ISEE Lower Level Math : ISEE Lower Level (grades 5-6) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #161 : How To Find The Solution To An Equation

Which of the following makes this equation true:

\(\displaystyle 2x-1=11\)

Possible Answers:

\(\displaystyle x=7\)

\(\displaystyle x=2\)

\(\displaystyle x=4\)

\(\displaystyle x=6\)

\(\displaystyle x=1\)

Correct answer:

\(\displaystyle x=6\)

Explanation:

To answer the question, we will solve for x.  So, we get

\(\displaystyle 2x-1=11\)

\(\displaystyle 2x-1+1=11+1\)

\(\displaystyle 2x-0=12\)

\(\displaystyle 2x=12\)

\(\displaystyle \frac{2x}{2} = \frac{12}{2}\)

\(\displaystyle x=6\)

Example Question #162 : How To Find The Solution To An Equation

Solve for y in the following equation:

\(\displaystyle 9y+3=30\)

Possible Answers:

\(\displaystyle y=3\)

\(\displaystyle y=7\)

\(\displaystyle y=6\)

\(\displaystyle y=12\)

\(\displaystyle y=9\)

Correct answer:

\(\displaystyle y=3\)

Explanation:

To solve for ywe want y to stand alone.  So, we get

\(\displaystyle 9y+3=30\)

\(\displaystyle 9y+3-3=30-3\)

\(\displaystyle 9y+0=27\)

\(\displaystyle 9y=27\)

\(\displaystyle \frac{9y}{9} = \frac{27}{9}\)

\(\displaystyle y=3\)

Example Question #163 : How To Find The Solution To An Equation

Solve for \(\displaystyle x\)

\(\displaystyle 4x-5=11\)

Possible Answers:

\(\displaystyle -3\)

\(\displaystyle 4\)

\(\displaystyle -2\)

\(\displaystyle 12\)

\(\displaystyle 6\)

Correct answer:

\(\displaystyle 4\)

Explanation:

First add \(\displaystyle 5\) to both sides of the equation:

\(\displaystyle 4x-5(+5)=11(+5)\)

\(\displaystyle 4x=16\)

Divide both sides by \(\displaystyle 4\):

\(\displaystyle \frac{4x}{4}=\frac{16}{4}\)

Reduce:

\(\displaystyle x=4\)

Example Question #931 : Isee Lower Level (Grades 5 6) Mathematics Achievement

If x is equal to 6 and y is equal is -2, what is the value of \(\displaystyle \frac{y}{x}\)?

Possible Answers:

\(\displaystyle -3\)

\(\displaystyle \frac{1}{3}\)

\(\displaystyle 3\)

\(\displaystyle -\frac{1}{3}\)

Correct answer:

\(\displaystyle -\frac{1}{3}\)

Explanation:

If x is equal to 6 and y is equal is -2, the value of \(\displaystyle \frac{y}{x}\) can be solved by plugging in the values of x and y. This results in:

Example Question #1 : Coordinate Geometry

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point W (2, 1); Point X (2, 6); Point Y (5, 1); Point Z (5, 6)

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

Possible Answers:

Rectangle

Trapezoid

Square

Rhombus

Correct answer:

Rectangle

Explanation:

Start by plotting the vertices and connecting them to form a quadrilateral.

Screenshot_2015-03-24_at_5.19.00_pm

 

The created figure has 4 right angles. This can describe a rhombus, square, and rectangle. Because the sides are not all the same length, the figure must be a rectangle.

Example Question #1 : How To Find A Rectangle On A Coordinate Plane

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point W (0, 0); Point X (7, 0); Point Y (7, 5); Point Z (0, 5)

 

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

Possible Answers:

Rectangle

Kite

Triangle

Trapezoid

Correct answer:

Rectangle

Explanation:

Start by plotting the vertices and connecting them to form a quadrilateral.

Screenshot_2015-03-24_at_5.25.52_pm

 

The figure that is created has four right angles. Out of the given answer choices, this can only describe a rectangle.

Example Question #1 : Coordinate Geometry

A shape is plotted on a coordinate plane using the following points: \(\displaystyle (0,0)\), \(\displaystyle (0,2)\), \(\displaystyle (3,0)\), and \(\displaystyle (3,2)\). What shape is it?

Possible Answers:

Trapezoid

Square

Rectangle

Triangle 

There is not enough information to determine the shape.

Correct answer:

Rectangle

Explanation:

If you plot these points on a coordinate plane, the shape has four sides and opposite sides are equal and parallel, but all sides are not equal.  

Therefore, it is a rectangle.

Example Question #1 : Coordinate Geometry

A shape with points \(\displaystyle (0,0)\), \(\displaystyle (0,4)\),\(\displaystyle (4,0)\), and \(\displaystyle (4,4)\) is plotted on a coordinate plane. What shape is it?

Possible Answers:

Prism

Square

Rectangle

Trapezoid

Triangle

Correct answer:

Square

Explanation:

Since each side is equal to each other, the shape must be a square.

Example Question #1 : How To Find A Square On A Coordinate Plane

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point W (5, 5); Point X (0, 5); Point Y (0, 0); Point Z (5, 0)

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

 

Possible Answers:

Kite

Trapezoid

Triangle

Square

Correct answer:

Square

Explanation:

Start by plotting and connecting the vertices to create a quadrilateral.

Screenshot_2015-03-24_at_5.45.58_pm

The figure that is created has 4 right angles and sides of equal length. The only answer choice that shares these characteristics is the square.

 

 

Example Question #1 : How To Find A Square On A Coordinate Plane

A square is plotted on a coordinate plane. It includes the following points: \(\displaystyle \left ( 0,2\right ), \left ( 2,0\right ), \left ( 2,2\right )\).  What is the remaining point?

Possible Answers:

\(\displaystyle \left ( -2,-2\right )\)

\(\displaystyle \left ( 1,1\right )\)

\(\displaystyle \left ( 1,2\right )\)

\(\displaystyle \left ( 2,1\right )\)

\(\displaystyle \left ( 0,0\right )\)

Correct answer:

\(\displaystyle \left ( 0,0\right )\)

Explanation:

Each of the points is written as an ordered pair.  The first number in each ordered pair shows where the point is located on the x-axis.  The second number in each ordered pair shows where the point is located on the y-axis.  If you plot the ordered pairs listed in the problem, the ordered pair that is needed to complete the points of a square is \(\displaystyle \left ( 0,0\right )\).

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