10th grade geometry
10th grade (Year 11 in England) · 16 questions · Common Core: HSG.C.A.2, HSG.C.A.3, HSN.VM.A.1, HSN.VM.B.4 · England: GCSE Higher Geometry, GCSE Higher Algebra, GCSE Foundation Geometry
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Score/ 16
Question 1
A sector of radius 2 cm has area 0.333333π cm². Find the angle of the sector in degrees.
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Question 2
Find the exact distance between (5, −2) and (−2, −5). Simplify the surd.
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Question 3
P divides AB so that AP : PB = 1 : 2. A is (1, −2) and P is (−2, −1). Find B. Type it like (2, −1).
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Question 4
Two angles at the circumference stand on the same arc. One is 75°. What is the other?
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Question 5
A slice of pizza is a sector with radius 3 cm and angle 120°. Its exact perimeter is a + bπ cm. Type the perimeter in that form.
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Question 6
A sector of a circle with radius 4 cm has an arc length of 3π cm. Find the angle of the sector in degrees.
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Question 7
A triangle is drawn in a semicircle with one side the diameter. One of the other angles is 73°. What is the third angle (not the right angle)?
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Question 8
Which is the equation of the circle with centre (−2, −5) and radius 3?
- A. (x + 2)² + (y + 5)² = 9
- B. (x + 2)² + (y + 5)² = 3
- C. (x − 2)² + (y − 5)² = 9
- D. (x − 2)² + (y − 5)² = 3
Question 9
Two similar shapes have lengths in the ratio 1 : 4. The smaller has area 29 cm². What is the area of the larger?
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Question 10
Two similar jugs have surface areas in the ratio 1 : 4. The smaller jug holds 3 ml. How much does the larger jug hold?
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Question 11
A cone with the same base and height is drilled out of a solid cylinder (radius 4 cm, height 9 cm). Give the exact remaining volume as a multiple of π.
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Question 12
The vector (−2, m) is parallel to (1, −4). Find m.
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Question 13
What is the radius of the circle (x − 5)² + (y + 1)² = 81?
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Question 14
In cyclic quadrilateral PQRS, ∠P = (4x + 7)° and ∠R = (x − 2)°. Find x.
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Question 15
Find the centre of the circle x² + y² − 12x + 4y − 24 = 0. Type it like (2, −1).
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Question 16
A model car is built to a length scale of 1 : 2 compared with a bigger model. The small model holds 17 cm³ of paint inside its body. How much would the bigger model hold?
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