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Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 3www.jmap.orgA.A.8: Analyze and solve verbal problems thatinvolve quadratic equations.17.21.Daniel's Print Shop purchased a new printerfor 35,000. Each year it depreciates (losesvalue) at a rate of 5%. What will itsapproximate value be at the end of the fourthyear?080817ia, P.I. A.A.8A rectangle has an area of 24 square units.The width is 5 units less than the length.What is the length, in units, of the rectangle?[A] 618.[B] 8[C] 3[D] 19060837ia, P.I. A.A.8A contractor needs 54 square feet of brick toconstruct a rectangular walkway. The lengthof the walkway is 15 feet more than thewidth. Write an equation that could be usedto determine the dimensions of the walkway.Solve this equation to find the length andwidth, in feet, of the walkway.fall0719ia, P.I. A.A.9[A] 28,507.72[B] 30,008.13[C] 33,250.00[D] 27,082.33A.A.10: Solve systems of two linear equations in twovariables algebraically.22.010937ia, P.I. A.A.10Solve the following system of equationsalgebraically:3x 2 y 44 x 3y 7A.A.9: Analyze and solve verbal problems thatinvolve exponential growth and decay.19.[Only an algebraic solution can receive fullcredit.]010908ia, P.I. A.A.9The New York Volleyball Association invited64 teams to compete in a tournament. Aftereach round, half of the teams were eliminated.Which equation represents the number ofteams, t, that remained in the tournament afterr rounds?20.[A] t 64(0.5) r[B] t 64( 0.5) r[C] t 64(r )[D] t 64(15.)0.5A.A.11: Solve a system of one linear and onequadratic equation in two variables, where onlyfactoring is required. Note: The quadratic equationshould represent a parabola and the solution(s)should be integers.23.060830ia, P.I. A.A.9Kathy plans to purchase a car that depreciates(loses value) at a rate of 14% per year. Theinitial cost of the car is 21,000. Whichequation represents the value, v, of the carafter 3 years?[A] v 21,000(014. )3060810ia, P.I. A.A.11Which ordered pair is a solution to the systemof equations y x and y x 2 2 ?r24.[A] (0, 0)[B] (-1, 1)[C] (2, 2)[D] (-2, -2)080812ia, P.I. A.A.11Which ordered pair is in the solution set ofthe system of equations y x 1 andy x 2 5x 6?[B] v 21,000(114. )3[A] (5, 2)[B] (-5, 6)[C] v 21,000(0.86)(3)[C] (5, -4)[D] (-5, -1)[D] v 21,000(0.86) 3ALGEBRA STRAND

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 4www.jmap.org25.31.010922ia, P.I. A.A.11Which ordered pair is a solution of the systemof equations y x 2 x 20 and y 3x 15?What is the product of 3x 2 y and[A] (-1, -18)[B] (5, -1)[A] 15x 3 y 3 3x 3 y 2[B] 15x 3 y 3 3x y[C] (0, 5)[D] (-5, -30)[C] 15x 2 y 2 3x 2 y[D] 15x 3 y 3 xyA.A.12: Multiply and divide monomial expressionswith a common base, using the properties ofexponents. Note: Use integral exponents only.26.(5xy 2 xy ) ?A.A.14: Divide a polynomial by a monomial orbinomial, where the quotient has no remainder.32.080827ia, P.I. A.A.12Which expression is equivalent to (3x 2 ) 3 ?[A] 27 x 527.[B] 9 x 5[C] 27 x 6[D] 9 x 6060813ia, P.I. A.A.12What is half of 2 6 ?[A] 1628.060807ia, P.I. A.A.13[B] 25[C] 2 3[D] 13fall0718ia, P.I. A.A.14The expression9 x 4 27 x 6is equivalent to3x 3[A] 3x (1 3x 2 )[B] 3x (1 3x )[C] 9 x 3 (1 x )[D] 3x (1 9 x 5 )A.A.15: Find values of a variable for which analgebraic fraction is undefined.fall0703ia, P.I. A.A.12Which expression represents(2 x 3 )(8 x 5 )in4x633.060817ia, P.I. A.A.15Which value of x makes the expressionsimplest form?[A] x 229.[B] x 9[C] 4 x 9undefined?[D] 4 x 2010932ia, P.I. A.A.12[A] -434.27 k 5m8Simplify:(4 k 3 )(9m2 )[B] -3[C] 0[D] 3010925ia, P.I. A.A.15The function y xis undefined whenx 92the value of x isA.A.13: Add, subtract, and multiply monomials andpolynomials.30.x 4x 3[A] 3, only[B] -3, only[C] 3 or -3[D] 0 or 3080819a, P.I. A.A.13When 3g 2 4 g 2 is subtracted from7 g 5g 1, the difference is35.fall0728ia, P.I. A.A.152For which value of x is[A] 4 g 2 g 1[B] 4 g 2 9 g 3[C] 4 g 2 9 g 3[D] 10 g 2 g 1[A] 4ALGEBRA STRAND[B] -2x 3undefined?x2 4[C] 0[D] 3

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 5www.jmap.orgA.A.16: Simplify fractions with polynomials in thenumerator and denominator by factoring both andrenaming them to lowest terms.A.A.18: Multiply and divide algebraic fractions andexpress the product or quotient in simplest form.40.36.x2 14xandx 13x 3expressed in simplest form?060824ia, P.I. A.A.16What is the product of2 x 12 xinx 62Which expression representssimplest form?[A] 037.[B] 2x[C] 2x 2080821ia, P.I. A.A.16Which expression represents[D] 4x25x 125inx 2 25simplest form?5[A]x4x3[D]4x23060815ia, P.I. A.A.18[A] x 3[B]x 33[C]x3[D] xfall0727ia, P.I. A.A.17What is the sum ofd2dandexpressed in2342.[A]7d5[B]3d5[C]3d6[D]7d6010935ia, P.I. A.A.18Perform the indicated operation and simplify:3x 6 x 2 4 4 x 12 x 3simplest form?39.4( x 1)3What is the product ofA.A.17: Add or subtract fractional expressions withmonomial or like binomial denominators.38.[B]x2 1x 3and3x 3x 1expressed in simplest form? 5[D]x25[C]x 54x2[A]3( x 1)[C]41.25[B]x 5080826ia, P.I. A.A.18A.A.19: Identify and factor the difference of twoperfect squares.010921ia, P.I. A.A.17What is[A]43.62in simplest form? 5x 3 x815x 2[B]415x[C]42xfall0706ia, P.I. A.A.19The expression x 2 16 is equivalent to[D]815x44.[A] ( x 2)( x 8)[B] ( x 8)( x 8)[C] ( x 2)( x 8)[D] ( x 4)( x 4)060804ia, P.I. A.A.19Factored, the expression 16 x 2 25 y 2 isequivalent to[A] (8x - 5y)(8x - 5y)[B] (8x - 5y)(8x 5y)[C] (4x - 5y)(4x 5y)[D] (4x - 5y)(4x - 5y)ALGEBRA STRAND

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 6www.jmap.org45.A.A.23: Solve literal equations for a given variable.010909ia, P.I. A.A.19The expression 9 x 100 is equivalent to2[A] (9x - 100)(x 1)51.If the formula for the perimeter of a rectangleis P 2l 2 w, then w can be expressed as[B] (3x - 10)(3x 10)[C] (3x - 100)(3x - 1)[D] (9x - 10)(x 10)A.A.20: Factor algebraic expressions completely,including trinomials with a lead coefficient of one(after factoring a GCF).46.52.080806ia, P.I. A.A.20Factored completely, the expression2 x 2 10 x 12 is equivalent to[B] 2(x - 2)(x - 3)[C] 2(x 2)(x 3)[D] 2(x - 6)(x 1)fall0724ia, P.I. A.A.21Which value of x is in the solution set of theinequality 2 x 5 17 ?P l2[C] w P 2l2[D] w P 2w2l080808ia, P.I. A.A.23If 3ax b c, then x equals[C][B] c b 3ac b3a[D]b c3aA.A.24: Solve linear inequalities in one variable.A.A.25: Solve equations involving fractionalexpressions. Note: Expressions which result inlinear equations in one variable.53.080820ia, P.I. A.A.25Which value of x is in the solution set of theinequality 4 x 2 10 ?[A][B] 12[B] 3[C] -6[C] -2[D] -8080801ia, P.I. A.A.22[C] 73126[C] 7[D] 3010906ia, P.I. A.A.26What is the solution ofWhich value of p is the solution of5 p 1 2 p 20 ?[B] 3[B]A.A.26: Solve algebraic proportions in one variablewhich result in linear or quadratic equations.54.19[A]335[D] -4A.A.22: Solve all types of linear equations in onevariable.50.[B] w 080805ia, P.I. A.A.21[A] 249.2l P2Which value of x is the solution of2x 1 7x 2 ?5 315[A] -448.[A] w [A] c b 3a[A] 2(x 6)(x - 1)A.A.21: Determine whether a given value is asolution to a given linear equation in one variable orlinear inequality in one variable.47.010911ia, P.I. A.A.23[A] 619[D]7fall0732ia, P.I. A.A.22Solve for g: 3 2 g 5g 9ALGEBRA STRAND[B] 1k 4 k 9? 23[C] 14[D] 5

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 7www.jmap.org55.60.010918ia, P.I. A.A.26What is the value of x in the equation226 3 ?xx[A] 856.1[B] 8[C] 8The set {1,2,3,4} is equivalent to[A] {x 0 x 4, where x is a whole number}[B] {x 1 x 4, where x is a whole number}1[D]8[C] {x 1 x 4, where x is a whole number}[D] {x 0 x 4, where x is a whole number}060826ia, P.I. A.A.26Which value of x is a solution of[A] -257.[B] -105 x 13 ?x6[C] -15[D] -3A.A.30: Find the complement of a subset of a givenset, within a given universe.61.x 1 7 xx 12[A] {-2, -1, 0, 1, 2, 3, 4, 5, 6}A.A.27: Understand and apply the multiplicationproperty of zero to solve quadratic equations withintegral coefficients and integral roots.[B] {-2, -1, 0, 2, 3, 4, 6}[C] {-1, 0, 2, 3, 4}[D] {0, 2, 3, 4}010914ia, P.I. A.A.2762.What are the roots of the equationx 2 10 x 21 0 ?[A] 1 and 21[B] -5 and -5[C] 3 and 7[D] -3 and -7A.A.28: Understand the difference and connectionbetween roots of a quadratic equation and factors ofa quadratic expression.A.A.29: Use set-builder notation and/or intervalnotation to illustrate the elements of a set, given theelements in roster form.59.060818ia, P.I. A.A.30Consider the set of integers greater than -2and less than 6. A subset of this set is thepositive factors of 5. What is the complementof this subset?fall0739ia, P.I. A.A.26Solve for x:58.010917ia, P.I. A.A.29080833ia, P.I. A.A.30Twelve players make up a high schoolbasketball team. The team jerseys arenumbered 1 through 12. The players wearingthe jerseys numbered 3, 6, 7, 8, and 11 are theonly players who start a game. Using setnotation, list the complement of this subset.A.A.31: Find the intersection of sets (no more thanthree sets) and/or union of sets, within a givenuniverse.63.fall0710ia, P.I. A.A.31Which interval notation represents the set ofall numbers from 2 through 7, inclusive?Given:Set A {( 2, 1),( 1,0),(1,8)}Set B {( 3, 4),( 2, 1),( 1,2),(1,8)}.What is the intersection of sets A and B?[A] (2,7)[A] {(1,8)}fall0704ia, P.I. A.A.29[B] [2,7][C] (2,7][D] [2,7)[B] {( 3, 4),( 2, 1),( 1,2),( 1,0),(1,8)}[C] {( 2, 1),(1,8)}ALGEBRA STRAND[D] {( 2, 1)}

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 8www.jmap.org64.68.060833ia, P.I. A.A.31Maureen tracks the range of outdoortemperatures over three days. She records thefollowing information.060820ia, P.I. A.A.33What is the slope of the line that passesthrough the points ( 6,1) and (4, 4) ?[A]12[B] -2[C] 12[D] 2A.A.34: Write the equation of a line, given its slopeand the coordinates of a point on the line.A.A.35: Write the equation of a line, given thecoordinates of two points on the line.69.What is an equation of the line that passesthrough the points (3, 3) and ( 3, 3) ?Express the intersection of the three sets as aninequality in terms of temperature, t.A.A.32: Explain slope as a rate of change betweendependent and independent variables.65.70.080823a, P.I. A.A.32[B] zero[C] undefined[D] positiveA.A.33: Determine the slope of a line, given thecoordinates of two points on the line.66.[B] x 3[C] x y[D] y 3fall0713ia, P.I. A.A.3571.3[A] y x 322[B] y x 233[C] y x 322[D] y x 23080836ia, P.I. A.A.35Write an equation that represents the line thatpasses through the points (5, 4) and ( 5, 0).fall0716ia, P.I. A.A.33What is the slope of the line containing thepoints (3,4) and (-6,10)?[A] 67.[A] y 3What is an equation for the line that passesthrough the coordinates (2,0) and (0,3)?In a linear equation, the independent variableincreases at a constant rate while thedependent variable decreases at a constantrate. The slope of this line is[A] negative010910ia, P.I. A.A.3523[B] 2[C] 32[D]12010913ia, P.I. A.A.33What is the slope of the line that passesthrough the points (2,5) and (7,3)?[A]89[B]98[C] 25[D] 52A.A.36: Write the equation of a line parallel to thex- or y-axis.72.080810ia, P.I. A.A.36Which equation represents a line parallel tothe x-axis?[A] y 5x 17[C] x ALGEBRA STRAND1y3[B] x 5[D] y 10

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 9www.jmap.orgA.A.37: Determine the slope of a line, given itsequation in any form.A.A.41: Determine the vertex and axis of symmetryof a parabola, given its equation.A.A.38: Determine if two lines are parallel, giventheir equations in any form.A.A.42: Find the sine, cosine, and tangent ratios ofan angle of a right triangle, given the lengths of thesides.73.060814ia, P.I. A.A.38Which equation represents a line parallel tothe line y 4 x 5?[A] y 1x 341[C] y x 5474.76.010919ia, P.I. A.A.42The diagram below shows right triangle UPC.[B] y 4 x 5[D] y 4 x 3010926ia, P.I. A.A.38Which equation represents a line that isparallel to the line y 3 2 x ?[A] y 4 x 2[B] y 3 4 x[C] 4 x 2 y 5[D] 2 x 4 y 1Which ratio represents the sine of U ?A.A.39: Determine whether a given point is on aline, given the equation of the line.A.A.40: Determine whether a given point is in thesolution set of a system of linear inequalities.75.080825ia, P.I. A.A.40Which ordered pair is in the solution set ofthe following system of inequalities?1y x 42y x 1[A] (3, -5)[B] (4, 0)[C] (-5, 3)[D] (0, 4)[A]77.817[B]158[C]1517[D]815fall0721ia, P.I. A.A.42In triangle MCT, the measure of T 90 ,MC 85 cm, CT 84 cm, and TM 13 cm.Which ratio represents the sine of C ?[A]ALGEBRA STRAND1385[B]8413[C]8485[D]1384

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 10www.jmap.orgA.A.43: Determine the measure of an angle of aright triangle, given an acute angle and the length ofanother side.78.80.080829ia, P.I. A.A.43In the diagram of ABC shown below,BC 10 and AB 16.080824ia, P.I. A.A.43Which equation could be used to find themeasure of one acute angle in the righttriangle shown below?To the nearest tenth of a degree, what is themeasure of the largest acute angle in thetriangle?[A] cos B 544[C] tan B 579.[B] sin A [A] 38.74581.The center pole of a tent is 8 feet long, and aside of the tent is 12 feet long as shown in thediagram below.In the right triangle shown in the diagrambelow, what is the value of x to the nearestwhole number?[A] 21[C] 56[D] 32.0010912ia, P.I. A.A.44If a right angle is formed where the centerpole meets the ground, what is the measure ofangle A to the nearest degree?[B] 48[C] 51.3A.A.44: Find the measure of a side of a righttriangle, given an acute angle and the length ofanother side.5[D] tan A 4060816ia, P.I. A.A.43[A] 42[B] 90.0[D] 34ALGEBRA STRAND[B] 28[C] 12[D] 14

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 11www.jmap.orgA.A.45: Determine the measure of a third side of aright triangle using the Pythagorean theorem, giventhe lengths of any two sides.82.83.fall0711ia, P.I. A.A.45Tanya runs diagonally across a rectangularfield that has a length of 40 yards and a widthof 30 yards, as shown in the diagram below.060825ia, P.I. A.A.45Don placed a ladder against the side of hishouse as shown in the diagram below.What is the length of the diagonal, in yards,that Tanya runs?Which equation could be used to find thedistance, x, from the foot of the ladder to thebase of the house?[A] x 20 19.5[B] x 20 19.5[C] x 202 19.52[D] x 20 19.52222[A] 7084.[B] 60[C] 80[D] 50080809ia, P.I. A.A.45The length of the hypotenuse of a righttriangle is 34 inches and the length of one ofits legs is 16 inches. What is the length, ininches, of the other leg of this right triangle?[A] 18ALGEBRA STRAND[B] 16[C] 25[D] 30

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 1www.jmap.orgA.G.1: Find the area and/or perimeter of figurescomposed of polygons and circles or sectors of acircle. Note: Figures may include triangles,rectangles, squares, parallelograms, rhombuses,trapezoids, circles, semi-circles, and regularpolygons (perimeter only).1.2.010931ia, P.I. A.G.1A window is made up of a single piece ofglass in the shape of a semicircle and arectangle, as shown in the diagram below.Tess is decorating for a party and wants to puta string of lights all the way around theoutside edge of the window.fall0733ia, P.I. A.G.1Serena's garden is a rectangle joined with asemicircle, as shown in the diagram below.Line segment AB is the diameter of semicircleP. Serena wants to put a fence around hergarden.To the nearest foot, what is the length of thestring of lights that Tess will need to decoratethe window?Calculate the length of fence Serena needs tothe nearest tenth of a foot.3.080815ia, P.I. A.G.1Luis is going to paint a basketball court on hisdriveway, as shown in the diagram below.This basketball court consists of a rectangleand a semicircle.Which expression represents the area of thisbasketball court, in square feet?[A] 80 16 [B] 80[C] 80 64 [D] 80 8 GEOMETRY STRAND

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance IndicatorsPage 2www.jmap.org4.7.060832ia, P.I. A.G.1A designer created the logo shown below.The logo consists of a square and fourquarter-circles of equal size.A cylindrical container has a diameter of 12inches and a height of 15 inches, as illustratedin the diagram below.Express, in terms of , the exact area, insquare inches, of the shaded region.What is the volume of this container to thenearest tenth of a cubic inch?A.G.2: Use formulas to calculate volume andsurface area of rectangular solids and cylinders.5.[A] 4,241.2[B] 2,160.0[C] 6,785.8[D] 1,696.5060809ia, P.I. A.G.2Lenny made a cube in technology class. Eachedge measured 1.5 cm. What is the volume ofthe cube in cubic centimeters?[A] 3.3756.fall0712ia, P.I. A.G.2[B] 9.0[C] 13.5[D] 2.25060827ia, P.I. A.G.2Mrs. Ayer is painting the outside of her son'stoy box, including the top and bottom. Thetoy box measures 3 feet long, 1.5 feet wide,and 2 feet high. What is the total surface areashe will paint?[A] 22.5 ft 2[B] 27.0 ft 2[C] 135. ft 2[D] 9.0 ft 28.010936ia, P.I. A.G.2A soup can is in the shape of a cylinder. Thecan has a volume of 342 cm3 and a diameterof 6 cm.

Integrated Algebra Regents Exam Questions Sorted by Content Strand Performance Indicators Page 2 www.jmap.org ALGEBRA STRAND 8. fall0715ia, P.I. A.A.5 An electronics store sells DVD players and cordless telephones. The store makes a 75 profit on the sale of each DVD player (d) and a 30 p