Geometry Regents Exam - January 2024

Geometry Regents New York State Exam - January 2024

Geometry Regents New York State Exam Questions January 2024 (pdf)

Geometry Regents Exam January 2024 (Solutions 1 - 24)

Geometry Regents Exam January 2024 (Solutions 25 - 35)

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1. Which expression is equal to sin 30°?
2. In the diagram of △SRA below,KP is drawn such that ∠SKP ≅ ∠SRA.
3. A rectangle is graphed on the set of axes below. A reflection over which line would carry the rectangle onto itself?
4. The surface of the roof of a house is modeled by two congruent rectangles with dimensions 40 feet by 16 feet, as shown below. Roofing shingles are sold in bundles. Each bundle covers 33 1/3 square feet. What is the minimum number of bundles that must be purchased to completely cover both rectangular sides of the roof?
5. Which equation represents a line that is perpendicular to the line whose equation is y - 3x = 4?
6. A vertical mine shaft is modeled in the diagram below. At a point on the ground 50 feet from the top of the mine, a ventilation tunnel is dug at an angle of 47°. What is the length of the tunnel, to the nearest foot?
7. On the set of axes below, △BLU has vertices with coordinates B(-3,-2), L(-2,5), and U(1,1). What is the area of △BLU?
8. In the diagram below, △CAR is mapped onto nBUS after a sequence of rigid motions. If AR = 3x + 4, RC = 5x - 10, CA = 2x + 6, and SB = 4x - 4, what is the length of SB?
9. In the diagram below, △GHJ is dilated by a scale factor of 1/2 centered at point B to map onto △CDF.
10. Directed line segment AJ has endpoints whose coordinates are A(5,7) and J(-10,-8). Point E is on AJ such that AE:EJ is 2:3. What are the coordinates of point E?
11. A tipping platform is a ramp used to unload trucks, as shown in the diagram below. The truck is on a 75-foot-long ramp. The ramp is tipped at an angle of 30°. What is the height of the upper end of the ramp, x, to the nearest tenth of a foot?
12. In the diagram below of right triangle MET, altitude ES is drawn to hypotenuse MT. If ME = 6 and SM = 4, what is MT?
13. In the diagram below of square CASH, diagonals AH and CS intersect at Z.
14. In the diagram below of circle O, secants CFD and CHE are drawn from external point C.
15. A right circular cylinder has a diameter of 8 inches and a height of 12 inches. Which two-dimensional figure shows a cross section that is perpendicular to the base and passes through the center of the base?
16. On the set of axes below, AB is drawn and passes through A(-2,6) and B(4,0).
17. In parallelogram ABCD with AC ⊥ BD, AC = 12 and BD = 16. What is the perimeter of ABCD?
18. In the diagram of △CAT below, m∠A = 90° and altitude AE is drawn from vertex A.
19. A sandbox in the shape of a rectangular prism has a length of 43 inches and a width of 30 inches. Jack uses bags of sand to fill the sandbox to a depth of 9 inches. Each bag of sand has a volume of 0.5 cubic foot. What is the minimum number of bags of sand that must be purchased to fill the sandbox?
20. Parallelogram EATK has diagonals ET and AK. Which information is always sufficient to prove EATK is a rhombus?
21. In the diagram below, ABCD || EHK, and MBHP and NCHL are drawn such that BC ≅ BH
22. Triangles YEG and POM are two distinct non-right triangles such that ∠G ≅ ∠M. Which statement is sufficient to prove △YEG is always congruent to △POM?
23. In the diagram of triangles ABD and CBE below, sides AD and CE intersect at F, and ∠ADB ≅ ∠CEB.
24. A small town is installing a water storage tank in the shape of a cylinder. The tank must be able to hold at least 100,000 gallons of water. The tank must have a height of exactly 30 feet. [1 cubic foot holds 7.48 gallons of water] What should the minimum diameter of the tank be, to the nearest foot?
25. In isosceles triangle ABC shown below, AB ≅ AC, and altitude AD is drawn.
26. The diagram below models the projection of light from a lighthouse, L. The sector has a radius of 38 miles and spans 102°. Determine and state the area of the sector, to the nearest square mile.
27. Segment CA is drawn below. Using a compass and straightedge, construct isosceles right triangle CAT where CA ⊥ CT and CA ≅ CT. Describe a sequence of rigid motions that maps △ABC onto △DEF.
28. In △ADC below, EB is drawn such that AB = 4.1, AE = 5.6, BC = 8.22, and ED = 3.42.
29. Using a compass and straightedge, construct a midsegment of △AHL below.
30. Determine and state the coordinates of the center and the length of the radius of the circle represented by the equation x² + 16x + y² + 12y - 44 = 0.
31. In the diagram below, △SBC ∼ △CMJ and cos J = 3/5.
32. Trish is a surveyor who was asked to estimate the distance across a pond. She stands at point C, 85 meters from point D, and locates points A and B on either side of the pond such that A, D, and B are collinear. Trish approximates the measure of angle DCB to be 35° and the measure of angle ACD to be 75°. Determine and state the distance across the pond, AB, to the nearest meter.
33. A candle in the shape of a right pyramid is modeled below. Each side of the square base measures 12 centimeters. The slant height of the pyramid measures 16 centimeters. Determine and state the volume of the candle, to the nearest cubic centimeter. The wax used to make the candle weighs 0.032 ounce per cubic centimeter. Determine and state the weight of the candle, to the nearest ounce.
34. In the diagram of quadrilateral ABCD below, AB ≅ CD, and AB || CD.
35. Quadrilateral MATH has vertices with coordinates M(-1,7), A(3,5), T(2,-7), and H(-6,-3). Prove that quadrilateral MATH is a trapezoid.

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