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  2. ALGEBRA 1 STRANDS • Number Properties, Operations, and Linear Equations • Graphing and Systems of Linear Equations • Quadratics and Polynomials • Functions and Rational Expressions

  3. Number Properties, Operations, and Linear Equations Is the equation 3(2x−4)=−18 equivalent to 6x −12 =−18? A Yes, the equations are equivalent by the Associative Property of Multiplication. B Yes, the equations are equivalent by the Commutative Property of Multiplication. C Yes, the equations are equivalent by the Distributive Property of Multiplication over Addition. D No, the equations are not equivalent. Which equation is equivalent to 3[7x − 4 (x−3)]+1 = 116 ? A 9x −2 = 216 B 9x +37 = 16 C 17x −2 = 216 D 17x +13 = 16

  4. Which statement is false? A The order in which two whole numbers are subtracted does not affect the difference. B The order in which two whole numbers are added does not affect the sum. C The order in which two rational numbers are added does not affect the sum. D The order in which two rational numbers are multiplied does not affect the product. Which number does not have a reciprocal? A –1 B 0 C D 3 Number Properties, Operations

  5. Linear Equations What is the solution set of the inequality 5 −|x - 4|≤ − 3? A −2 ≤ x ≤6 B x ≤−2 or x ≥ 6 C −12 ≤ x ≤4 D x ≤−12 or x ≥ 4 What is the solution for this equation?|2x −3|=35 A x =−4 or x =4 B x =−4 or x =3 C x =−1 or x =4 D x =−1 or x =3

  6. A 120-foot-long rope is cut into 3 pieces. The first piece of rope is twice as long as the second piece of rope. The third piece of rope is three times as long as the second piece of rope. What is the length of the longest piece of rope? A 20 feet C 60 feet B 40 feet D 80 feet Beth is two years older than Julio. Gerald is twice as old as Beth. Debra is twice as old as Gerald. The sum of their ages is 38. How old is Beth? A 3 C 6 B 5 D 8

  7. Graphing & system of Linear Equations What is the x-intercept of the line defined by −2x + 3y=12? A 6 B 4 C −4 D −6 What is the y-intercept of the graph of 4x + 2y = 12 ? A – 4 B – 2 C 6 D 12

  8. What is the equation of the line that has a slope of 4 and passes through the point(3,-10)? A y = 4x - 22 B y =4x + 22 C y = 4x - 43 D y = 4x + 43 Graphing Which point lies on the line defined by 3x + 6y= 12? A (0, 2) B (0, 6) C (1, -) D (1, -)

  9. Which inequality is shown on the graph below? A y < x −1 B y ≤ x −1 C y > x −1 D y ≥ x −1

  10. Which best represents the graph of y =2x −2?

  11. Which inequality does the shaded region of the graph represent? A 3x + y ≤ 2 B 3x + y ≥ 2 C 3x + y ≤ −2 D 3x + y ≥ −2

  12. Which equation best represents the graph above? A y = x B y = 2x C y = x + 2 D y = 2x + 2

  13. The equation of line l is 6x +5y =3, and the equation of line q is 5x −6y =0. Which statement about the two lines is true? A Lines l and q have the same y- intercept. B Lines l and q are parallel. C Lines l and q have the same x- intercept. D Lines l and q are perpendicular. Graph the following inequalities? Know the differences between the two. A 3x + y≤ 2 B3x + y≥ −2

  14. Marcy has a total of 100 dimes and quarters. If the total value of the coins is $14.05, how many quarters does she have? A 27 B 40 C 56 D 73 Graph the following system of equations and identify the solution. 2x ≥ y – 1 2x - 5y≤ 10

  15. Systems Members of a senior class held a car wash to raise funds for their senior prom. They charged $3 to wash a car and $5 to wash a pick-up truck or a sport utility vehicle. If they earned a total of $275 by washing a total of 75 vehicles, how many cars did they wash? A 25 B 34 C 45 D 50 Which of the following best describes the graph of this system of equations? y=−2x + 3 5y =−10x + 15 A two identical lines B two parallel lines C two lines intersecting in only one point D two lines intersecting in only two points

  16. QUADRATICS & polynomials The sum of two binomials is 5−6x. If one of the binomials is 3−2x, what is the other binomial? A 2−4x B 2−8x C 8+4x D 8−8x Which of the following expressions is equal to (x +2) + (x − 2 )(2x +1) ? A 2−2x B 2 −4x C 2 +x D 4 +2x

  17. A volleyball court is shaped like a rectangle. It has a width of x meters and a length of 2x meters. Which expression gives the area of the court in square meters? A 3x B 2x2 C 3x2 D 2x3 Which is a factor of - 11x -24? A x +3 B x −3 C x +4 D x −4

  18. Which of the following shows 9t2 +12t +4 factoredcompletely? A (3t +2)2 B (3t +4)(3t +1) C (9t +4)(t +1) D 9t2 +12 t +4 What is the complete factorization of 32 −8z2? A -8(2 + z)(2 − z) B8(2 +z)(2 −z) C−8(2+z)2 D 8(2 - z)2

  19. Leanne correctly solved the equation x2 +4x =6 by completing the square. Which equation is part of her solution? A (x +2)2 =8 B (x +2)2 =10 C (x + 4)2 =10 D (x + 4)2 =22 Carter is solving this equation by factoring. 10x2 −25x +15 =0 Which expression could be one of his correct factors? A x +3 B x −3 C 2x +3 D 2x −3

  20. What are the solutions for the quadratic equation x2 −8x =9? A 3 B 3, -3 C 1,-9 D -1,9 Which statement best explains why there is no real solution to the quadratic equation? 2x2 + x + 7 = 0? A The value of 12 −4(2)(7)is positive. B The value of 12 − 4(2)(7) is equal to 0. C The value of 12 − 4(2)(7) is negative. D The value of 12 − 4(2)(7) is not a perfect square.

  21. Graph the equation y =x2 −3x −4. For what value or values of x is y =0? A x =−1 only B x =−4 only C x =−1 and x =4 D x =1 and x =−4 Which quadratic function, when graphed, has x-intercepts of 4 and −3? A y =(x - 3)(x + 4) B y =(x + 3)(2x - 8) C y =(3x −1)(4x +1) D y =(3x +1)(8x −2)

  22. How many times does the graph of y =2x2 − 2x + 3 intersect the x-axis? A none B one C two D three An object that is projected straight downward with initial velocity v feet per second travels a distance s=vt + 16t2, wheret =time in seconds. If Ramón is standing on a balcony 84 feet above the ground and throws a penny straight down with an initial velocity of 10 feet per second, in how many seconds will it reach the ground? A 2 seconds B 3 seconds C 6 seconds D 8 seconds

  23. The height of a triangle is 4 inches greater than twice its base. The area of the triangle is 168 square inches. What is the base of the triangle? A 7 in. B 8 in. C 12 in. D 14 in. What is reduced to lowest terms? A B C D

  24. FUNCTIONS & RATIONAL EXPRESSIONS A pharmacist mixed some 10%-saline solution with some 15%-saline solution to obtain 100 mL of a 12%-saline solution. How much of the 10%-saline solution did the pharmacist use in the mixture? A 60 Ml B 45 mL C 40 mL D 25 mL Andy’s average driving speed for a 4-hour trip was 45 miles per hour. During the first 3 hours he drove 40 miles per hour. What was his average speed for the last hour of his trip? A 50 miles per hour B 60 miles per hour C 65 miles per hour D 70 miles per hour

  25. One pipe can fill a tank in 20 minutes, while another takes 30 minutes to fill the same tank. How long would it take the two pipes together to fill the tank? A 50 min B 25 min C 15 min D 12 min Two airplanes left the same airport traveling in opposite directions. If one airplane averages 400 miles per hour and the other airplane averages 250 miles per hour, in how many hours will the distance between the two planes be 1625 miles? A 2.5 B 4 C 5 D 10.8

  26. Lisa will make punch that is 25% fruit juice by adding pure fruit juice to a 2-liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add? A 0.4 liter B 0.5 liter C 2 liters D 8 liters Which relation is a function? A {(–1, 3), (–2, 6), (0, 0), (–2, –2)} B {(–2, –2), (0, 0), (1, 1), (2, 2)} C {(4, 0), (4, 1), (4, 2), (4, 3)} D {(7, 4), (8, 8), (10, 8), (10, 10)}

  27. Which fraction is equivalent to ? A B C D What is reduced to lowest terms? A B C D Rational Expressions

  28. GEOMETRY STRANDS • Logic and Geometric Proofs • Volume and Area Formulas • Angle Relationships, Constructions, and Lines • Trigonometry

  29. Logic & geometric proofs Which of the following best describes deductive reasoning? A using logic to draw conclusions based on accepted statements B accepting the meaning of a term without definition C defining mathematical terms to correspond with physical objects D inferring a general truth by examining a number of specific examples Consider the arguments below. I. Every multiple of 4 is even. 376 is a multiple of 4. Therefore, 376 is even. II. A number can be written as a repeating decimal if it is rational. Pi cannot be written as a repeating decimal. Therefore, pi is not rational. Which one(s), if any, use deductive reasoning? A I only B II only C both I and II D neither I nor II

  30. Theorem: A triangle has at most one obtuse angle. Eduardo is proving the theorem above by contradiction. He began by assuming that in ABC, ∠A and ∠B are both obtuse. Which theorem will Eduardo use to reach a contradiction? A If two angles of a triangle are equal, the sides opposite the angles are equal. B If two supplementary angles are equal, the angles each measure 90°. C The largest angle in a triangle is opposite the longest side. D The sum of the measures of the angles of a triangle is 180°. “Two lines in a plane always intersect in exactly one point.” Which of the following best describes a counterexample to the assertion above? A coplanar lines B parallel lines C perpendicular lines D intersecting lines

  31. In the figure to the right, AB >BC. If we assume thatm∠A=m∠C, it follows that AB =BC. This contradicts the given statement that AB >BC. What conclusion can be drawn from this contradiction? A m∠A = m∠B B m∠A≠ m∠B C m∠A = m∠C D m∠A ≠ m∠C

  32. In the diagram below, ∠1≅∠4. Which of the following conclusions does not have to be true? A ∠ 3 and ∠4 are supplementary angles. B Line l is parallel to line m. C ∠1 ≅ ∠3 D ∠2 ≅ ∠3

  33. Which figure can serve as a counterexample to the conjecture below? If one pair of opposite sides of a quadrilateral is parallel, then the quadrilateral is a parallelogram. A rectangle B rhombus C square D trapezoid Given: TRAP is an isosceles trapezoid with diagonals RP and TA. Which of the following must be true? A RP ⊥TA B RP TA C RP ≅TA D RP bisects TA

  34. Which triangles must be similar? A two obtuse triangles B two scalene triangles with congruent bases C two right triangles D two isosceles triangles with congruent vertex angles In parallelogram FGHI, diagonals IG and FH are drawn and intersect at point M. Which of the following statements must be true? A ∆FGI must be an obtuse triangle. B ∆ HIG must be an acute triangle. C ∆FMG must be congruent to ∆HMG. D ∆ GMH must be congruent to IMF.

  35. VOLUME & AREA A right circular cone has radius 5 inches and height 8 inches. What is the lateral area of the cone? (Lateral area of cone =πrl, where l =slant height ) A 40πsq in. B 445πsq in. C 5π 39 sq in. D 5π 89 sq in.

  36. Figure ABCD is a kite. What is the area of figure ABCD, in square centimeters? A 120 B 154 C 168 D 336

  37. If a cylindrical barrel measures 22 inches in diameter, how many inches will it roll in 8 revolutions along a smooth surface? A 121πin. B 168πin. C 176πin. D 228πin. A sewing club is making a quilt consisting of 25 squares with each side of the square measuring 30 centimeters. If the quilt has five rows and five columns, what is the perimeter of the quilt? A 150 cm B 300 cm C 600 cm D 900 cm

  38. The four sides of this figure will be folded up and taped to make an open box. What will be the volume of the box? A 50 cm3 B 75 cm3 C 100 cm3 D 125 cm3

  39. The minute hand of a clock is 5 inches long. What is the area of the circle, in square inches, created as the hand sweeps an hour? A 10π B 20π C 25π D 100π A sewing club is making a quilt consisting of 25 squares with each side of the square measuring 30 centimeters. If the quilt has five rows and five columns, what is the perimeter of the quilt? A 150 cm B 300 cm C 600 cm D 900 cm

  40. If RSTW is a Rhombus what is the area of WXT? A 18 B 36 C 36 D 48

  41. What is the area, in square meters (m), of the trapezoid shown below? A 28 B 36 C 48 D 72

  42. What is the area, in square inches (in.), of the triangle below? A 25 B 25 C 50 D 50

  43. ANGLE RELATIONSHIPS, CONSTRUCTIONS & lINES Two angles of a triangle have measures of 55° and 65°. Which of the following could not be a measure of an exterior angle of the triangle? A 115° B 120° C 125° D 130° If the measure of an exterior angle of a regular polygon is120°,how many sides does the polygon have? A 3 B 4 C 5 D 6

  44. What ism ∠ x ? A 35° B 60° C 85° D 95°

  45. The measures of the interior angles of a pentagon are 2x, 6x, 4x-6, 2x-16, and 6x+2.What is the measure, in degrees, of the largest angle? A 28 B 106 C 170 D 174 A regular polygon has 12 sides. What is the measure of each exterior angle? A 15 B 30 C 45 D 60

  46. What is m∠1? A 34 B 56 C 64 D 92

  47. Given: p II q ; m II n ; m∠1 = 175° What is m∠2? A 15° B 75° C 90° D 105°

  48. Constructions Given: angle A What is the first step in constructing the angle bisector of angle A? A Draw ray AD. B Draw a line segment connecting points B and C. C From points B and C, draw equal arcs that intersect at D. D From point A, draw an arc that intersects the sides of the angle at points B and C.

  49. What geometric construction is shown in the diagram below? A an angle bisector B a line parallel to a given line C an angle congruent to a given angle D a perpendicular bisector of a segment

  50. Marsha is using a straightedge and compass to do the construction shown below.Whichbest describes the construction Marsha is doing? A a line through P parallel to line l B a line through P intersecting line l C a line through P congruent to line l D a line through P perpendicular to line l