, E
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New Jersey 07458.All rights reserved.Printed in the United States of America.This publication is o
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protected by copyright,and permission should be obtained from the publisher prior to any prohibited ar
e
reproduction,storage in a retrieval system,or transmission in any form or by any means,electronic, © P
mechanical,photocopying,recording,or likewise.
ISBN:0-13-115750-7
1 2 3 4 5 6 7 8 9 10 07 06 05 04 03
TAKS Correlation to Prentice Hall Algebra and Prentice Hall Geometry
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
Objective 1
The student will describe functional relationships in a variety of ways.
A(b)(1)Foundations for functions.The student understands that a function represents a dependence of one
quantity on another and can be described in a variety of ways.
(A)The student describes 1,2,3 1 1 2-4,2-7
independent and dependent
quantities in functional
relationships.
(B) The student [gathers and 4,5,7, 2,9,58 2-4,2-7
records data,or] uses data sets, 8,11,12,
to determine functional
(systematic) relationships
between quantities.
(C) The student describes 8,9,13, 2,5,7, 3,4,5,
functional relationships for 10 12,16,18,
given problem situations and 58
writes equations or inequalities
to answer questions arising
from the situations.
(D) The student represents 4,5,6,8, 2,5,10 2,4,8, 2-2,2-3
relationships among quantities 10,11,12, 12 9,11,12,
using [concrete] models,tables, 17 16,18,58
graphs,diagrams,verbal
descriptions,equations,and
inequalities.
(E) The student interprets and 7,8,10, 3,7,12 3,5,12 2-4,2-7
makes inferences from 13
functional relationships.
Objective 2
The student will demonstrate an understanding of the properties and attributes of functions.
A(b)(2)Foundation for functions.The student uses the properties and attributes of other functions.
(A) The student identifies [and 1,2,3 6,17,21, 2-4,2-5,7-1,7-2 MT (58,89)
sketches] the general forms of 22
linear (y(cid:1)x) and quadratic
(y(cid:1)x2) parent functions.
(B) For a variety of situations, 4,5,18 4 2-4
the student identifies the
c. mathematical domains and
n
n, I ranges and determines
atio reasonable domain and range
uc values for given situations.
d
E
on (C) The student interprets 6,12,13 7 2-2
s
ar situations in terms of given
e
P graphs [or creates situations
©
that fit given graphs].
TAKS Practice Workbooks iii
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
(D) In solving problems,the 7,13,18 11 1-8,1-9,2-1,2-2,
student [collects and] organizes 2-3,2-4,2-6,2-7,
data,[makes and] interprets 5-6,6-7 MT (235)
scatterplots,and models,
predicts,and makes decisions
and critical judgments.
A(b)(3)Foundations for functions.The student understands how algebra can be used to express
generalizations and recognizes and uses the power of symbols to represent situations.
(A) The student uses symbols 8,9,10, 2,5,10, 2,4,8,9, 1-2
to represent unknowns and 11 24,25 16,18,58
variables.
(B) Given situations,the 10,11,18 10 2,9,18 1-1
student looks for patterns and
represents generalizations
algebraically.
A(b)(4)Foundations for functions.The student understands the importance of the skills required to
manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify
algebraic expressions and solve equations and inequalities in problem situations.
(A) The student finds specific 14,15,16, 4,6 10 3-1,3-2,3-3,4-1,
function values,simplifies 17 4-2,4-4,10-1,10-2,
polynomial expressions, 10-3,10-4,10-5,
transforms and solves 10-6,10-7,
equations,and factors as MT (480,496)
necessary in problem
situations.
(B) The student uses the 14,15,16 6 10,60 3-4,MT (35)
commutative,associative,and
distributive properties to
simplify algebraic expressions.
Objective 3
The student will demonstrate an understanding of linear functions.
A(c)(1)Linear functions.The student understands that linear functions can be represented in different ways
and translates among their various representations.
(A) The student determines 1,2,3 7 2,4
whether or not given situations
can be presented in different
ways and translates among
their various representations.
(C) The student translates 1,3,7,11, 2,4,6,11, 2-5,2-6,2-7,
among and uses algebraic, 12 17,18 MT (89)
tabular,graphical,or verbal nc.
descriptions of linear functions. n, I
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A(c)(2)Linear functions.The student understands the meaning of the slope and intercepts of linear uc
d
functions and interprets and describes the effects of changes in parameters of linear functions in real-world E
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and mathematical situations. so
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(A) The student develops the 4,5,13 8,24,25 14 5-1,5-2 © P
concepts of slope as a rate of
change and determines slopes
from graphs,tables,and
algebraic situations.
iv TAKS Practice Workbooks
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
(B) The student interprets the 11,13,16, 9,24 12,15 5-1,5-4,5-9
meaning of slope and 17,18
intercepts in situations using
data,symbolic representations,
or graphs.
(C) The student investigates, 6,8,16, 13 5-4
describes,and predicts the 17,18
effects of changes in m and b
on the graph of y(cid:1)mx(cid:2)b.
(D) The student graphs and 7,9,10 14 5-5,5-6,5-7
writes equations of lines given
characteristics such as two
points,a point and a slope,or a
slope and a y-intercept.
(E) The student determines the 11,14,15 9 15 5-9
intercepts of linear functions
from graphs,tables,and
algebraic representations.
(F) The student interprets and 8,16,17, 15 5-4
predicts the effects of changing 18
slope and y-intercept in
applied situations.
(G) The student relates direct 14,20,21 5 5-3
variation to linear functions
and solves problems involving
proportional change.
Objective 4
The student will formulate and use linear equations and inequalities.
A(c)(3)Linear functions.The student formulates equations and inequalities based on linear functions,uses a
variety of methods to solve them,and analyzes the solutions in terms of the situation.
(A) The student analyzes 1,2,3,9, 10 4,16,18, 3-1,3-2,3-3,4-2,
situations involving linear 13,17 58 4-5,4-6,4-7,4-8,
functions and formulates linear 5-5,6-5
equations or inequalities to
solve problems.
(B) The student investigates 4,5,7 17 3-1,3-2,3-3,4-2,
methods for solving linear 4-5,4-6,4-7,4-8,
equations and inequalities 6-5,MT (201)
using [concrete] models,
graphs,and the properties of
c. equality,selects a method,and
n
n, I solves the equations and
atio inequalities.
c
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E
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o
ars determines the reasonableness
e
P of solutions to linear equations
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and inequalities.
A(c)(4)Linear functions.The student formulates systems of linear equations from problem situations,uses a
variety of methods to solve them,and analyzes the situations in terms of the situation.
TAKS Practice Workbooks v
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
(A) The student analyzes 9,11,13 18,20 6-4
situations and formulates
systems of linear equations
to solve problems.
(B) The student solves systems 12,14,15 19 6-1,6-2,6-3, MT (348)
of linear equations using MT (169)
[concrete] models,graphs,
tables,and algebraic methods.
(C) For given contexts,the 6,16,18 12 20 6-1,6-2,6-3,6-4
student interprets and
determines the reasonableness
of solutions to systems of
linear equations.
Objective 5
The student will demonstrate an understanding of quadratic and other nonlinear functions.
A(d)(1)Quadratic and other nonlinear functions.The student understands that the graphs of quadratic
functions are affected by the parameters of the function and can interpret and describe the effects of
changes in the parameters of quadratic functions.
(B) The student investigates, 1,2,3 21 7-1,7-2,7-3
describes,and predicts the
effects of changes in a on the
graph of y(cid:1)ax2.
(C) The student investigates, 4,5,6 13 22 7-1,7-2,7-3
describes,and predicts the
effects of changes in c on the
graph of y(cid:1)x2(cid:2)c.
(D) For problem situations,the 7,8,9 22 7-2,7-3
student analyzes graphs of
quadratic functions and draws
conclusions.
A(d)(2)Quadratic and other nonlinear functions.The student understands there is more than one way to
solve a quadratic equation and solves them using appropriate methods.
(A) The student solves 7,10,11, 14 23 7-5
quadratic equations using 12,13,14,
[concrete] models,tables, 18,19
graphs,and algebraic methods.
(B) The student relates the 13,14,15, 24 MT (342)
solutions of quadratic 18,19
equations to the roots of
their functions.
c.
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A(d)(3)Quadratic and other nonlinear functions.The student understands there are situations modeled by n, I
functions that are neither linear nor quadratic and models the situations. atio
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(A) The problem uses [patterns 15,16,17 15 25 8-1,8-2,8-3,8-6, Ed
to generate] the laws of 8-7,8-8 on
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exponents and applies them in ar
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problem-solving situations. P
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Objective 6
The student will demonstrate an understanding of geometric relationships and spatial reasoning.
G(b)(4)Geometric reasoning.The student uses a variety of representations to describe geometric
relationships and solve problems.
vi TAKS Practice Workbooks
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
(A) The student selects an 1,2,3,5, 15,17,38 26
appropriate representation 8
([concrete],pictorial,graphical,
verbal,or symbolic) in order to
solve problems.
G(c)(1)Geometric reasoning.The student identifies,analyzes,and describes patterns that emerge from two-
and three-dimensional geometric figures.
(A) The student uses numeric 2,3,4,5, 15,16,17, 26,27 1-1
and geometric patterns to 6,12 18,21,
make generalizations about 28–33
geometric properties,including
properties of polygons,ratios in
similar figures and solids,and
angle relationshipsin polygons
and circles.
(B) The student uses the 6,7,8,9, 19,21 28,31,32 3-1,3-2,3-3,3-4,
properties of transformations 10 3-6
and their compositions to
make connections between
mathematics and the real
world in applications such as
tesselations or fractals.
(C) The student identifies and 7,11,12 20,30 29,30 5-4
applies patterns from right
triangles to solve problems,
including special right triangles
(45-45-90 and 30-60-90) and
triangles whose sides are
Pythagorean triples.
G(e)(3)Congruence and the geometry of size.The student applies the concept of congruence to justify
properties of figures and solve problems.
(A) The student uses 7,9,10 21 31,32 3-1,3-2,3-3
congruence transformations to
make conjectures and justify
properties of geometric figures.
Objective 7
The student will demonstrate an understanding of two- and three-dimensional representations of geometric
relationships and shapes.
G(d)(1)Dimensionality and the geometry of location.The student analyzes the relationship between three-
dimensional objects and related two-dimensional representations and uses these representations to solve
problems.
c.
n
n, I (B) The student uses nets to 1,2,3 22 33 6-1
o represent [and construct]
ati
c three-dimensional objects.
u
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n (C) The student uses top,front, 4,5,12 23 34
o
ars side,and corner views of three-
e
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©
accurate and complete
representations and solve
problems.
TAKS Practice Workbooks vii
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
G(d)(2)Dimensionality and the geometry of location.The student understands that coordinate systems
provide convenient and efficient ways of representing geometric figures and uses them accordingly.
(A) The student uses one- and 8,9,11 24,25,26, 11,32,37, MT (58) 1-8,2-3
two-dimensional coordinate 27 38,39
systems to represent points,
lines,line segments,and figures.
(B) The student uses slopes 6,7,8, 24,25 35,36,37 5-1,5-8
and equations of lines to
investigate geometric
relationships,including parallel
lines,perpendicular lines,and
[special segments of] triangles
and other polygons.
(C) The student [develops and] 9,10,11, 26,27 38,39 9-2 5-1,5-2,5-3,5-5,
uses formulas including 5-6,5-7,5-8,6-2,
distance and midpoint. 6-3,6-4,6-5,6-6,
6-7,10-5,10-6,
11-6
G(e)(2)Congruence and the geometry of size.The student analyzes properties and describes relationships
in geometric figures.
(D) The student analyzes the 9,10,11 22,23 33,34 MT (307)
characteristics of three-
dimensional figures and their
component parts.
Objective 8
The student will demonstrate an understanding of the concepts and uses of measurement and similarity.
G(e)(1)Congruence and the geometry of size.The student extends measurement concepts to find area,
perimeter,and volume in problem situations.
(A) The student finds the area 1,2,3,4, 28,29 25,40,42 5-2,5-5,5-6,6-7
of polygons and composite 20
figures.
(B) The student finds areas of 4,5,6 29,38 41 5-8
sectors and arc lengths of
circles using proportional
reasoning.
(C) The student [develops, 7,8,9 30 29,30,42 9-1 5-3
extends and] uses the
Pythagorean Theorem.
(D) The student finds surface 10,11,12 31,33 43,46 6-2,6-3,6-4,6-5,
area and volumes of prisms, 6-6,10-6 c.
n
pyramids,spheres,cones,and n, I
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cylinders in problem situations. ati
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G(f)(1)Similarity and the geometry of shape.The student applies the concepts of similarity to justify Ed
properties of figures and solve problems. on
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(A) The student uses similarity 13,14,15, 32 44,45 2-6,3-1,3-2,3-3 Pe
properties and transformations 17,23 ©
to [explore and] justify
conjectures about geometric
figures and solve problems.
viii TAKS Practice Workbooks
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
(B) The student uses ratios to 15,16,17, 32.33 44,45 10-1,10-4
solve problems involving 18,22,23
similar figures.
(C) In a variety of ways,the 15,18,19 32 45 9-3,MT (419) 10-3,11-1,
student [develops,] applies,and 20 MT (550)
justifies triangle similarity
relationships,such as right
triangle ratios,[trigonometric
ratios,] and Pythagorean
triples.
(D) The student describes the 19,21,22 33 56
effect on the perimeter,area, 23
and volume when length,width,
or height of a three-dimensional
solid is changed and applies
this idea in solving problems.
Objective 9
The student will demonstrate an understanding of percents,proportional relationships,probability,and
statistics in application problems.
(8.3)Patterns,relationships,and algebraic thinking.The student identifies proportional relationships in
problem situations and solves problems.The student is expected to:
(B) estimate and find solutions 1,2,3 34 50,57 3-7,3-8,4-1 10-1
to application problems
involving percents and
proportional relationships such
as similarity and rates.
(8.11)Probability and statistics.The student applies the concepts of theoretical and experimental probability
to make predictions.The student is expected to:
(A) find the probabilities of 3,4,5,6, 35 46,47 2-8,3-6,11-6,11-7 6-8,MT (11)
compound events (dependent 7,8
and independent);and
(B) use theoretical 6,7,8,9 35 47 1-7
probabilities and experimental
results to make predictions and
decisions.
(8.12)Probability and statistics.The student uses statistical procedures to describe data.The student is
expected to:
(A) select the appropriate 9,10,11, 36,37 49,50,53
measure of central tendency to 12,
describe a set of data for a
nc. particular purpose;and
n, I
atio (C) construct circle graphs,bar 12,13,14, 58
uc graphs,and histograms,with 15,17
d
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n
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ar (8.13)Probability and statistics.The student evaluates predictions and conclusions based in statistical data.
e
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(B) recognize misuses of 14,15,16 37 48
graphical or numerical 17,
information and evaluate
predictions and conclusions
based in data analysis.
TAKS Practice Workbooks ix
Practice Mixed Sample Prentice Hall Prentice Hall
Objectives and Set Review Test Algebra Geometry
Instructional Targets Items Items Items Chapter Lesson Chapter Lesson
SK:Skills Handbook MT:Math Toolbox
Objective 10
The student will demonstrate an understanding of the mathematical processes and tools used in problem solving.
(8.14)Underlying processes and mathematical tools.The student applies Grade 8 mathematics to solve
problems connected to everyday experiences,investigations in other disciplines,and activities in and outside
of school.The student is expected to:
(A) identify and apply 1-12,16, 12,34,35 9,16,47,
mathematics to everyday 17 38–40,44 49,51–54,
experiences,to activities in and 60
outside of school,with other
disciplines,and with other
mathematical topics;
(B) use a problem-solving 1–4,6, 12,34,35 16,47,
model that incorporates 8–12,16, 38–40,44 49–52,59,
understanding the problem, 17 60
making a plan,carrying out the
plan,and evaluating the
solution for reasonableness;
and
(C) select or develop an 1–4,6–12, 34,35, 9,47,
appropriate problem-solving 16,17 38–40,44 49,51,52,
strategy from a variety of 54,59,60
different types,including
drawing a picture,looking for
a pattern,systematic guessing
and checking,acting it out,
making a table,working a
simpler problem,or working
backwoods to solve a problem.
(8.15)Underlying processes and mathematical tools.The student communicates about Grade 8 mathematics
through informal and mathematical language,representations,and models.The student is expected to;
(A) communicate 5,6,8-12 12,37, 16,49,54
mathematical ideas using 38–40
language,efficient tools,
appropriate units,and
graphical,numerical,physical,
or algebraic mathematical
tools.
(8.16)Underlying processes and mathematical tools.The student uses logical reasoning to make conjectures
and verify conclusions.The student is expected to:
(A) make conjectures from 11,12,17 41,43 9,54
patterns or sets of examples
and nonexamples;and nc.
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(B) validate his/her conclusions 11,13-15 37,42 55 atio
using mathematical properties c
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and relationships E
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x TAKS Practice Workbooks