Limits of Accuracy
A rope is measured to be 5.6 m to the nearest 0.1 m. What is the upper bound of the rope’s length?
5.65 m (Upper bound = 5.6 + 0.05)
Find the surface area of a rectangular prism with dimensions 6 cm × 4 cm × 3 cm.
108 cm² (SA = 2(6×4 + 4×3 + 6×3))
Find the volume of a rectangular prism with dimensions 5 cm × 3 cm × 2 cm.
30 cm³ (5×3×2)
A triangle has angles of 50° and 60°. What is the third angle?
70° (180 − (50 + 60))
What are the four tests for triangle congruence?
SSS, SAS, ASA, RHS
A mass is recorded as 2.0 kg to the nearest 0.1 kg. What is the least it could actually weigh?
1.95 kg (Lower bound = 2.0 – 0.05)
What is the surface area of a box with dimensions of 10 cm × 6 cm × 4 cm?
248 cm² = 2(10×6 + 10×4 + 6×4)
A triangular prism has a base area of 15 cm² and height of 10 cm. What is its volume?
150 cm³ (Base area × height = 15 × 10)
A quadrilateral has angles of 80°, 90°, and 70°. Find the fourth angle.
120° (180×2 = 360; 360 − (80 + 90 + 70))
A shape is enlarged by a scale factor of 3. If the original side was 4 cm, what is the new side length?
12 (4x3=12)
A book’s width is measured as 12 cm, correct to the nearest centimetre. State the range of possible actual widths.
11.5 cm to 12.5 cm (±0.5 cm)
A wooden block has a length of 12 cm, width of 5 cm, and height of 3 cm. What is the surface area?
222 cm² = 2(12×5 + 12×3 + 5×3)
Calculate the volume of a cylinder with radius 4 cm and height 6 cm. Calculate this to two decimal places.
301.59 cm³ (πr²h = 3.14×16×6)
In a quadrilateral, three of the angles are 95°, 85°, and 110°. What is the fourth angle?
70° (95 + 85 + 110 = 290 ⇒ 360 − 290 = 70°)
A triangle is enlarged by a scale factor of 4. One side of the original triangle is 5 cm. What is the length of the corresponding side in the enlarged triangle?
5 × 4 = 20 cm
A field is said to be 100 m long to the nearest 10 m. What are the upper and lower bounds?
Lower bound = 95 m, Upper bound = 105 m
A cylindrical tin has a radius of 7 cm and a height of 10 cm. What is its surface area to two decimal places?
747.69 cm² = 2×3.14×7² + 2×3.14×7×10
A square prism has a base side length of 6 cm and height of 9 cm. Find its volume.
324 cm³ (6²×9 = 36×9)
An isosceles triangle has two equal angles and one angle of 40°.What is the size of one of the missing anlges?
140° ÷ 2 = 70°.
A small rectangle has a width of 6 cm. A similar larger rectangle has a width of 15 cm. What is the scale factor of the enlargement?
Scale factor = 15 ÷ 6 = 2.5
A machine cuts metal rods to a length of 4.8 cm, correct to the nearest millimetre. What is the maximum possible error?
±0.05 cm (Half of the smallest unit, 0.1 mm)
A cylinder has a radius of 5 cm and height of 8 cm. Find its surface area to two decimal places
408.41cm² (SA = 2πr² + 2πrh = 2×3.14×25 + 2×3.14×5×8)
A hexagonal prism has a base area of 72 cm² and a height of 10 cm. What is its volume?
720 cm³ (Base area × height = 72 × 10)
What is the missing angle in a triangle if the other two angles add to be 12²
36° (12² =144 -> 180-144=36°)
A triangle has sides measuring 8 cm, 12 cm, and 15 cm. It is enlarged by a scale factor of 1.5. What are the lengths of the sides of the enlarged triangle?
8 × 1.5 = 12 cm
12 × 1.5 = 18 cm
15 × 1.5 = 22.5 cm