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24:[["$","$L33",null,{"feature":"flashcards"}],"$L34",["$","$L35",null,{"href":"/igcse/maths/cie/grade-4-4-16-bearings/flashcards","label":"Bearings","subjectCode":"igcse_maths__cie","surface":"flashcards"}],["$","$L36",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L37",null,{"decks":[{"id":"6f2fe072-6346-4770-b6ca-c1ccbce065ac","title":"Bearings Flashcards","topicId":"541fe683-38d9-4003-8149-1e3af09676f5","topicSlug":"grade-4-4-16-bearings","cards":[{"id":"21024028-c806-40dd-aa21-12b121635993","cardType":"cloze","points":null,"front":"A full turn is [ ]; a straight line is [ ].","back":"A full turn is 360°; a straight line is 180°.","mcqOptions":[{"text":"A full turn is 360°; a straight line is 180°.","correct":true,"explanation":"One complete rotation returns to the starting direction and measures 360°, while the angle formed by a straight line is half a turn, measuring 180°."},{"text":"A full turn is 180°; a straight line is 360°.","correct":false,"explanation":"This reverses the two standard angle facts. A full turn measures 360°, whereas a straight line represents half a turn and measures 180°."},{"text":"A full turn is 360°; a straight line is 90°.","correct":false,"explanation":"A 90° angle is a quarter turn, not a straight line. A full turn measures 360°, and a straight line measures 180°."},{"text":"A full turn is 180°; a straight line is 90°.","correct":false,"explanation":"This confuses a half turn with a full turn and a quarter turn with a straight line. The correct measures are 360° and 180°, respectively."}]},{"id":"14701ba3-4185-4de3-b465-57658fabdf4b","cardType":"basic","points":1,"front":"What do angles in a triangle add up to?","back":"180°.","mcqOptions":[{"text":"180°.","correct":true,"explanation":"The three interior angles of any triangle have a total of 180°, regardless of the triangle’s side lengths or individual angle sizes."},{"text":"360°.","correct":false,"explanation":"A total of 360° applies to angles around a point or the interior angles of a quadrilateral. The angles inside a triangle add to 180°."},{"text":"90°.","correct":false,"explanation":"A right angle measures 90°, but that is not the total for every triangle. The three interior angles of a triangle add to 180°."},{"text":"270°.","correct":false,"explanation":"A total of 270° may result from confusing three right angles with a triangle’s angle sum. Every triangle’s interior angles instead total 180°."}]},{"id":"2561db21-99d0-4c92-9a28-70bbde208e67","cardType":"basic","points":1,"front":"A bearing is measured from which reference direction?","back":"North.","mcqOptions":[{"text":"North.","correct":true,"explanation":"Bearings always begin from the North line at the relevant starting point. The angle is then measured clockwise from North to the required direction."},{"text":"East.","correct":false,"explanation":"East corresponds to a bearing of 090°, but it is not the reference direction. Bearings are measured clockwise starting from North, which is 000°."},{"text":"South.","correct":false,"explanation":"South corresponds to a bearing of 180°, so it is a possible destination direction rather than the reference direction. Bearings start from North."},{"text":"West.","correct":false,"explanation":"West corresponds to a bearing of 270°, but bearings do not start there. Their reference direction is always North at the starting point."}]},{"id":"ab577f99-f582-46b2-a4f2-cb62c4a47ec0","cardType":"basic","points":1,"front":"A bearing is measured clockwise or anticlockwise?","back":"Clockwise.","mcqOptions":[{"text":"Clockwise.","correct":true,"explanation":"By convention, a bearing is the angle turned clockwise from North to the required direction. This ensures that each direction has one standard three-figure bearing."},{"text":"Anticlockwise.","correct":false,"explanation":"Measuring anticlockwise would generally produce a different angle and is not the bearings convention. Bearings are measured clockwise from the North line."},{"text":"Either direction.","correct":false,"explanation":"A bearing uses one specified direction of rotation, rather than whichever direction gives the smaller angle. It must be measured clockwise from North."},{"text":"The shortest direction.","correct":false,"explanation":"Using the shortest direction can lead to an anticlockwise angle, which is not a standard bearing. The angle must always be measured clockwise from North."}]},{"id":"dde73fe8-c230-4e15-a29c-e2ae53b40fa0","cardType":"basic","points":1,"front":"How many digits must a three-figure bearing have before °?","back":"Three digits.","mcqOptions":[{"text":"Three digits.","correct":true,"explanation":"A three-figure bearing contains exactly three digits before the degree symbol. Leading zeros are added when necessary, such as writing 8° as 008°."},{"text":"Two digits.","correct":false,"explanation":"Using two digits omits a required leading zero for bearings below 100°. A three-figure bearing must contain exactly three digits before the degree symbol."},{"text":"One digit.","correct":false,"explanation":"A single digit gives an ordinary angle notation rather than a three-figure bearing. Leading zeros must be included to make exactly three digits."},{"text":"Four digits.","correct":false,"explanation":"Four digits would add an unnecessary leading zero and would no longer be a three-figure bearing. Exactly three digits must appear before the degree symbol."}]},{"id":"ad8672ab-01b7-4d3a-8a49-4c2f7252136e","cardType":"cloze","points":null,"front":"In the bearing of B from A, stand at [ ] and look towards [ ].","back":"In the bearing of B from A, stand at A and look towards B.","mcqOptions":[{"text":"In the bearing of B from A, stand at A and look towards B.","correct":true,"explanation":"The word “from” identifies the observation point, so the bearing of B from A is measured while standing at A and facing towards B."},{"text":"In the bearing of B from A, stand at B and look towards A.","correct":false,"explanation":"This reverses the starting point and destination, giving the bearing of A from B. For B from A, stand at A and look towards B."},{"text":"In the bearing of B from A, stand at A and look towards A.","correct":false,"explanation":"Looking towards the same point at which you are standing does not define the required direction. For B from A, stand at A and look towards B."},{"text":"In the bearing of B from A, stand at B and look towards B.","correct":false,"explanation":"Standing at B and looking towards B gives no direction between the two locations. The wording “B from A” requires standing at A and looking towards B."}]},{"id":"8602f5ce-4a48-44c7-8806-98dd3e0d4a33","cardType":"basic","points":1,"front":"A bearing from A must use which North line?","back":"The North line at A.","mcqOptions":[{"text":"The North line at A.","correct":true,"explanation":"The phrase “from A” makes A the starting point of the bearing. Therefore, the clockwise angle must be measured from the North line drawn at A."},{"text":"The North line at B.","correct":false,"explanation":"Using the North line at B would measure an angle from the destination and could give the reverse bearing. A bearing from A uses North at A."},{"text":"The South line at A.","correct":false,"explanation":"Bearings are measured from North, not South, at the named starting point. Since the bearing is from A, the correct reference is North at A."},{"text":"The North line at the midpoint.","correct":false,"explanation":"The reference line must pass through the starting point, not a point between the locations. A bearing from A is measured from the North line at A."}]},{"id":"458fe453-cf98-45a3-a20e-830fd6e2773c","cardType":"basic","points":1,"front":"Write 8° as a three-figure bearing.","back":"008°.","mcqOptions":[{"text":"008°.","correct":true,"explanation":"A three-figure bearing must have exactly three digits, so two leading zeros are placed before 8. The angle itself remains unchanged at 8°."},{"text":"080°.","correct":false,"explanation":"Placing the zero after 8 changes the value from 8° to 80°. Leading zeros must instead be added before the angle, giving 008°."},{"text":"800°.","correct":false,"explanation":"Adding zeros after the digit changes the angle to 800°, which is not the original direction. Two leading zeros produce the required bearing 008°."},{"text":"08°.","correct":false,"explanation":"This has only two digits before the degree symbol, so it is not a three-figure bearing. One more leading zero is required, giving 008°."}]},{"id":"5fa3dd89-7ff7-49a5-ad70-ed54c92fed32","cardType":"cloze","points":null,"front":"As three-figure bearings, East is [ ] and South is [ ].","back":"As three-figure bearings, East is 090° and South is 180°.","mcqOptions":[{"text":"As three-figure bearings, East is 090° and South is 180°.","correct":true,"explanation":"Bearings are measured clockwise from North. East is a quarter-turn clockwise, giving 090°, while South is a half-turn clockwise, giving 180°."},{"text":"As three-figure bearings, East is 180° and South is 090°.","correct":false,"explanation":"This swaps the bearings for East and South. From North, East is 90° clockwise and South is 180° clockwise, so their bearings are 090° and 180° respectively."},{"text":"As three-figure bearings, East is 270° and South is 180°.","correct":false,"explanation":"The bearing 270° points West, not East. East is reached by turning 90° clockwise from North, so its three-figure bearing is 090°; South is 180°."},{"text":"As three-figure bearings, East is 090° and South is 270°.","correct":false,"explanation":"The bearing 270° points West, not South. South is a half-turn clockwise from North, so its bearing is 180°, while East is correctly represented by 090°."}]},{"id":"bfef8b55-a6b1-47f1-b00c-88bfd8a34ec3","cardType":"cloze","points":null,"front":"As three-figure bearings, North is [ ] and West is [ ].","back":"As three-figure bearings, North is 000° and West is 270°.","mcqOptions":[{"text":"As three-figure bearings, North is 000° and West is 270°.","correct":true,"explanation":"North is the starting direction for measuring bearings, so it is 000°. West is three-quarters of a full clockwise turn from North, which gives 270°."},{"text":"As three-figure bearings, North is 090° and West is 270°.","correct":false,"explanation":"The bearing 090° points East, not North. North is the zero direction and must be written as 000° in three-figure form; West is 270°."},{"text":"As three-figure bearings, North is 000° and West is 090°.","correct":false,"explanation":"The bearing 090° points East rather than West. Travelling clockwise from North to West requires three quarter-turns, so West has a bearing of 270°."},{"text":"As three-figure bearings, North is 180° and West is 090°.","correct":false,"explanation":"This confuses North with South and West with East. North is the starting direction at 000°, while West is 270° clockwise from North."}]},{"id":"bab5d057-e467-40d3-b567-679195a4afe5","cardType":"basic","points":1,"front":"What is the three-figure bearing of South-West?","back":"225°.","mcqOptions":[{"text":"225°.","correct":true,"explanation":"South-West lies halfway between South at 180° and West at 270°. Adding 45° to 180° gives the three-figure bearing 225°."},{"text":"135°.","correct":false,"explanation":"The bearing 135° points South-East, showing that East and West have been confused. South-West lies between 180° and 270°, exactly halfway at 225°."},{"text":"215°.","correct":false,"explanation":"This uses an incorrect 35° offset from South. The eight principal compass directions are separated by 45°, so South-West is 180° + 45° = 225°."},{"text":"315°.","correct":false,"explanation":"The bearing 315° points North-West, not South-West. South-West is halfway between South at 180° and West at 270°, giving a bearing of 225°."}]},{"id":"3adfc286-df40-4490-9d1b-1225d1199d79","cardType":"basic","points":1,"front":"A direction is 34° anticlockwise from North. What clockwise bearing is it?","back":"326°.","mcqOptions":[{"text":"326°.","correct":true,"explanation":"A 34° anticlockwise turn from North is equivalent to a clockwise turn of the remainder of a full circle. Therefore, the bearing is 360° - 34° = 326°."},{"text":"034°.","correct":false,"explanation":"This treats an anticlockwise angle as though it were clockwise. Subtracting 34° from a full turn converts it correctly: 360° - 34° = 326°."},{"text":"304°.","correct":false,"explanation":"This results from subtracting 56° rather than the stated 34°. The equivalent clockwise bearing is found using 360° - 34°, which equals 326°."},{"text":"336°.","correct":false,"explanation":"This subtracts 24° from 360°, losing ten degrees from the given angle. The correct conversion is 360° - 34° = 326°."}]},{"id":"fd366662-4c07-48d5-803a-0bf7458e6eca","cardType":"basic","points":1,"front":"When drawing a bearing, where should the protractor centre be placed?","back":"On the starting point.","mcqOptions":[{"text":"On the starting point.","correct":true,"explanation":"A bearing describes the turn made at the starting point, so the protractor’s centre must be placed there. This allows the angle to be measured from North accurately."},{"text":"On the destination point.","correct":false,"explanation":"Placing the centre at the destination measures the reverse direction instead. The bearing begins at the starting point, so the protractor’s centre must be positioned there."},{"text":"On the North arrow.","correct":false,"explanation":"The North arrow shows the reference direction but is not necessarily the angle’s vertex. The protractor’s centre belongs on the starting point, where the bearing begins."},{"text":"On the line midpoint.","correct":false,"explanation":"The midpoint is not the vertex from which the direction is measured. Bearings are measured at the starting point, so the protractor’s centre must be placed there."}]},{"id":"2a15e79e-ced6-4001-aaca-d92aa6ea8919","cardType":"basic","points":1,"front":"When drawing a bearing, what should the protractor 0° line line up with?","back":"The North line at the starting point.","mcqOptions":[{"text":"The North line at the starting point.","correct":true,"explanation":"Bearings are measured clockwise from North, so the protractor’s 0° line must align with the North line drawn through the starting point."},{"text":"The South line at the starting point.","correct":false,"explanation":"Aligning with South introduces a 180° error because bearings use North as their reference direction. The 0° line must align with the North line at the starting point."},{"text":"The travel line at the starting point.","correct":false,"explanation":"The line of travel shows the final direction, not the zero reference. The protractor’s 0° line should align with North before the clockwise angle is marked."},{"text":"The East line at the starting point.","correct":false,"explanation":"Using East as zero shifts the measurement by 90°. Bearings always begin from North, so the protractor’s 0° line must align with the North line."}]},{"id":"f160c043-abc6-42ad-9e22-f918e17e645b","cardType":"basic","points":1,"front":"If protractor numbers get smaller as you move clockwise from North, what is wrong?","back":"You are using the wrong scale.","mcqOptions":[{"text":"You are using the wrong scale.","correct":true,"explanation":"Bearing angles must increase as you move clockwise from North. If the numbers decrease, you are reading the protractor’s opposite scale and must switch scales."},{"text":"You have misplaced the protractor centre.","correct":false,"explanation":"A misplaced centre affects the angle’s vertex but does not determine whether the numbers increase clockwise. Decreasing numbers show that the wrong protractor scale is being read."},{"text":"You have aligned with the East line.","correct":false,"explanation":"Aligning with East would create a 90° offset, but it does not explain the decreasing numbers. That pattern means you are reading the wrong protractor scale."},{"text":"You have marked the destination point.","correct":false,"explanation":"Marking the destination does not control the order of the protractor numbers. If they decrease clockwise from North, the wrong scale is being used."}]},{"id":"ea1272ed-6752-4968-9f61-5aa2c0d327c6","cardType":"cloze","points":null,"front":"To measure a bearing from a diagram, measure [ ] from North to the [ ].","back":"To measure a bearing from a diagram, measure clockwise from North to the line of travel.","mcqOptions":[{"text":"To measure a bearing from a diagram, measure clockwise from North to the line of travel.","correct":true,"explanation":"A bearing is defined as the clockwise angle measured from the North line at the starting point to the line showing the direction of travel."},{"text":"To measure a bearing from a diagram, measure anticlockwise from North to the line of travel.","correct":false,"explanation":"This uses the wrong direction of rotation. Bearings are always measured clockwise from North to the line of travel and are written using three figures."},{"text":"To measure a bearing from a diagram, measure clockwise from North to the North line.","correct":false,"explanation":"Measuring back to the North line would give zero rather than the required direction. The clockwise angle must finish at the line of travel."},{"text":"To measure a bearing from a diagram, measure anticlockwise from North to the starting point.","correct":false,"explanation":"This confuses both the rotation and the endpoint of the angle. A bearing is measured clockwise from North to the line of travel, with its vertex at the starting point."}]},{"id":"866490d0-ad39-4875-b0b0-60d439a72f2e","cardType":"cloze","points":null,"front":"Reverse bearings differ by [ ] because the opposite direction is a [ ].","back":"Reverse bearings differ by 180° because the opposite direction is a half-turn.","mcqOptions":[{"text":"Reverse bearings differ by 180° because the opposite direction is a half-turn.","correct":true,"explanation":"A reverse bearing points in exactly the opposite direction. Opposite directions are separated by 180°, which is one half-turn around a point."},{"text":"Reverse bearings differ by 90° because the opposite direction is a quarter-turn.","correct":false,"explanation":"A 90° quarter-turn gives a perpendicular direction, not the opposite direction. Reverse bearings differ by 180° because changing direction is a half-turn."},{"text":"Reverse bearings differ by 360° because the opposite direction is a full-turn.","correct":false,"explanation":"A 360° full-turn returns to the original direction rather than reversing it. Reverse bearings differ by 180°, corresponding to a half-turn."},{"text":"Reverse bearings differ by 180° because the opposite direction is a full-turn.","correct":false,"explanation":"The angular difference of 180° is correct, but 180° is a half-turn, not a full-turn. A full-turn is 360° and returns to the original direction."}]},{"id":"f42ca7a9-56bc-4e48-b414-7b4dfaac21b5","cardType":"basic","points":1,"front":"To find a reverse bearing, what do you do if the bearing is less than 180°?","back":"Add 180°.","mcqOptions":[{"text":"Add 180°.","correct":true,"explanation":"Adding 180° makes a half-turn to obtain the opposite direction. Since the original bearing is below 180°, the result remains below 360°."},{"text":"Subtract 180°.","correct":false,"explanation":"Subtracting 180° from a bearing below 180° produces a negative value. The reverse bearing is found by adding 180°, giving a valid three-figure bearing."},{"text":"Add 90°.","correct":false,"explanation":"Adding 90° produces a perpendicular direction, which is only a quarter-turn. A reverse bearing requires a half-turn, so 180° must be added."},{"text":"Subtract 90°.","correct":false,"explanation":"Subtracting 90° makes only a quarter-turn and may also produce a negative value. The opposite direction is reached by adding 180°."}]},{"id":"6b244e7b-cc3c-4c79-81fb-8b60c5eb673b","cardType":"basic","points":1,"front":"To find a reverse bearing, what do you do if the bearing is 180° or more?","back":"Subtract 180°.","mcqOptions":[{"text":"Subtract 180°.","correct":true,"explanation":"For a bearing of 180° or more, subtracting 180° gives the opposite direction while keeping the result within the standard bearing range from 000° to 360°."},{"text":"Add 180°.","correct":false,"explanation":"Adding 180° produces a value of 360° or more, which is not immediately a standard bearing. Subtracting 180° gives the reverse bearing directly."},{"text":"Subtract 90°.","correct":false,"explanation":"Subtracting 90° changes the direction by only a quarter-turn. Reverse bearings point in opposite directions, so the required change is 180°."},{"text":"Subtract 360°.","correct":false,"explanation":"Subtracting 360° represents a full rotation and leaves the direction unchanged, often producing a negative representation. The reverse bearing is found by subtracting 180°."}]},{"id":"f5830e92-7ef0-45c0-9612-a2a8048d1db7","cardType":"basic","points":1,"front":"The bearing of B from A is 070°. What is the bearing of A from B?","back":"250°.","mcqOptions":[{"text":"250°.","correct":true,"explanation":"Because 070° is less than 180°, add 180° to reverse the direction: 070° + 180° = 250°."},{"text":"110°.","correct":false,"explanation":"This comes from calculating 180° - 70°, which does not make a half-turn from the original bearing. Adding 180° gives the reverse bearing, 250°."},{"text":"290°.","correct":false,"explanation":"This uses 360° - 70°, which reflects the direction around the north line rather than reversing it. The reverse bearing is 070° + 180° = 250°."},{"text":"140°.","correct":false,"explanation":"Doubling 070° does not produce the opposite direction. A reverse bearing is found by changing the bearing by 180°, giving 250°."}]},{"id":"260644db-eebe-4a93-8562-fe5664d61a9b","cardType":"basic","points":1,"front":"The bearing of D from C is 238°. What is the bearing of C from D?","back":"058°.","mcqOptions":[{"text":"058°.","correct":true,"explanation":"Because 238° is at least 180°, subtract 180° to find the reverse bearing: 238° - 180° = 58°, written as the three-figure bearing 058°."},{"text":"122°.","correct":false,"explanation":"This comes from calculating 360° - 238°, which reflects the direction rather than reversing it. Subtracting 180° gives 058°."},{"text":"418°.","correct":false,"explanation":"Adding 180° gives 418°, which lies outside the standard bearing range and has not been normalised. Subtracting 180° directly gives the reverse bearing 058°."},{"text":"068°.","correct":false,"explanation":"This results from an arithmetic slip when subtracting 180° from 238°. The correct calculation is 238° - 180° = 58°, written 058°."}]},{"id":"a164776c-42d6-4494-8a18-e4ad8dd84406","cardType":"basic","points":1,"front":"When finding an angle at B, from which point must both directions be measured before subtracting?","back":"From B.","mcqOptions":[{"text":"From B.","correct":true,"explanation":"Angle ABC has its vertex at B, so both directions must be considered from B. Their bearings can then be subtracted to find the angle at B."},{"text":"From A.","correct":false,"explanation":"Measuring both directions from A would describe an angle with vertex A, not angle ABC. Since B is the middle letter, both directions must be measured from B."},{"text":"From C.","correct":false,"explanation":"Measuring from C would find an angle with vertex C rather than B. For angle ABC, the middle letter identifies B as the common starting point."},{"text":"From north.","correct":false,"explanation":"Individual bearings are measured clockwise from north, but the two directions used for angle ABC must share B as their starting point before their bearings are subtracted."}]},{"id":"67431075-095a-4c9c-9646-eb6d6224f6d0","cardType":"basic","points":1,"front":"From A, B is on a bearing of 040°. What is the bearing of A from B?","back":"220°.","mcqOptions":[{"text":"220°.","correct":true,"explanation":"The original bearing 040° is below 180°, so add 180° to reverse it: 040° + 180° = 220°."},{"text":"140°.","correct":false,"explanation":"This comes from calculating 180° - 40°, which does not turn the direction through 180°. The reverse bearing is 040° + 180° = 220°."},{"text":"320°.","correct":false,"explanation":"This uses 360° - 40°, reflecting the bearing about north instead of finding the opposite direction. Adding 180° gives 220°."},{"text":"080°.","correct":false,"explanation":"Doubling the original bearing does not create a reverse direction. Reverse bearings differ by exactly 180°, so the correct bearing is 220°."}]},{"id":"18c94e65-c69b-4c7a-be82-3060c809a4dd","cardType":"basic","points":1,"front":"From B, BA has bearing 220° and BC has bearing 120°. What is angle ABC?","back":"100°.","mcqOptions":[{"text":"100°.","correct":true,"explanation":"Both bearings are measured from B, so their difference gives the angle between BA and BC: 220° - 120° = 100°."},{"text":"260°.","correct":false,"explanation":"This is the reflex angle obtained from 360° - 100°. The smaller angle ABC is found directly from the bearing difference, 220° - 120° = 100°."},{"text":"140°.","correct":false,"explanation":"This comes from subtracting 220° from 360°, using only one bearing. The angle between the two directions is their difference, which is 100°."},{"text":"340°.","correct":false,"explanation":"Adding the bearings gives 340°, but bearings from a common point must be subtracted to find the angle between them. Their difference is 100°."}]}]}],"examCountdown":null,"heading":"Bearings","title":"Bearings Flashcards","topbar":{"backHref":"/igcse/maths/cie/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"541fe683-38d9-4003-8149-1e3af09676f5","walled":"$L39"}],"$L3a","$L3b"]