Math Assessment - Key Concepts
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Questions and Answers

What is the numerical representation of ten thousand, four hundred and twenty-seven?

  • 10,540
  • 10,240
  • 14,270
  • 10,427 (correct)

Which of the following is an improper fraction?

  • 5/6
  • 3/2 (correct)
  • 1/2
  • 52/72 (correct)

How many studs were delivered in total by both trucks?

  • 1,059 (correct)
  • 947
  • 800
  • 1,059 (correct)

What is the total amount of ceiling tiles needed if each of the 18 offices on 37 stories requires 21 tiles?

<p>14,280 (B)</p> Signup and view all the answers

What is the result of dividing 1,518 by 46?

<p>33 (A)</p> Signup and view all the answers

If insulation installation covers 1,400 square feet per hour, how many days will it take to install 29,400 square feet?

<p>5 days (A)</p> Signup and view all the answers

What is the simplified form of the fraction 14/16?

<p>7/8 (C)</p> Signup and view all the answers

What is the common denominator for the fractions 1/3 and 3/4?

<p>12 (D)</p> Signup and view all the answers

If a flooring adhesive covers 87 sq.ft. per gallon, how many sq.ft. will be covered by 5 gallons?

<p>435 sq.ft. (B)</p> Signup and view all the answers

What is the value of the fraction $\frac{13}{16}$?

<p>0.8125 (D)</p> Signup and view all the answers

How many square feet of carpet have been installed out of 47,440 sq.ft. if 62.5% has been completed?

<p>25,404 sq.ft. (A)</p> Signup and view all the answers

Complete the proportion: 63:21 ; 75:_______.

<p>35 (D)</p> Signup and view all the answers

What is the total cost of purchasing 75 gallons of concrete sealer and 2 concrete sprayers with the given prices?

<p>$8,234.75 (C)</p> Signup and view all the answers

Convert 0.875 into a fraction in lowest terms.

<p>$\frac{7}{8}$ (D)</p> Signup and view all the answers

Convert the fraction $\frac{5}{12}$ into a decimal rounded to the nearest hundredths.

<p>0.49 (A)</p> Signup and view all the answers

How many hours did the carpenter crew work if $3,928.05$ was paid at a rate of $6.45$ per hour?

<p>592 hours (D)</p> Signup and view all the answers

What is the length of the longer leg in a right triangle if the shorter legs are 3' and 4'?

<p>5' (B)</p> Signup and view all the answers

What is the area of a rectangle that measures 14' by 9'?

<p>126 square feet (A)</p> Signup and view all the answers

How many meters are equivalent to 1,500 cm?

<p>1.5 meters (C)</p> Signup and view all the answers

What is the area of a triangle with a base of 17' and a height of 9'?

<p>76.5 square feet (C)</p> Signup and view all the answers

What is the correct formula for calculating the area of a circle?

<p>π × r² (A)</p> Signup and view all the answers

What is the volume in cubic meters of a tank measuring 1.5m wide, 2.7m long, and 0.7m high?

<p>2.27 cubic meters (D)</p> Signup and view all the answers

What is the area of a circular insert with a diameter of 8'?

<p>50.27 square feet (A)</p> Signup and view all the answers

Which term describes lines that are equal distances apart?

<p>Parallel (D)</p> Signup and view all the answers

Flashcards

Ten thousand, four hundred and twenty-seven

The number represented as 10,427

Improper Fraction

A fraction where the numerator is greater than or equal to the denominator.

51/72

Improper fraction.

847 + 212

1059 studs

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Tile needed for 18 offices x 37 floors

11,922 tile

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1,518 ÷ 46

33

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29,400 sq ft / 1,400 sq ft/hr

21 hr

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14/16 simplified

7/8

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51/24 simplified

17/8

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(3/10) + (3/10)

6/10 = 3/5

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Common denominator for 5/8 and 1/4

8

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Common denominator for 1/3 and 3/4

12

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Plywood thickness range

1/4 to 1 inch

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Stacked plywood thickness

1 7/8 inches

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8/12 - 4/12

4/12 = 1/3

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11/16 - 1/4

9/16

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Remaining concrete form sq ft (725 sq ft/day * 2/2)

725 sq ft

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Triangle's longer leg length

To find the length of the missing side of a right-angled triangle, use the Pythagorean theorem (a² + b² = c²). Given two shorter legs, calculate the longer one.

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Area of a Square

The area of a square is calculated by multiplying its side length by itself (side × side).

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Area of a Rectangle

The area of a rectangle is the product of its length and width.

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Area of a Triangle

The area of a triangle is calculated by halfing the product of its base and height.

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Area of a Circle

The area of a circle is calculated using the formula: π × radius²

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1,500 cm to meters

1500 cm is equal to 15 meters.

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Area of a rectangular room (14ft x 9ft)

126 sq ft

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Area of a triangle (17ft base, 9ft height)

76.5 sq ft

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Area of a circular insert (diameter 8ft)

50.27 sq ft (approximately)

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Parallel lines

Lines that are always the same distance apart and never touch.

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Perpendicular lines

Lines that intersect at a 90-degree angle.

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Level line

A horizontal line that is parallel to the horizon.

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Circumference of a circle

The distance around the circle.

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Volume of a rectangular tank(1.5m, 2.7m, 0.7m)

2.835 cubic meters

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34,991 cubic inches to cubic yards

6.24 cubic yards

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Flooring coverage (sq ft)

The area in square feet that a gallon of adhesive covers.

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Multiplying fractions (13*16)

Multiply the numerators and denominators, then simplify.

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Dividing fractions (1/16 ÷ 1/16)

Invert the second fraction (reciprocal) and multiply.

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Time to align pump shafts (fraction)

Calculate the time needed to align a given number of pump shafts, given the time to align a different number.

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Proportion (63:21; 75:?)

Finding the missing value in a proportion, where ratios are equivalent.

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Equivalent Fractions (40/6 = x)

Find the missing numerator or denominator to create equivalent fractions.

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Nine hundredths (decimal)

Represent the fraction 9/100 as a decimal.

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Eighty-seven thousandths (decimal)

Represent the fraction 87/1000 as a decimal.

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Decimal addition (3.6 + 4.7 + 0.5)

Adding decimals based on place values.

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Decimal subtraction (7.2 - 1.06)

Subtracting decimals based on place values.

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Hours worked (carpenter crew)

Calculate the number of hours worked by a carpenter crew given the total pay and the hourly rate.

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Decimal Multiplication (4 * 1.74)

Multiplying decimal numbers.

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Decimal division (65 ÷ 1.5)

Divide decimal numbers. Round the answer if necessary.

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Total cost (concrete)

Calculate the total cost of purchasing multiple items.

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Decimal to fraction conversion (0.875)

Convert a decimal number to a fraction in lowest terms.

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Fraction to decimal (5/12)

Divide numerator by denominator to express the fraction as a decimal. Round if applicable.

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Percentage to decimal (79%)

Convert a percentage to its decimal equivalent.

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Carpet installed (sq ft)

Determine the area of carpet installed based on a percentage of the total area.

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Feet and inches to inches (5'3")

Convert a measurement given in feet and inches to a measurement in inches (ex. converting 5 feet and 3 inches to a measurement purely in inches).

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Yards to inches (6 yards)

Convert a measurement from yards to inches (unit conversion).

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Value of pi (rounded to 4 decimal places)

Approximate value of mathematical constant pi.

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Study Notes

Math Assessment - Key Concepts

  • Number Writing: Ten thousand, four hundred, and twenty-seven is written as 10,427.

  • Improper Fractions: The improper fraction is 51/2.

  • Studs Delivered: A total of 1,069 studs were delivered. (847 + 212 = 1059)

  • Ceiling Tiles: 21 tiles are needed per office, 18 offices per floor, and there are 37 floors; so 13,716 tiles are needed. (211837=13716)

  • Division: 1,518 divided by 46 equals 33. (1,518 ÷ 46 = 33)

  • Installation Rate: If insulation can be installed at 1400 sq ft/hr and 29400 sq ft needs installing, the job will take 21 hours. (29400 ÷ 1400 = 21)

  • Fraction Simplification: 14/16 simplifies to 7/8. (14 ÷ 2 = 7, 16÷2 =8)

  • Fraction Simplification (2): 51/24 simplifies to 17/8.

  • Fraction Addition: 3/8 + 3/10 = 39/40.

  • Common Denominator: The lowest common denominator for 5/8 and 1/4 is 8.

  • Common Denominator (2): The lowest common denominator for 3/4 and 1/3 is 12.

  • Plywood Thicknesses: Plywood generally comes in thicknesses ranging from 1/4" to 1 1/8".

  • Stacked Plywood Thickness: Given thicknesses of 1/4", 3/8", 1/2" and 5/8", a stack of these will be 2 1/8" thick. (1/4 + 3/8 + 1/2 + 5/8 = 2 1/8)

  • Fraction Subtraction: 8/12 - 4/12 = 4/12, which simplifies to 1/3.

  • Fraction Subtraction (2): 11/16 - 1/4 =7/16

  • Concrete Forms: A two-man crew sets approximately 725 sq ft of concrete forms per day. If they've completed half that amount, 362.5 sq ft of forms remain. (725/2 = 362.5)

  • Flooring Adhesive: 5 gallons of flooring adhesive covers 437 square feet. (5 * 87.5 = 437.5)

  • Multiplication: 13 * 16= 208

  • Time to Align Motors (hours): Aligning 6 more motors will take 12 hours. (24/11 * 6 = 12 hours)

  • Proportion Completion: The proportion continues 63:21; 75:25.

  • Equivalent Fractions: 5/6 x 8/8 = 40/48

  • Decimal Conversion: Nine hundredths = 0.09.

  • Decimal Conversion (2): Eighty-seven thousandths is 0.087

  • Addition: 3.6 + 4.7 + 0.5 = 8.8

  • Subtraction: 7.2 - 1.06 = 6.14

  • Contractor's Payment: The carpenter crew worked 609 hours. (3,928.05 / 6.45= 609)

  • Multiplication (2): 4* 1.74 = 6.96

  • Division (2): .65 / 1.5 = 0.43

  • Total Cost: The total cost for 75 gallon of sealer and 2 sprayers is 860.56.(75/5∗860.56. (75/5 * 860.56.(75/5∗109.75 + 2 * 104.59=104.59 = 104.59=860.56)

  • Decimal to Fraction: 0.875 = 7/8.

  • Fraction to Decimal: 12/5 = 2.4

  • Percentage to Decimal: 79% is 0.79

  • Carpet Installation: 29,650 square feet of carpet have been installed. (47,440 sq. ft * 62.5% = 29,650 square feet)

  • Feet and Inches to Inches: 5 feet and 3 inches is equal to 63 inches. (5 * 12 + 3 = 63)

  • Yards to Inches: 2 2/3 yards equal 252 inches.((2 2/3) x 3 x 12 = 252)

  • Pi Approximation: Pi is approximately 3.1416.

  • Triangle Sides: If the shorter legs of a right triangle are 3 and 4, the length of the longer leg is 5. (3² + 4² = 5²)

  • Units Conversion: 1,500 cm equals 15 meters. (1,500 cm / 100 cm/meter = 15 meters)

  • Rectangle Area: The area of a rectangular room that is 14 ft by 9 ft is 126 sq ft. (14*9=126)

  • Triangle Area: The area of a triangle with a base of 17' and a height of 9' is 76.5 square feet. (1/2 * 17 * 9 = 76.5)

  • Circle Area: The area of a circle with a diameter of 8 ft. is 50.27 square feet. (Ï€*(8/2)^2 = 50.27)

  • Tank Volume: The volume of the rectangular tank is 1.09 cubic meters (approximately. 1.5 x .7 x.2.7 = 2.835 m³. Rounded to thousandths.)

  • Inch Conversion: 34,991 cubic inches equals 62 cubic yards.
    (34,991 cu. in. / 46,656 cu. in./cu. yd. = approximately 0.75)

  • Ruler Measurements: Measurements A, B,C,D need the diagram to determine the measurements.

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