## Wednesday, June 24, 2015

### New York State Geometry Regents, June 2015 Part 1: Multiple Choice

Here is Part 1 of the New York Geometry Regents (non-Common Core) exam, the multiple choice.
Part 2 was posted here. And Parts 3 and 4 were posted here.

Illustrations and diagrams will be added when available.

### Part 1

1. Quadrilateral ABCD undergoes a transformation, producing a quadrilateral A'B'C'D'. For which transformation would the area of A'B'C'D' not be equals to the area of ABCD?

(3) a dilation by a scale factor of 2. A dilation of 2 would increase the area by a factor of 4 (2 x 2).

2. The diameter of a sphere is 12 inches. What is the volume of the sphere to the nearest cubic inch?

(3) 905. Remember that the radius is only 6. Use the formula from the reference sheet: 4/3 (3.141592...)(6)2 = 905, to the nearest integer.

3. A right rectangular prism is shown in the diagram below.

Which line segments are coplanar?

(4) EA and GC are both in a vertical plane. The other pairs of lines are skew.

4. What are the coordinates of the image of point A(2, -7) under the translation (x,y) -> (x - 3, y + 5)?

(1) (-1, -2). (2 - 3 = -1, -7 + 5 = -2)

5. Point M is the midpoint of AB. If the coordinates of M are (2, 8) and the coordinates of A are (10, 12), what are the coordinates of B?

(2) (-6, 4). 10 - 2 = 8; 2 - 8 = -6. 12 - 8 = 4; 8 - 4 = 4.

6. In the diagram below, QM is an altitude of right triangle PQR, PM = 8, and RM = 18.

What is the length of QM?

(3) 12. Right-Triangle Altitude Theorem. Use the proportion 8/x = x/18. Cross multiply: x2 = 144. x = 12.

7. What is an equation of the line that passes through the point (2, 4) and is perpendicular to the line whose equation is 3y = 6x + 3?

(1) y = -1/2 x + 5. The slope of the given line is 6/3 = 2, so the perpendicular line has a slope of -1/2. (Eliminate choices 3 and 4.) Plug in 2 for x and 4 for y and you get the first equation.

8. In all isosceles triangles, the exterior angle of a base angle must always be

(3) an obtuse angle. The base angles of an isosceles triangle must be acute, so the exterior angle must be obtuse.

9. If triangle W'X'Y' is the image of WXY after the transformation R90, which statement is false?

(2) WX || W'X'. If it's rotated 90 degrees, it can't be parallel to the original. The sides, angles, and the entire triangle will be congruent.

10. Which equation represents the circle shown in the graph below?

(1) (x - 2)2 + y2 = 9. Use the formula. Flip the sign, square the radius.

11. In quadrilateral ABCD, each diagonal bisects opposite angles. If m<DAB = 70, then ABCD must be a

(3) rhombus. Bisecting the opposite angles is true of rhombuses and squares (which are rhombuses), but the angle is not 90 degrees.

12. Which diagram illustrates a correct construction of an altitude of triangle ABC?

(2). It's the only construction that shows an altitude. Choice (1) shows a median. Choice (3) shows an angle bisector. Choice (4) shows a perpendicular bisector. The perpendicular bisector will come in handy in Part 2!

13. From external point A, two tangents to circle O are drawn. The points of tangency are B and C. Chord BC is drawn to form triangle ABC. If m<ABC = 66, what is m<A?

(2) 48. ABC is an isosceles triangle with base angles of 66. 66 + 66 = 132. 180 - 132 = 48.

14. Point A lies on plane P. How many distinct lines passing through point A are perpendicular to plane P?

(1) 1. By definition, really. Not much to say.

15. Students made four statements about a circle.
A: The coordinates of its center are (4, -3).
B: The coordinates of its center are (-4, 3).
C: The length of the radius is 5(2)^.5.
D: The length of the radius is 25. If the equation of the circle (x + 4)2 + (y - 3)2 = 50, which statements are corrct?

(3) B and C. Another formula of a circle question, asked in a totally different way. Flip the signs, square root of r2.

16. Points A, B, C, and D are located on circle O, forming trapezoid ABCD with AB || DC. Which statement must be true?

(2) AD = BC. The intercepted arcs of to parallel chords are congruent.

17. If triangle ABC ~ LMN, which statement is not always true?

(1) m<A = m<N. When presented with two triangles that are stated as similar or congruent, proper notation is that angle A corresponds to angle L, angle B corresponds to angle M, and angle C corresponds to angle N. Pick two letters for a side, and the corresponding two letters indicate the corresponding side. I point this out because some students are a little careless about naming conventions when they write, so they might have forgotten this, if they were ever aware of it. Some teachers might even be too lax at enforcing this. Here is one of the times where it is important to know that the test writers following the rules.

18. The equations representing lines k, m, and n are given below.
k: 3y + 6 = 2x
m: 3y + 2x + 6 = 0
n: 2y = 3x + 6
Which statement is true?

(4) m is perpendicular to n. The slope of k is 2/3. The slope of m is -2/3. The slope of n is 3/2.

19. A regular polygon with an exterior angle of 40o is a

(3) nonagon. 360/x = 40. x = 360/40 = 9. Nine sides is a nonagon.

20. In triangle ABC shown below, L is the midpoint of BC, M is the midpoint of AB, and N is the midpoint of AC.

If MN = 8, ML = 5, and NL = 6, the perimeter of trapezoid BMNC is

(4) 35. Midpoints are connected by midsegments, which are half the length of the third side and also parallel to it. The perimeter is 5 + 8 + 6 + 8 + 8 = 35.

21. The sum of the interior angles of a regular polygon is 720 degrees. How many sides does the polygon have?

(2) 6. This is such a common question that you should have known it, but ...

180(n - 2) = 720
n - 2 = 4
n = 6

22. In the prism shown below, AD is perpendicular to AE and AD is perpendicular to AB.
Which plane is perpendicular to AD? (3) EAB. The bottom and top of the prism are perpendicular to AD. The bottom is listed as a choice.

23. In triangle ABC, m<A = 65 and m<B is greater than m<A. The lengths of the sides of triangle ABC in order from smallest to largest are

(1) AB, BC, AC. If B > A, then A + B > 130 and C < 50. Therefore C < A < B, and AB < BC < AC.

24. Which equation represents a circle whose center is the origin and that passes through the point (-4, 0)?

(2) x2 + y2 = 16. Square the radius: 42 = 16.

25. The lengths of two sides of a triangle are 7 and 11. Which inequality represents all possible values for x, the length of the third side of the triangle?

(4) 4 < x < 18. Triangle Inequality Theorem: 11 - 7 < x < 11 + 7.

26. Which statement is the inverse of "If x + 3 = 7, then x = 4"?

(3) If x + 3 =/= 7, then x =/= 4. Inverse adds "NOT" (or removes it if it was already there).

27. In the diagram below of triangle MAR, medians MN, AT, and RH intersect at O.

If TO = 10, what is the length of TA?

(1) 30. AO is twice the length of TO, and TA is three times the length of TO.

28. What is an equation of the line that passes though the point (4, 5) and is parallel to the line whose equation is y = 2/3 x - 4?

(4) 3y - 2x = 7. Choices (1) and (2) have a slope of -3/2, so eliminate them. Calculate 3(5) - 2(4) = 7, which is choice (4).

That's it. It's up. Everyone happy?

#### 2 comments:

Anonymous said...

For number 24, did you mean to put y^2 instead of 7^2?

(x, why?) said...

Thank you. Good catch. The 7 key is right above the y on the keyboard.