Level 2 — RecallBasic Geometry

Basic Geometry

⏱ 30 minutes40 marksprintable — key stays hidden on paper

Level: 2 (Recall — definitions, standard problems, short derivations) Time Limit: 30 minutes Total Marks: 40

Use $\pi = 3.14$ or $\dfrac{22}{7}$ where required. Show working.

Q1. Match each term with its correct description. (4 marks) (a) Line segment (b) Ray (c) Point (d) Line

(i) Has no length, only a position
(ii) Extends infinitely in both directions
(iii) Has two endpoints and a definite length
(iv) Has one endpoint and extends infinitely in one direction

Q2. Classify each angle as acute, right, obtuse, straight, reflex or complete: (4 marks) (a) $90^\circ$ (b) $215^\circ$ (c) $47^\circ$ (d) $180^\circ$

Q3. (4 marks) (a) Find the complement of $32^\circ$ . (b) Find the supplement of $118^\circ$ .

Q4. Two parallel lines are cut by a transversal. One of the angles measures $70^\circ$ . (4 marks) (a) State the size of its co-interior (allied) angle. (b) State the size of its alternate angle.

Q5. In a triangle, two angles are $55^\circ$ and $65^\circ$ . (4 marks) (a) Find the third angle. (b) Classify the triangle by its angles (acute / right / obtuse).

Q6. In triangle $ABC$ , the exterior angle at $C$ is $110^\circ$ and one interior opposite angle is $48^\circ$ . Find the other interior opposite angle. (4 marks)

Q7. State whether each statement is True or False: (4 marks) (a) A square is a special type of rectangle. (b) The diagonals of a rhombus bisect each other at right angles. (c) A trapezium has two pairs of parallel sides. (d) The diagonals of a rectangle are equal in length.

Q8. A circle has radius $7$ cm. Taking $\pi = \dfrac{22}{7}$ : (4 marks) (a) Find its circumference. (b) Find its area.

Q9. (4 marks) (a) Find the area of a triangle with base $12$ cm and height $9$ cm. (b) Find the area of a trapezium with parallel sides $8$ cm and $14$ cm and height $6$ cm.

Q10. A cuboid measures $5$ cm $\times$ $4$ cm $\times$ $3$ cm. (4 marks) (a) Find its volume. (b) Find its total surface area.

Answer keyMark scheme & solutions

Q1. (4 marks — 1 each)

(a) → (iii): a segment has two endpoints, so definite length.
(b) → (iv): a ray starts at one endpoint, extends infinitely one way.
(c) → (i): a point marks position only, no dimension.
(d) → (ii): a line extends infinitely both directions.

Q2. (4 marks — 1 each)

(a) $90^\circ$ = right angle
(b) $215^\circ$ = reflex angle (between $180^\circ$ and $360^\circ$ )
(c) $47^\circ$ = acute angle (less than $90^\circ$ )
(d) $180^\circ$ = straight angle

Q3. (4 marks) (a) Complement $= 90^\circ - 32^\circ = 58^\circ$ (2) (b) Supplement $= 180^\circ - 118^\circ = 62^\circ$ (2) Complementary angles sum to $90^\circ$ ; supplementary to $180^\circ$ .

Q4. (4 marks) (a) Co-interior angles are supplementary: $180^\circ - 70^\circ = 110^\circ$ (2) (b) Alternate angles are equal: $70^\circ$ (2)

Q5. (4 marks) (a) Angle sum $=180^\circ$ , so third $=180^\circ-55^\circ-65^\circ=60^\circ$ (2) (b) All angles ( $55^\circ, 65^\circ, 60^\circ$ ) are less than $90^\circ$ → acute triangle (2)

Q6. (4 marks) Exterior angle = sum of the two interior opposite angles. $110^\circ = 48^\circ + x$ (2) $x = 110^\circ - 48^\circ = 62^\circ$ (2)

Q7. (4 marks — 1 each)

(a) True (square = rectangle with equal sides)
(b) True
(c) False (trapezium has exactly one pair of parallel sides)
(d) True

Q8. (4 marks) (a) $C = 2\pi r = 2 \times \dfrac{22}{7} \times 7 = 44$ cm (2) (b) $A = \pi r^2 = \dfrac{22}{7} \times 7^2 = \dfrac{22}{7}\times 49 = 154$ cm² (2)

Q9. (4 marks) (a) $A = \dfrac12 \times 12 \times 9 = 54$ cm² (2) (b) $A = \dfrac12 (8+14)\times 6 = \dfrac12 \times 22 \times 6 = 66$ cm² (2)

Q10. (4 marks) (a) $V = 5\times4\times3 = 60$ cm³ (2) (b) $SA = 2(lw+wh+lh)=2(20+12+15)=2(47)=94$ cm² (2)

[
  {"claim":"Complement of 32 is 58 and supplement of 118 is 62","code":"result = (90-32==58) and (180-118==62)"},
  {"claim":"Triangle third angle is 60","code":"result = (180-55-65==60)"},
  {"claim":"Circle r=7: circumference 44, area 154","code":"from sympy import Rational; C=2*Rational(22,7)*7; A=Rational(22,7)*49; result = (C==44) and (A==154)"},
  {"claim":"Trapezium area 66 and triangle area 54","code":"result = (Rational(1,2)*(8+14)*6==66) and (Rational(1,2)*12*9==54)"},
  {"claim":"Cuboid volume 60 and surface area 94","code":"result = (5*4*3==60) and (2*(20+12+15)==94)"}
]