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Sets and Geometry

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Sets and Geometry

Working with Sets

GEOMETRY

Formula given on the Regents:

Formula not given on the Regents

Area of a circle = πr2 Circumference of a circle = 2πr

Relative Error

Any measurement made with a measuring device is approximate.

If you measure the same object two different times, the two measurements may not be exactly the same. The difference between two measurements is called a variation in the measurements.

Another word for this variation - or uncertainty in measurement - is "error." This "error" is not the same as a "mistake." It does not mean that you got the wrong answer. The error in measurement is a mathematical way to show the uncertainty in the measurement. It is the difference between the result of the measurement and the true value of what you were measuring.

When the accepted or true measurement is known, the relative error is found using:

Note that the relative error is always a positive answer – that is why the formula uses the absolute value on the top line. If your calculation gives you a negative answer, just write it as a positive value in the final step.

Wendy measures the floor in her rectangular bedroom for new carpeting. Her measurements are 24 feet by 14 feet. The actual measurements are 24.2 feet by 14.1 feet. Determine the relative error in calculating the area of her bedroom. Express your answer as a decimal to the nearest thousandth

Solution:

Measured value = 24 x 14 = 336 ft2

Actual value = 24.2 x 14.1 = 341.22 ft2

= 336 – 341.22 = -0.015298

341.22

Finally change the negative to a positive value and round to the ‘nearest thousandth ‘

The answer is 0.015. (Note there are no units)

1. Which interval notation represents -3 ≤ x ≤ 3?

(1) [-3,3] (2) (-3,3] (3) [-3,3) (4) (-3,3)

- 2. Which set builder notation describes {-2, -1, 0, 1, 2, 3}?
- {x│-3 ≤ x ≤ 3, where x is an integer}
- (2) {x│-3 < x ≤ 4, where x is an integer}
- (3) {x│-2 < x < 3, where x is an integer}
- (4) {x│-2 ≤ x < 4, where x is an integer}

3. Given: R = {1,2,3,4} A = {0,2,4,6} P = {1,3,5,7}

What is R∩P?

(1) {0,1,2,3,4,5,6,7} (2) {1,2,3,4,5,7} (3) {1,3} (4) {2,4}

4. Given:A = {2,4,5,7,8} and B = {3,5,8,9}

What is A U B?

(1) {5} (2) {5,8} (3) {2,3,4,7,9} (4) {2,3,4,5,7,8,9}

5. A garden is in the shape of an isosceles trapezoid and a semicircle, as shown in the diagram below. A fence will be put around the perimeter of the entire garden.

Which expression represents the length of fencing, in meters, that will be needed?

1) 22 + 6π 2) 22 + 12π 3) 15 + 6π 4) 15 + 12π

6. In the diagram below of rectangle AFEB and a semicircle with diameter CD, AB = 5 inches, AB = BC = DE = FE, and CD = 6 inches. Find the area of the shaded region, to the nearest hundredth of a square inch.

7. Oatmeal is packaged in a cylindrical container, as shown in the diagram below.

The diameter of the container is 13 centimeters and its height is 24 centimeters. Determine, in terms of π, the volume of the cylinder, in cubic centimeters

8. If the volume of a cube is 8 cubic centimeters, what is its surface area, in square centimeters?

1) 32 2) 24 3) 12 4) 4

9. Students calculated the area of a playing field to be 8,100 square feet. The actual area of the field is 7,678.5 square feet. Find the relative error in the area, to the nearest thousand

10 To calculate the volume of a small wooden cube, Ezra measured an edge of the cube as 2 cm. The actual length of the edge of Ezra’s cube is 2.1 cm. What is the relative error in his volume calculation to the nearest hundredth?

1) 0.13 2) 0.14 3) 0.15 4) 0.16