In this assessment, you will encounter a number of different questions that will assess both your understanding of mathematics and your ability to reason quantitatively.
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Do not use a calculator in this assessment. You shouldn’t need one to answer these questions, and the extra practice with arithmetic (long division, multi-digit multiplication, etc.) will just make you a better math student!
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You may encounter different types of questions:
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If the area of a square is \(49\) cm\(^2\), what is the perimeter?
The perimeter of a rectangle is \(12\) inches. If the length and width are both integer values, which of the following could NOT be the area of the rectangle?
Using the information given, compare the quantity in Column A to the quantity in Column B.
Circle \(A\), which has a radius of \(2\) meters, sits inside Circle \(B\). The radius of Circle \(B\) is \(50\)% greater than the radius of Circle \(A\).
Column A The area of the shaded region, in square meters | Column B \(5\pi\) |
Rectangles \(ABDC\) and Rectangle \(WXZY\) are similar, with \(WX\) equal to half of \(AB\). If \(AB=8\) and \(BD=4\), what is the area of the shaded region, in square units?
Using the information given, compare the quantity in Column A to the quantity in Column B.
The diameters of Circle \(L\) and Circle \(M\) are both equal to side \(AC\) of Rectangle \(ABDC\) below. The radius of Circle \(L\) is \(3\) feet.
Column A Area of the shaded region, in square feet | Column B \(72-9\pi\) |
If triangle \(ACX\) is an isosceles right triangle, what is the perimeter of parallelogram \(ABDC\)?
Using the information given, compare the quantity in Column A to the quantity in Column B.
A rectangle with sides \(11\) and \(8\) has smaller rectangles each measuring \(2\) inches by \(3\) inches cut out from two of its corners, resulting in an octagon.
Column A The perimeter of the octagon, in inches | Column B \(36\) inches |
Using the information given, compare the quantity in Column A to the quantity in Column B.
Square \(WXYZ\) is inscribed in Square \(ABCD\). \(W\), \(X\), \(Y\), and \(Z\) are the midpoints of each side of Square \(ABCD\).
Column A The perimeter of Square \(ABCD\), if \(WX=\frac{4}{\sqrt{2}}\) | Column B \(16\sqrt{2}\) units |
The shaded figure, which is made up of \(12\) individual squares, has an area of \(108\) yards\(^2\). What is the perimeter of the shaded figure, in yards?
What is the area of isosceles trapezoid \(ABDC\) below?
A semi-circle is attached to Rectangle \(WXYZ\), as shown below. If \(WZ=8\), and the ratio of \(WX\) to \(WZ\) is \(3:2\), what is the perimeter of the figure?
The figure below shows four congruent squares, with the two outer squares overlapping the two inner squares. A vertex of each white square hits the midpoint of a gray square. If the perimeter of each square is \(24\) units, what is the area of the visible shaded region?
Circle \(C\) is inscribed in Square \(JKML\). If the radius of Circle \(C\) is \(4\) units, what is the area of the shaded region?
Using the information given, compare the quantity in Column A to the quantity in Column B.
A figure is formed from two congruent right triangles and a semi-circle. The hypotenuse of each triangle is \(10\) units and the base of each triangle is \(6\) units. If the perimeter of the outer figure is \(36+6\pi\), which column is greater?
Column A Area of the entire figure | Column B \(18\pi+30\) |
Using the information given, compare the quantity in Column A to the quantity in Column B.
Column A The area of a square with perimeter of \(48\) cm | Column B The area of a rhombus with sides lengths of \(12\) cm |
A figure (not shown) is made up of \(9\) individual squares. The each square has a side length of \(3\) inches. What is the area of the figure?
A trapezoid is shown. What is the area, in square units?
If all angles shown are \(90^{\circ}\), what is the area of the figure below?
If a regular hexagon has a side of \(6\) cm, what is its area?
A circle is inscribed in an equilateral triangle, as shown in the diagram. If the radius of the circle is \(3\) units and a side of the triangle measures \(6\sqrt3\), what is the area of the triangle?
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