High School Math based on the topics required for the Regents Exam conducted by NYSED. The following are the worked solutions for the Geometry (Common Core) Regents High School Examination January 2019.
The following are questions from the past paper Regents High School Geometry, January 2019 Exam (pdf). Scroll down the page for the step by step solutions.
Geometry - January 2019 Regents - Questions and solutions 1 - 12
Geometry - January 2019 Regents - Questions and solutions 13 - 24
13. From a point on the ground one-half mile from the base of a historic monument, the angle of elevation to its top is 11.87°. To the nearest foot, what is the height of the monument?
14. The area of a sector of a circle with a radius measuring 15 cm is 75π cm2. What is the measure of the central angle that forms the sector?
15. Point M divides AB so that AM:MB = 1:2. If A has coordinates (-1,-3) and B has coordinates (8,9), the coordinates of M are
16. In the diagram below of triangle ABC, AC is extended through point C to point D, and BE is drawn to AC.
17. In the diagram below of right triangle ABC, AC = 8, and AB = 17.
Which equation would determine the value of angle A?
18. Francisco needs the three pieces of glass shown below to complete a stained glass window. The shapes, two triangles and a trapezoid, are measured in inches.
Glass can be purchased in rectangular sheets that are 12 inches wide. What is the minimum length of a sheet of glass, in inches, that Francisco must purchase in order to have enough to complete the window?
19. In the diagram of quadrilateral NAVY below, m∠YNA = 30°, m∠YAN = 38°, m∠AVY = 94°, and m∠VAY = 46°.
Which segment has the shortest length?
20. What is an equation of a circle whose center is (1,4) and diameter is 10?
21. On the set of axes below, ABC, altitude CG, and median CM are drawn.
Which expression represents the area of ABC?
22. In right triangle ABC, m∠C = 90° and AC ≠ BC. Which trigonometric ratio is equivalent to sin B?
23. As shown in the diagram below, the radius of a cone is 2.5 cm and its slant height is 6.5 cm
How many cubic centimeters are in the volume of the cone?
24. What is an equation of the image of the line y = 2/3 x - 4 after a dilation of a scale factor of 3/4 centered at the origin?
Geometry - January 2019 Regents - Questions and solutions Parts 2-4
25. Write an equation of the line that is parallel to the line whose equation is 3y + 7 = 2x and passes through the point (2,6).
26. Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and FC intersects AGD at H.
If m∠B = 118° and m∠AHC = 138°, determine and state m∠GFH
27. As shown in the diagram below, secants PWR and PTS are drawn to circle O from external point P
If m∠RPS = 35° and mRS = 121°, determine and state mWT.
28. On the set of axes below, ABC is graphed with coordinates A(-2,-1), B(3,-1), and C(-2,-4). Triangle QRS, the image of ABC, is graphed with coordinates Q(-5,2), R(-5,7), and S(-8,2).
Describe a sequence of transformations that would map ABC onto QRS.
29. Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD is a parallelogram.
[Leave all construction marks.]
30. On the set of axes below, DEF has vertices at the coordinates D(1,-1), E(3,4), and F(4,2), and point G has coordinates (3,1). Owen claims the median from point E must pass through point G.
Is Owen correct? Explain why.
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