ISEE Lower Level Quantitative Reasoning - ISEE Lower Level (grades 5-6) Mathematics Achievement

What is the length of a rectangular room with a perimeter of and a width of

Explanation

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

$\frac{50}{2}=\frac{2l}{2}$

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point W (2, 4); Point X (3, 6); Point Y (5, 4); Point Z (6, 6)

A polygon is formed with vertices W, X, Y, and Z. Which type of polygon is formed?

Parallelogram

Trapezoid

Kite

Pentagon

Square

Explanation

Begin by plotting the points and connecting the vertices.

Screenshot_2015-03-24_at_4.55.16_pm

The quadrilateral that is created has two sets of parallel sides. Out of the possible answer choices, this can describe both squares and parallelograms. Because the figure does not contain right angles and the sides are not all the same length, it must be a parallelogram.

What number is nine hundred thirty-four?

Explanation

in word form is nine hundred thirty-four.

$2,5,11,23,47, \square$

What is the next number in the series?

Explanation

First, determine what the pattern is in the series. The pattern here is to multiply the previous number by 2 and then add 1. Therefore, multiply 47 by 2 (which is 94), and then add 1. The result is 95.

Find the product.

$-7\times -11$

Explanation

When multiplying two negative numbers, the product will be positive. The correct answer is 77.

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.

What digit is in the hundreds place?

Explanation

The hundreds place is always the third number on the right. In this case, is the third number on the right.

The perimeter of a triangle is 14 inches. One side is 4 inches long. Another side is 5 inches long. How long is the 3rd side?

$5\ inches$

$2\ inches$

$\dpi{100} 4\ inches$

$6\ inches$

Explanation

Add up all of the sides of a triangle to get the perimeter. Here, 2 of the sides add up to give you 9 inches. The third side must equal the difference between 14 inches and 9 inches.

$14-9=5\ inches$

What digit is in the tens place?

Explanation

The tens place is always the second number on the right. In this case, is the second number on the right.

What is the area of the right triangle in the following figure?

$36\textup{ in}^2$

$37\textup{ in}^2$

$38\textup{ in}^2$

$39\textup{ in}^2$

$40\textup{ in}^2$

Explanation

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=8\times 9$

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .