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
Name
Date
Score/ 16
Question 1
O is the centre of a circle. A, B and C are on the circle, with C on the major arc. ∠ACB = 39°. Find ∠AOB.
Answer
Question 2
Two similar jugs have surface areas in the ratio 4 : 9. The smaller jug holds 48 ml. How much does the larger jug hold?
Answer
Question 3
A cone has base radius 10 cm and perpendicular height 24 cm. Find its total surface area, in terms of π.
Answer
Question 4
A cone of volume 486π cm³ has its top cut off. The removed cone is similar with a length scale factor of 1/3. What fraction of the original volume is left? Give a fraction.
Answer(as a fraction)
Question 5
Find the perimeter of a sector with radius 12 cm and angle 30°. Give your answer to 1 decimal place.
Answer
Question 6
A circle has centre (1, −3) and passes through (1, −4). Its equation is (x − 1)² + (y + 3)² = k. Find k.
Answer
Question 7
A sector of a circle with radius 4 cm has an arc length of 6π cm. Find the angle of the sector in degrees.
Answer
Question 8
The circle x² + y² = r² passes through (−6, 8). What is r?
Answer
Question 9
OA = a and OB = b. M is the midpoint of AB. Find MB in terms of a and b.
- A. a − b
- B. ½b − ½a
- C. ½a − ½b
- D. b − a
Question 10
P divides AB so that AP : PB = 1 : 3. A is (3, 0) and P is (6, 3). Find B. Type it like (2, −1).
Answer
Question 11
O is the centre of the circle. Which theorem justifies this step? ∠AOB = 2 × ∠ACB
- A. The angle at the centre is twice the angle at the circumference
- B. Opposite angles of a cyclic quadrilateral add up to 180°
- C. A tangent is perpendicular to the radius
- D. Angles in the same segment are equal
Question 12
A tangent touches a circle at A. Triangle ABC is drawn in the circle. The angle between the tangent and AB is 62°, and ∠ABC = 58°. Find ∠BAC.
Answer
Question 13
A model car is built to a length scale of 1 : 4 compared with a bigger model. The small model holds 33 cm³ of paint inside its body. How much would the bigger model hold?
Answer
Question 14
P is (−5, −1) and the vector PQ is (6, 6). Find the coordinates of Q. Type them like (2, −1).
Answer
Question 15
Triangles KLM and STU have KL = ST and LM = TU. Which extra fact would prove them congruent by SAS?
- A. ∠M = ∠U
- B. ∠L = ∠T
- C. ∠K = ∠S
- D. MK = TU
Question 16
A, B, C and D lie on a circle, and the chords AC and BD cross. ∠ABD = 40° and ∠BAC = 67°. Find ∠ACD.
Answer
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