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Questions 1 - 10

A certain cube has a side length of 25 m. How many square tiles, each with an area of 5 m2, are needed to fully cover the surface of the cube?

100

200

500

750

1000

Explanation

A cube with a side length of 25m has a surface area of:

25m * 25m * 6 = 3,750 m2

(The surface area of a cube is equal to the area of one face of the cube multiplied by 6 sides. In other words, if the side of a cube is s, then the surface area of the cube is 6_s_2.)

Each square tile has an area of 5 m2.

Therefore, the total number of square tiles needed to fully cover the surface of the cube is:

3,750m2/5m2 = 750

Note: the volume of a cube with side length s is equal to _s_3. Therefore, if asked how many mini-cubes with side length n are needed to fill the original cube, the answer would be:

s3/n3

Which of the following statements demonstrates the associative property of addition?

None of the examples in the other responses demonstrates the associative property of addition.

Explanation

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only

demonstrates this property, so it is the correct choice.

What is the slope of the line that passes through and ?

Explanation

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-7-7}{-3-4}=\frac{-14}{-7}=2$

Explanation

To subtract decimals you place the first decimal over the top of the other aligned by the decimal point. If there are no numbers after a tens, hundredths, or thousandths place or further to the right of the decimal just add a zero in the required areas.

For example becomes

Then go through each place and subtract the top number by the bottom number. Subtract the numbers in each place like you would any number.

The example we are working with will look like this

The answer after subtraction is

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Explanation

A square that has an area of 81 has sides that are the square root of 81 (side2 = area for a square). Thus each of the four sides is 9. The sum of three of these sides is .

A trapezoid has height 32 inches and bases 25 inches and 55 inches. What is its area?

$1,280 ; \textrm{in}^{2}$

$800; \textrm{in}^{2}$

$1,760; \textrm{in}^{2}$

$1,375; \textrm{in}^{2}$

$1,920; \textrm{in}^{2}$

Explanation

Use the following formula, with :

$A = \frac{1}{2} (B+b)h = \frac{1}{2} (55+25) \cdot 32 = 1,280$

What is the area of the figure below?

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

6.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 12$ $A=7\times 5$

To find our final answer, we need to add the areas together.

Find the area of a square if the length is .

Explanation

The area of a square is:

Substitute the length and simplify.

Spinner target

Above is a target. The radius of the smaller quarter-circles is half that of the larger quarter-circles.

A blindfolded man throws a dart at the above target. Assuming the dart hits the target, and that no skill is involved, give the odds against the dart landing in the yellow region.

39 to 1

13 to 1

14 to 1

40 to 1

Explanation

Call the radius of one of the smaller quarter-circles 1 (the reasoning is independent of the actual radius). Then the area of each quarter-circle is

$\frac{1}{4} \cdot \pi r ^{2} = \frac{1}{4} \cdot \pi \cdot 1 ^{2} = \frac{1}{4} \pi$ .

Each of the four wedges of one such quarter-circle has area

$\frac{1}{4} \cdot \frac{1}{4} \pi = \frac{\pi}{16}$ .

The yellow region is one such wedge.

The radius of each of the larger quarter-circles is 2, so the area of each is $\frac{1}{4} \cdot \pi r ^{2} = \frac{1}{4} \cdot \pi \cdot 2 ^{2} = \pi$