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Geometry Assessment Preparation

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Geometry Assessment Preparation

Solve the design problems for a community skate park. Show working, include units, and use π = 3.14 where needed. Give exact answers where requested and round other answers to 1 decimal place.

Plan and build

1.A ramp side is a right-angled triangle with a horizontal run of 2.4 m and a vertical rise of 0.7 m. Use Pythagoras’ theorem to find the length of the sloping side. Show your calculation.

2.The flat top of a platform is a trapezium. Its parallel sides are 3.2 m and 1.8 m, and the perpendicular distance between them is 2.5 m. Find its area.

3.A storage drum is a cylinder with radius 0.45 m and height 1.2 m. Calculate its volume in cubic metres, using π = 3.14.

4.A safety mat has an area of 2.35 m². Convert this area to cm². Remember that area units are squared.

Angles and scale

5.Select every statement that is always true. (More than one answer.)

Angles on a straight line add to 180°.
Vertically opposite angles are equal.
The interior angles of a triangle add to 360°.
Corresponding angles are equal when parallel lines are crossed by a transversal.

6.On the number line below, the marked values are −4, −1, 2 and 5. Write them in order from least to greatest, then state the distance between −4 and 5.

7.Two parallel rails are crossed by a support bar. At the upper intersection, the lower-right angle is 68°. At the lower intersection, x is the upper-left angle. Find x and explain the angle relationship.

8.On a site plan, 1 cm represents 4 m. A path measures 7.5 cm on the plan. What is its real length in metres?

Design challenge

9.A rectangular practice area measures 8 m by 5 m. A semicircular seating bay is attached along one 5 m side, so its diameter is 5 m. Find the total area of the rectangle and semicircle. Use π = 3.14.

10.A circular feature has radius 6 m. A student says its circumference is 113.04 m because they calculated 3.14 × 6². Identify the mistake, then give the correct circumference.