MTEL Prep Workshop  Geometry and Measurement

            The questions below are taken from recent 4th, 6th, and 8th grade MCAS tests.  Most questions are multiple-choice, but there are a few open-response questions included.  Questions are classified by objectives on the MTEL test (many questions could fit into more than one category).  Answers are at the end.

1. Recognizing types and properties of geometric figures

2. Using basic geometric concepts (e.g., similarity, congruence, tessellations) and spatial sense to solve problems.

3. Identifying and applying geometric transformations and classifying figures according to symmetries

4. Using coordinate systems on lines and planes to solve problems

5. Estimating and converting measurements within the customary and metric systems and applying procedures for using measurement to describe and compare phenomena

6.  Identifying appropriate measurement instruments, units, and procedures for various measurement problems involving length, area, angles, volume, mass, temperature, etc.

1. Recognizing types and properties of geometric figures

1. Which angles in the figure are ACUTE angles?

 

A. angles A and B

B. angles B and E

C. angles C and E

D. angles A and D.

 

 

 

 

 

 

2. Eva has four sets of straws. The measurements of the straws are given below. Which set of straws could not be used to form a triangle?

A. Set 1: 4 cm, 4 cm, 7 cm

B. Set 2: 2 cm, 3 cm, 8 cm

C. Set 3: 3 cm, 4 cm, 5 cm

D. Set 4: 5 cm, 12 cm, 13 cm

3. Which is the best estimate of the angle between the two hands on a clock at 5:10?

A. 45°

B. 30°

C. 90°

D. 60°

4. Ricardo drew a rectangle. Which statement must be true?

A. Ricardo's figure is a parallelogram.

B. Ricardo's figure is a regular polygon.

C. Ricardo's figure is a square.

D. Ricardo's figure is a rhombus

 

 

 

 

 

 

 

 

 

5. Which figure is a polygon?

6.

A right triangle has one right angle.

An isosceles triangle has at least 2 congruent sides.

An acute triangle contains three acute angles.

An obtuse triangle contains one obtuse angle.

a. Is it possible to draw a right triangle that is isosceles?

  • If it is possible, draw such a triangle. Label the parts of the triangle that make it right and isosceles.
  • If it is not possible, explain why it is not possible.

b. Is it possible to draw an acute triangle that is isosceles?

  • If it is possible, draw such a triangle. Label the parts of the triangle that make it acute and isosceles.
  • If it is not possible, explain why it is not possible.

c. Is it possible to draw a right triangle that is obtuse?

  • If it is possible, draw such a triangle. Label the parts of the triangle that make it right and obtuse.

If it is not possible, explain why it is not possible.

 

2. Using basic geometric concepts (e.g., similarity, congruence, tessellations) and spatial sense to solve problems.

7.

8. Which two SHAPES below can you put together to make the larger shape above?

 

9.

 

If the hexagon equals one whole, what fractional part of the hexagon is one rhombus?

A. 1/3

B. 1/2

C. 1/6

D. 1/4

10. The pattern shown below is for a square prism. The lengths of the line segments in the pattern were chosen so that the pattern could be folded along the dotted lines into the prism shown.

a. Make a sketch of a pattern for a triangular prism. Label each line segment with a length that will make it possible to fold the pattern into the triangular prism.

b. Make a sketch of a pattern for a cylinder. Label each line segment and diameter in your pattern with a length that will make it possible to create the cylinder from the pattern

 

 

11.

Lines m and n are parallel. What is the measure of angle 4?

 

12.

How many degrees are in angle EFG?

A. 80o

B. 240o

C. 60o

D. 120o

13. Which triangles are congruent?

A. K and M only

B. L and N only

C. K, L, M, and N

D. No two figures shown are congruent.

 

 

14. Which two figures have the same area?

A. Figures 1 and 4

B. Figures 1 and 2

C. Figures 2 and 3

D. Figures 2 and 4

 

 

15. Polygon KMNO is a rectangle and the lengths of and are equal. What is the measure of angle LON?

A. 30°

B. 45°

C. 90°

D. 135°

3. Identifying and applying geometric transformations and classifying figures according to symmetries

 

16. Kayla is assembling a bookcase. She has put a metal piece into a hole in a shelf as shown below. The instructions say to rotate the piece 90° counterclockwise. How will the piece look after the rotation?

17. The following figure is to be rotated 90o clockwise.

What will the figure look like after the rotation?

 

18.If Figure ABCD is translated so that the image of A is A' at (-3,2), then the coordinates of the image of point B will be

A. (0,0).

B. (-1,4).

C. (-2,-1).

D. (-3,1).

19. Which shows the translation of pentagon ABCDE two units to the left?

 

 

4. Using coordinate systems on lines and planes to solve problems

20. Which graph contains the points given in the table below?


 

 

 

 

21. distance yz equals distance zw and

distance xy equals distance yw.

Distance yz equals 4. Distance xw equals

A. 4.

B. 8.

C. 16.

D. 12.

22. Write the rule for the table shown below.

 

 

 

 

 

 

 

5. Estimating and converting measurements within the customary and metric systems and applying procedures for using measurement to describe and compare phenomena

23. Which is the best approximation of ?

A. 7.2

B. 9.1

C. 8.9

D. 8.5

24. A hole in a piece of metal has a diameter of 3 1/2 inches. Which of the following pipes is the largest that will fit through the hole?

A. a pipe with a diameter of 3 3/8 inches

B. a pipe with a diameter of 3 7/8 inches

C. a pipe with a diameter of 3 5/16 inches

D. a pipe with a diameter of 3 7/16 inches

25. The shaded parts of the diagram represent the spaces that are reserved. What percent of the spaces is reserved?

A. 20%

B. 30%

C. 40%

D. 50%

26. How many 1-in. cubes will completely fill the carton shown?

A. 14

B. 33

C. 90

D. 105

 

27. Donna wants to use ready-made 6-foot long fence sections for her yard. The yard measures 24 feet long and 30 feet wide. How many fence sections would she need to enclose her entire yard?

A. 120

B. 18

C. 108

D. 20

 

28. A light year is approximately 6 X 1012 miles. What is another way to write this

number?

A. 6,000,000,000,000

B. 6,000,000,000

C. 600,000,000,000

D. 60,000,000,000,000

 

6.  Identifying appropriate measurement instruments, units, and procedures for various measurement problems involving length, area, angles, volume, mass, temperature, etc.

 

29. The volume of this cube is 1 cubic centimeter.

What is the volume of this figure?

 

 

30.The formula for the volume (V) of a cube is

V = e3

where e is the length of an edge.

An edge of a silver cube is twice as long as an edge of a gold cube. How many times greater is the volume of a silver cube than that of a gold cube?

A. 2 times greater

B. 9 times greater

C. 8 times greater

D. 6 times greater

31. The largest natural lake in Massachusetts is Assawompsett Pond which has an area of 2,656 acres. What is the approximate area in square miles?

A. 4 sq. mi.

B. 7 sq. mi.

C. 17 sq. mi.

D. 40 sq. mi.

 

32. The squares in the figure above are congruent. The perimeter of the entire figure is 24 units. What is the area of one of the small squares?

A. 2 square units

B. 4 square units

C. 6 square units

D. 8 square units

 

 33. The formula for the surface area (SA) of a cube is

SA = 6e2, where e is the length of an edge of the cube.

An edge of a red cube is twice as long as an edge of a blue cube. How many times greater is the surface area of the red cube than that of the blue cube?

A. 2 times greater

B. 4 times greater

C. 6 times greater

D. 12 times greater

 

34. Which of the following measurements would most likely be given with a negative exponent in scientific notation?

A. the diameter of a blood cell in centimeters

B. the distance to the Sun in kilometers

C. the weight of a pencil in grams

D. the mass of a rocket in kilograms

kilograms

35. In the figure on the right, the perimeter of the equilateral triangle is 24 inches.
What is the area of the square?

A. 32 sq. in.

B. 64 sq. in.

C. 476 sq. in.

D. 12 sq. in.

 

 

36. All of the sides of this hexagon have the same length, s. Which expression represents the perimeter of this hexagon?

A. s + 6

B. s X 6

C. s / 6

D. s6

37. A circle has a radius of 5 inches. Which is the best estimate of its circumference?

A. 15 inches

B. 30 inches

C. 7 1/2 inches

D. 75 inches

 

 

 

 

 

Answers:

1. D     2. B (2+3<8)  3. C     4. A     5. C     6. a. yes (45-45-90)  b. yes (equilateral)

c. impossible 7-8 (oops, same question) D  9. A   10. many answers – learn this one!   11. 55°   12. C.  13. B   14. A.   15. B   16. C   17. D   18.  A.   19. D. 

20. B   21. C   22.  y = 2x –1  23.  D  24. D  25. C  26.  C.  27. B  28.  A  29. 14

30. C  31. A  (1 acre = approx 640 sq miles, I had to look it up!  I think the kids had a reference sheet)  32. B   33. B   34.  A  35.  B   36.  B  37. A

 

  To Commentary               Doc File                       PDF File                      Home