Nicholas Zhao Teaches Math

CBE: Algebra Prep

Category focus

Expressions, Equations, and Relationships

Back to bank

Solve equations and inequalities and reason about geometric relationships and measurement.

Questions

101

Skill type

expressions and-equations

Study mode

Practice + review

Sample questions

Question

Four triangles are shown. One side of each triangle lies on a ray, and the triangles are not drawn to scale. 56° 60° 35° 91° 120°60° 120° 30° 20° 140° 130° x° Based on these triangles, which statement about x is true?Open full-size question
  • F.
    Answer F: x = 160, because 180 (130 + 30) = 20 and 180 20 = 160
  • G.
    Answer G: x = 20, because 130 + 30 = 160 and 180 160 = 20
  • H.
    Answer H: x = 80, because 180 130 = 50 and 50 + 30 = 80
  • J.
    Answer J: x = 340, because 130 + 30 = 160 and 160 + 180 = 340

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

On a map scale, 2 inches represents 60 miles. Which graph best shows the relationship between x, the number of inches on the map, and y, the actual distance in miles? y Map Scale y Map Scale 225 225 200 200 175 175 150 150 A 125 C 125 100 100 75 75 50 50 25 25 0 123456789 x 0 123456789 x Number of Inches on Map Number of Inches on Map y Map Scale y Map Scale 225 225 200 200 175 175 150 150 B 125 D 125 100 100 75 75 50 50 25 25 0 123456789 x 0 123456789 x Number of Inches on Map Number of Inches on MapOpen full-size question
  • A.
    Answer A: Answer A (see image)
  • B.
    Answer B: Answer B (see image)
  • C.
    Answer C: Answer C (see image)
  • D.
    Answer D: Answer D (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Quadrilateral PQRS was translated 5 units to the right and 3 units up to create quadrilateral PQ′′R′S.′ Which rule describes this transformation?Open full-size question
  • F.
    Answer F: (xy, ) o (x 5, y 3)
  • G.
    Answer G: (xy, ) o (x + 5, y + 3)
  • H.
    Answer H: (xy, ) o (x 3, y 5)
  • J.
    Answer J: (xy , ) o (x + 3, y + 5)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Trapezoid WKRP was translated 4 units to the left and 5 units up on a coordinate grid to create trapezoid WKRP′′′ .′ Which rule describes this transformation?Open full-size question
  • A.
    Answer A: (xy, ) → (x −− 4, y + 5)
  • B.
    Answer B: (xy, ) → (x + 4, y −− 5)
  • C.
    Answer C: (xy, ) → (x + 4, y + 5)
  • D.
    Answer D: (xy, ) → (x −− − 4, y − 5)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

A bowling ball shaped like a sphere has a diameter of 21.6 centimeters. Which measurement is closest to the volume of the bowling ball in cubic centimeters?Open full-size question
  • A.
    Answer A: 1,954.3 cm 3
  • B.
    Answer B: 5,276.7 cm 3
  • C.
    Answer C: 488.6 cm 3
  • D.
    Answer D: 42,213.4 cm 3

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Triangle XYZ is rotated 90° clockwise about the origin to form triangle XY′′Z .′ y 7 6 5 Z 4 Y 3 2 1 −7 7−6 −5 −4 −3 −2 −11 2 3 4 5 6x −1 −2 −3 X −4 −5 −6 −7 Which statement is true?Open full-size question
  • F.
    Answer F: The sum of the angle measures of triangle XYZ is 90° less than the sum of the angle measures of triangle XY′′′Z.
  • G.
    Answer G: The angle measures of triangle XYZ are less than the corresponding angle measures of triangle XY′′′Z.
  • H.
    Answer H: Triangle XYZ is not congruent to triangle XY′′′Z.
  • J.
    Answer J: The area of triangle XYZ is equal to the area of triangle XY′′′Z.

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

A water tank currently contains 275 gallons of water. The amount of water in the tank will decrease at a constant rate of 15 gallons per week. Which function can be used to find t, the total number of gallons of water in the tank after w weeks?Open full-size question
  • F.
    Answer F: t = 15 w −− 275
  • G.
    Answer G: t = − 15 w− + 275
  • H.
    Answer H: t = 275 w −− 15
  • J.
    Answer J: t = − 275 w− + 15

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

A teacher bought markers at a cost of $3 per set. The teacher had a $2-off coupon to use toward the total cost of the markers bought. Which table shows the relationship between x, the number of sets of markers bought by the teacher, and y, the total cost of the markers? A Markers C Markers Sets of Sets of Markers Total Cost, y Markers Total Cost, y Bought, x Bought, x 3 $7 3 $11 9 $25 9 $29 12 $34 12 $38 24 $70 24 $74 B Markers D Markers Sets of Sets of Markers Total Cost, y Markers Total Cost, y Bought, x Bought, x 9 $1 9 $5 12 $2 12 $6 15 $3 15 $7 24 $6 24 $10Open full-size question
  • A.
    Answer A: Answer A (see image)
  • B.
    Answer B: Answer B (see image)
  • C.
    Answer C: Answer C (see image)
  • D.
    Answer D: Answer D (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The diameter of a cylinder is 2.5 inches, and the height is 7.5 inches. Which equation can be used to find V, the volume of the cylinder in cubic inches?Open full-size question
  • F.
    Answer F: V = π(2.5) (7.5)2
  • G.
    Answer G: V = π(7.5) (2.5)2
  • H.
    Answer H: V = π(1.25) (7.5)2
  • J.
    Answer J: V = π(3.75) (2.5)2

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The table shows the diagonal lengths of TV screens at a store. TV Screen Diagonal Lengths Screen Length (feet) W 12.25 X 12 6 Y 37 144 Z 83 Which TV screen has the smallest diagonal length in feet?Open full-size question
  • F.
    Answer F: W
  • G.
    Answer G: X
  • H.
    Answer H: Y
  • J.
    Answer J: Z

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The diagram shows the height of a cone that holds ice cream. The cone has a volume of 1.5 π cubic inches. 4.5 in. Which measurement is closest to the radius of the cone in inches?Open full-size question
  • F.
    Answer F: 0.6 in.
  • G.
    Answer G: 1.4 in.
  • H.
    Answer H: 1.0 in.
  • J.
    Answer J: 0.5 in.

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

In each diagram, line g is parallel to line k, and line t intersects lines g and k. 61° g 123° g 61° k 123° k t t 42° g g 136° 42° k k x° t t Based on the diagrams, which statement about x is true?Open full-size question
  • A.
    Answer A: The value of x is 180, because the labeled angles in each diagram are supplementary and the sum of the measures of supplementary angles is 180 degrees.
  • B.
    Answer B: The value of x is 90, because the labeled angles in each diagram are complementary and the sum of the measures of complementary angles is 90 degrees.
  • C.
    Answer C: The value of x is 44, because the sum of the measures of the labeled angles in each diagram is 180 degrees.
  • D.
    Answer D: The value of x is 136, because the labeled angles in each diagram are congruent.

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The side lengths in yards of a triangle and a square are shown in the diagram. 2x yd (4x − 2) yd 2(x + 7) yd 2.5x yd The perimeter of the triangle is equal to the perimeter of the square. What is the value of x?Open full-size question
  • F.
    Answer F: − 4−
  • G.
    Answer G: 23
  • H.
    Answer H: 6
  • J.
    Answer J: 52

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

A figure was transformed on a coordinate grid using the rule .(, )xy − y ) → (− x,− − Which of the following describes this transformation?Open full-size question
  • F.
    Answer F: A reflection across the x-axis
  • G.
    Answer G: A reflection across the y-axis
  • H.
    Answer H: A 90° clockwise rotation about the origin
  • J.
    Answer J: A 180° clockwise rotation about the origin

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

A survey of customers at a restaurant revealed that 7 out of 10 customers preferred the restaurant’s new spaghetti sauce. Which graph shows the relationship between y, the number of customers who preferred the new spaghetti sauce, and x, the total number of customers? New Spaghetti Sauce New Spaghetti Sauce y y 63 63 56 56 49 49 42 42 A 35 C 35 28 28 21 21 14 14 7 7 0 10 20 30 40 x 0 10 20 30 40 x Total Number of Customers Total Number of Customers New Spaghetti Sauce New Spaghetti Sauce y y 45 45 40 40 35 35 30 30 B 25 D 25 20 20 15 15 10 10 5 5 0 14 28 42 56 x 0 14 28 42 56 x Total Number of Customers Total Number of CustomersOpen full-size question
  • A.
    Answer A: Answer A (see image)
  • B.
    Answer B: Answer B (see image)
  • C.
    Answer C: Answer C (see image)
  • D.
    Answer D: Answer D (see image)

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Triangle ABC and triangle DEF are similar. B 6 in. E 4 in. A C D7 in. x in. F Which proportion must be true?Open full-size question
  • F.
    Answer F: 7 4= x 6
  • G.
    Answer G: 4 x= 6 7
  • H.
    Answer H: 6 x= 4 7
  • J.
    Answer J: 4 7= x 6

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Which list shows these numbers in order from least to greatest? 38 , − 6.35,− − 63%, − 19 3Open full-size question
  • A.
    Answer A: − −− 6.35, − ,19 63%, 38 3
  • B.
    Answer B: 63%, 38 , −− − ,19 − 6.35 3
  • C.
    Answer C: − −− 6.35, − ,19 38 , 63% 3
  • D.
    Answer D: − −− ,19 − 6.35, 63%, 38 3

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

Rectangle ABCD is shown with the dimensions given in units. A 9x − 16 units B 1.5x + 42 units D C The length of AB is greater than the length of AD . Which inequality represents this situation?Open full-size question
  • A.
    Answer A: 9 x −− 16 < 1.5 x + 42
  • B.
    Answer B: 9 x −− 16 > 1.5 x + 42
  • C.
    Answer C: 10.5 x < 26
  • D.
    Answer D: 10.5 x > 26

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The coordinate grid shows XY . y 7 6 X 5 4 3 2 1 −7 Y−6 −5 −4 −3 −2 −1 1 2 3 4 5 67x −1 −2 −3 −4 −5 −6 −7 Which measurement is closest to the length of XY in units?Open full-size question
  • F.
    Answer F: 7.8 units
  • G.
    Answer G: 16.0 units
  • H.
    Answer H: 13.0 units
  • J.
    Answer J: 11.7 units

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.

Question

The graph shows a relationship between x and y. y 9 8 7 6 5 4 3 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 −1 x 1 2 3 4 5 6 7 8 9 −2 −3 −4 −5 −6 −7 −8 −9 Which statement is true?Open full-size question
  • A.
    Answer A: The graph shows a non-proportional relationship because the graph has a negative slope.
  • B.
    Answer B: The graph shows a non-proportional relationship because the graph does not contain the origin.
  • C.
    Answer C: The graph shows a proportional relationship because the x and y intercepts both contain 7.
  • D.
    Answer D: The graph shows a proportional relationship because the graph passes through 3 different quadrants.

Imported from a released STAAR assessment item. Review recommended for final answer key alignment.