Geometry and Measurement: Test Review

Key facts

Where marks get lost

• ×Using "corresponding angles are equal" when the lines are not marked or stated as parallel. Without parallel lines, the relationship does not hold. (Angles, Parallel Lines and Polygons)
• ×Setting co-interior angles equal to each other instead of adding them to $180^{\circ }$ (they are equal only when both are $90^{\circ }$). (Angles, Parallel Lines and Polygons)
• ×Using $180^{\circ }\times n$ instead of $180^{\circ }(n-2)$ for the interior angle sum; a quadrilateral's angles add to $360^{\circ }$, not $720^{\circ }$. (Angles, Parallel Lines and Polygons)
• ×Dividing the angle sum by $n$ when the angles are not known to be equal. That works for a regular polygon, but an irregular pentagon's five angles usually differ, so the sum tells you their total, not each one. (Angles, Parallel Lines and Polygons)
• ×Mixing up complementary ($90^{\circ }$) and supplementary ($180^{\circ }$). Memory hook: "c" comes before "s" in the alphabet and $90$ comes before $180$. (Angles, Parallel Lines and Polygons)
• ×Getting the factor of 2 backwards: the central angle is the bigger one. If the central angle is $80^{\circ }$, the inscribed angle on the same arc is $40^{\circ }$, not $160^{\circ }$. (Triangle and Circle Properties in Design)
• ×Calling three lengths a triangle when the two short sides add to exactly the long side (like 4, 5, 9). That makes a flat line, not a triangle. (Triangle and Circle Properties in Design)
• ×Checking the triangle inequality with the wrong pair: adding the longest side to a short side always beats the third side, so that check proves nothing. Add the two shortest sides. (Triangle and Circle Properties in Design)
• ×Setting an exterior angle equal to the sum of all three interior angles, or including the interior angle right next to it. Use only the two interior angles at the other corners. (Triangle and Circle Properties in Design)
• ×Treating two inscribed angles as equal when their vertices are on opposite sides of the chord. On opposite arcs they add to 180° instead. (Triangle and Circle Properties in Design)
• ×Multiplying when you should divide. Going to a bigger unit (cm to m, g to kg) must give a smaller number. (Units and Measurement Systems)
• ×Converting area with the length factor: $3{\text{ m}}^2$ is $30000{\text{ cm}}^2$, not $300{\text{ cm}}^2$. (Units and Measurement Systems)
• ×Reading 5.8 ft as 5 ft 8 in. A foot has 12 inches, not 10, so 5.8 ft is 5 ft 9.6 in. (Units and Measurement Systems)
• ×Rounding a conversion factor early (for example using 1 kg = 2.2 lb in the middle of a calculation) and then reporting too many digits as if they were exact. (Units and Measurement Systems)
• ×Thinking 1 L = 100 mL. Milli means one thousandth, so 1 L = 1000 mL. (Units and Measurement Systems)
• ×Adding the squares when finding a leg. With hypotenuse 13 and leg 5, the other leg is $\sqrt{169-25}=12$, not $\sqrt{169+25}$. (The Pythagorean Theorem)
• ×Stopping at $c^2$. If $c^2=169$, the side is $c=13$, not 169. (The Pythagorean Theorem)
• ×Thinking $\sqrt{a^2+b^2}=a+b$. With legs 3 and 4, $\sqrt{9+16}=5$, not 7. (The Pythagorean Theorem)
• ×Using the theorem on a triangle with no right angle, or using a leg as c. The hypotenuse is the side across from the right angle. (The Pythagorean Theorem)
• ×Testing the converse with the wrong side as $c$. Always square the longest side by itself and compare it with the sum of the other two squares. (The Pythagorean Theorem)
• ×Thinking that doubling every length doubles the area. Area is multiplied by 2 × 2 = 4. (How Changing Dimensions Changes Area and Volume)
• ×Using $k^2$ for volume. Volume uses three lengths, so it is multiplied by $k^3$: doubling gives $\times 8$, not $\times 4$. (How Changing Dimensions Changes Area and Volume)
• ×Applying $k^2$ or $k^3$ when only one dimension changed. Doubling only the height of a box doubles its volume. (How Changing Dimensions Changes Area and Volume)
• ×Working backwards by dividing instead of taking a root: an area $\times 16$ means $k=4$, not $k=8$. (How Changing Dimensions Changes Area and Volume)
• ×Forgetting that a radius is squared in circle and cylinder formulas, so tripling only the radius multiplies the area or volume by 9. (How Changing Dimensions Changes Area and Volume)
• ×Forgetting the $\frac{1}{3}$ for a pyramid or cone, which gives an answer three times too big. (Volume: Prisms, Pyramids, Cylinders and Cones)
• ×Using the slant height instead of the perpendicular height. (Volume: Prisms, Pyramids, Cylinders and Cones)
• ×Using the diameter in place of the radius. A can 7 cm across has $r=3.5$ cm. (Volume: Prisms, Pyramids, Cylinders and Cones)
• ×Mixing units, such as a radius in centimetres with a height in metres, without converting first. (Volume: Prisms, Pyramids, Cylinders and Cones)
• ×Converting ${\text{cm}}^3$ to litres by dividing by 100 instead of 1000. (Volume: Prisms, Pyramids, Cylinders and Cones)

Practice test

24 questions from across the unit. Each one shows the lesson it comes from.

Endless drill

Fresh numbers every time, for the calculation questions in this unit.