HSPT Math - Problem Solving

What is the area of the figure below?

6.5

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

$A=5\times 10$ $A=5\times 3$

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

On a particular November day, it is $110^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-15^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$125^\circ F$

$152^\circ F$

$150^\circ F$

$115^\circ F$

$80^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $15^\circ F$ below zero and in Tucson it is $110^\circ F$ above zero; therefore we can say:

$15+110=125^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp10

We can see that Tucson is $125^\circ F$ warmer than New Castle.

Menu 1

The above is a menu at the concession stand at a drive-in movie.

Gary wants to order two hamburgers and two small orders of fries. He wants to order two sodas of the same size. If he has just a twenty-dollar bill on hand, what is the largest size soda of which he can order two?

Gary can afford two large sodas

Gary can afford two medium sodas, but not two large sodas

Gary can afford two small sodas, but not two medium or large sodas

Gary cannot afford two sodas

Explanation

The easiest way to think of this is to note that Gary seems to be ordering for two people, himself and a friend. He has $20, so half of this will be for himself and half for his friend - and half of $20 is $10.

Each hamburger costs $4.89, and each small order of fries costs $2.29. This leaves

to spend on a soda for each person. This will enable to him to buy both himself and his friend a large soda.

Your backyard is wide and long, what is its area?

$60ft^{2}$

$16ft^{2}$

$50ft^{2}$

$10ft^{2}$

Explanation

The area of a rectangle is

So for this you just multiple those two values together to get,

$A=L\cdot w$

Remeber that the units of area are squared.

On a particular November day, it is $65^\circ F$ and sunny in Tucson, Arizona. On the eastern side of the United States, it is $-23^\circ F$ and sleeting in New Castle, Pennsylvania. How many degrees warmer is it in Tucson than New Castle?

$88^\circ F$

$87^\circ F$

$78^\circ F$

$98^\circ F$

$97^\circ F$

Explanation

There are several ways that we could solve this problem. First, we can say that the temperature in New Castle is $23^\circ F$ below zero and in Tucson it is $65^\circ F$ above zero; therefore we can say:

$23+65=88^\circ F$

Also, we can solve this problem by using a number line. New Castle’s temperature is units away from zero and Tucson’s is units away.

Temp1

We can see that Tucson is $88^\circ F$ warmer than New Castle.

Your backyard is wide and long, what is its area?

$60ft^{2}$

$16ft^{2}$

$50ft^{2}$

$10ft^{2}$

Explanation

The area of a rectangle is

So for this you just multiple those two values together to get,

$A=L\cdot w$

Remeber that the units of area are squared.

Find the area of a square if the length is .

Explanation

The area of a square is:

Substitute the length and simplify.

Solve:

$8\times(57-45)$

Explanation

$8\times(57-45)$

When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.

$8\times12=96$

$\frac{4}{5}*\frac{2}{3}=$

$\frac{8}{15}$

$\frac{6}{8}$

$\frac{6}{15}$

$\frac{8}{8}$

Explanation

Multiply the numerators then denominators:

$\frac{4}{5}* \frac{2}{3}=\frac{8}{15}$

Answer: $\frac{8}{15}$

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

Problem Solving

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