HSPT Mathematics

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Questions 1 - 10

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.

12.5

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

$A=6\times 8$ $A=7\times 5$

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

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

The total area of the target is

$\frac{1}{4}\pi + \frac{1}{4} \pi + \pi + \pi = \frac{5 \pi}{2}$

Therefore, the yellow wedge is

$\frac{\pi}{16} \div \frac{5 \pi}{2} = \frac{\pi}{16} \cdot \frac{2}{5 \pi}= \frac{1}{8} \cdot \frac{1}{5 }= \frac{1}{40}$

of the target, and the odds against the dart landing in that region are 39 to 1.

Find the area of a square if the length is .

Explanation

The area of a square is:

Substitute the length and simplify.

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.

11.5

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

$A=7\times 3$ $A=6\times 3$

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

A square is 9 feet long on each side. How many smaller squares, each 3 feet on a side can be cut out of the larger square?

Explanation

Each side can be divided into three 3-foot sections. This gives a total of $3\times3=9$ squares. Another way of looking at the problem is that the total area of the large square is 81 and each smaller square has an area of 9. Dividing 81 by 9 gives the correct answer.

Solve:

$\frac{1}{2}-\frac{3}{7}$

$\frac{1}{14}$

$\frac{3}{5}$

$-\frac{3}{5}$

$-\frac{1}{14}$

$\frac{1}{7}$

Explanation

The lowest common denominator of 2 and 7 is 14.

$\frac{1}{2}=\frac{7}{14}$

$\frac{3}{7}=\frac{6}{14}$

$\frac{7}{14}-\frac{6}{14}=\frac{1}{14}$

Find the sum of the following:

$5\frac{1}{8}+6\frac{3}{16}?$

Explanation

To get the decimal from a fraction, divide the numerator by the denominator

$\frac{1}{8}=0.125$

$5\frac{1}{8}=5.125$

$\frac{3}{16}=0.1875$

$6\frac{3}{16}=6.1875$

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