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

Solve for x: 3x + 7 = 22.

  • A.
    x = 3
  • B.
    x = 5
  • C.
    x = 6
  • D.
    x = 7

Subtract 7 from both sides to get 3x = 15, then divide by 3 to get x = 5.

Question

What is the area of a rectangle with length 8 cm and width 5 cm?

  • A.
    26 cm²
  • B.
    40 cm²
  • C.
    45 cm²
  • D.
    80 cm²

Area of a rectangle is length multiplied by width: 8 × 5 = 40 square centimeters.

Question

A sphere and its dimension are shown in the diagram. 15 in. Which measurement is closest to the volume of the sphere in cubic inches?Open full-size question
  • F.
    Answer F: 1,325.4 in.3
  • G.
    Answer G: 188.5 in.3
  • H.
    Answer H: 94.2 in.3
  • J.
    Answer J: 1,767.1 in.3

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

Question

The two lines graphed on the coordinate grid each represent an equation. y 9 8 (−2, 6) 7 6 5 4 (3, 5) (−6, 2) 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 (−6, −6) −8−7 −9 Which ordered pair represents a solution to both equations?Open full-size question
  • A.
    Answer A: (4 ,0)
  • B.
    Answer B: (3 ,3)
  • C.
    Answer C: (3, 3)
  • D.
    Answer D: (0, 4)

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

Question

Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute. Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallon per minute. After how many minutes will both aquariums contain the same amount of water?Open full-size question
  • A.
    Answer A: 148 min
  • B.
    Answer B: 125 min
  • C.
    Answer C: 25 min
  • D.
    Answer D: 50 min

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

Question

The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closest to the length of this rectangle in feet?Open full-size question
  • F.
    Answer F: 9ft
  • G.
    Answer G: 17 ft
  • H.
    Answer H: 12.4 ft
  • J.
    Answer J: 13.6 ft

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

Question

Triangle ABC was transformed to create triangle ABC′′ ′. y 7 6 A 5 4 3 2 1 B C −7 7−6 −5 −4 −3 −2 −11 2 3 4 5 6x −1 ′ −2 A −3 −4 −5 −6 B′ C′ −7 Which rule best describes this transformation?Open full-size question
  • F.
    Answer F: (,xy) o (xy, 7)
  • G.
    Answer G: (,xy) o (x , y)
  • H.
    Answer H: (,xy) o (x 7, y)
  • J.
    Answer J: (,xy) o ( xy, )

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

Question

A coach is ordering shirts for a team. • The coach pays a one-time fee of $24. • The coach also pays $8 for each shirt ordered. Which function can be used to find c, the total amount the coach pays in dollars when k shirts are ordered?Open full-size question
  • F.
    Answer F: c = 8 k + 32
  • G.
    Answer G: c = 8 k + 24
  • H.
    Answer H: c = 32 k + 8
  • J.
    Answer J: c = 24 k + 8

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

Question

What value of x makes this equation true? 12 x 15 = 6 3 xOpen full-size question
  • F.
    Answer F: 7 3
  • G.
    Answer G: 3 7
  • H.
    Answer H: 5 7
  • J.
    Answer J: 7 5

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

Question

A silo is a building shaped like a cylinder used to store grain. The diameter of a particular silo is 6.5 meters, and the height of the silo is 12 meters. 6.5 m 12 m Which equation can be used to find V, the volume of this silo in cubic meters?Open full-size question
  • A.
    Answer A: V = S(3.25)2 (12)
  • B.
    Answer B: V = S(6.5)2 (12)
  • C.
    Answer C: V = S(12)2 (3.25)
  • D.
    Answer D: V = S(6)2 (6.5)

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

Question

The table shows the completion times of four runners in a race. Race Times Runner Time (seconds) Joe 112 2 Ellen 12.09 Steve 212 5 Patty 12.8 Which list shows the runners in order by their completion times from fastest to slowest?Open full-size question
  • A.
    Answer A: Patty, Joe, Steve, Ellen
  • B.
    Answer B: Ellen, Joe, Steve, Patty
  • C.
    Answer C: Ellen, Steve, Joe, Patty
  • D.
    Answer D: Patty, Steve, Joe, Ellen

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

Question

The diagram shows three squares that are joined at vertices to form a right triangle. Square K Square N Square L Which statement is true?Open full-size question
  • A.
    Answer A: The sum of the areas of Square N and Square L is equal to the area of Square K.
  • B.
    Answer B: The sum of the areas of Square N and Square L is greater than the area of Square K.
  • C.
    Answer C: The sum of the areas of Square N and Square K is equal to the area of Square L.
  • D.
    Answer D: The sum of the areas of Square N and Square K is less than the area of Square L.

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

Question

Quadrilateral KMPT is dilated by a scale factor of ′3to create quadrilateral KM′′P′T . The 4 perimeter of quadrilateral KMPT is x units. What is the perimeter in units of quadrilateral KM′′P′ T′?Open full-size question
  • F.
    Answer F: x units
  • G.
    Answer G: 3 x units 4 2
  • H.
    Answer H: § 3 · units ¨ ¸ x4 © ¹
  • J.
    Answer J: 4 x units 3

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

Question

A polygon is graphed on a coordinate grid with (,xy) representing the location of a certain point on the polygon. The polygon is transformed using the rule (,x y ) o (ax , ay ). Which statement must be true?Open full-size question
  • F.
    Answer F: If a is greater than 1, the image of the polygon is congruent to the polygon.
  • G.
    Answer G: If a is between 0 and 1, the image of the polygon is congruent to the polygon.
  • H.
    Answer H: If a is greater than 1, the image of the polygon is smaller than the polygon.
  • J.
    Answer J: If a is between 0 and 1, the image of the polygon is smaller than the polygon.

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

Question

At a store each notebook has a cost of x dollars. Which situation can be represented by this inequality? 5 x < 3 x + 2Open full-size question
  • A.
    Answer A: The cost of 5 notebooks is greater than the cost of 3 notebooks plus a $2 pen.
  • B.
    Answer B: The cost of 5 notebooks is less than the cost of 3 notebooks with a $2-off coupon.
  • C.
    Answer C: The cost of 5 notebooks is less than the cost of 3 notebooks plus a $2 pen.
  • D.
    Answer D: The cost of 5 notebooks is $2 greater than the price of 3 notebooks.

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

Question

A can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. Which measurement is closest to the total surface area of the can in square centimeters?Open full-size question
  • F.
    Answer F: 603.19 cm2
  • G.
    Answer G: 245.04 cm2
  • H.
    Answer H: 376.99 cm2
  • J.
    Answer J: 188.50 cm2

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

Question

The diagonal lengths of three rectangles are shown. The rectangles are not drawn to scale. Rectangle P Rectangle S Rectangle T 34 cm 6.7 cm 36.5 cm5 Which list shows the rectangles in order by their diagonal lengths from shortest to longest?Open full-size question
  • A.
    Answer A: Rectangle T, Rectangle S, Rectangle P
  • B.
    Answer B: Rectangle T, Rectangle P, Rectangle S
  • C.
    Answer C: Rectangle S, Rectangle T, Rectangle P
  • D.
    Answer D: Rectangle S, Rectangle P, Rectangle T

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

Question

The graph shows the relationship between the number of gallons of fuel remaining in the tank of a semitruck and the number of miles traveled by the semitruck. y Semitruck Fuel 270 240 210 180 150 120 90 60 30 0 100 200 300 400 x Number of Miles Traveled Which function can be used to find y, the number of gallons of fuel remaining in the tank of the semitruck after it has traveled x miles?Open full-size question
  • F.
    Answer F: y = 240 x 30
  • G.
    Answer G: y = x1 + 240 6
  • H.
    Answer H: y = 240 x 10
  • J.
    Answer J: y = x1 + 240 10

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

Question

The height of a cylinder is 5 centimeters. The circumference of the base of the cylinder is 16 centimeters.S Which measurement is closest to the volume of the cylinder in cubic centimeters?Open full-size question
  • A.
    Answer A: 251.3 cm3
  • B.
    Answer B: 4,021.2 cm3
  • C.
    Answer C: 1,005.3 cm3
  • D.
    Answer D: 628.3 cm3

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

Question

The table shows the linear relationship between the number of hours Francis worked, x, and the amount of money Francis earned, y. Francis’s Earnings Number of Hours Worked 1.25 3.75 5.5 Amount Earned $17.50 $52.50 $77.00 Based on the table, how much did Francis earn per hour?Open full-size question
  • A.
    Answer A: $17.50 per hour
  • B.
    Answer B: $14.00 per hour
  • C.
    Answer C: $35.00 per hour
  • D.
    Answer D: $24.50 per hour

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