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No rounding or truncation should be applied."},{"text":"Copy every digit shown after rounding.","correct":false,"explanation":"Rounding changes the digits displayed and therefore does not follow the instruction. The correct response is to copy every digit exactly without rounding."},{"text":"Copy only the first digits without rounding.","correct":false,"explanation":"Stopping before the end of the display is truncation, even if the copied digits are unchanged. Every displayed digit must be copied exactly."},{"text":"Copy the answer to three decimal places.","correct":false,"explanation":"Three decimal places should be used only when specifically requested. Here, every digit visible on the calculator display must be copied without rounding."}]},{"id":"3aabd69a-6a7e-eb7f-9858-5d63098f21e8","cardType":"basic","points":1,"front":"On a calculator, which key converts a fraction answer into a decimal answer?","back":"The S-D (or $S \\iff D$) key.","mcqOptions":[{"text":"The S-D (or $S \\iff D$) key.","correct":true,"explanation":"This key switches the displayed answer between exact forms, such as fractions, and decimal form without requiring the calculation to be entered again."},{"text":"The Ans (previous answer) key.","correct":false,"explanation":"The Ans key recalls the previous result rather than changing its format. The S-D, or $S \\iff D$, key converts a fraction display into a decimal."},{"text":"The = (or EXE) key.","correct":false,"explanation":"The equals or EXE key completes a calculation but does not normally switch the answer format. The S-D, or $S \\iff D$, key performs the conversion."},{"text":"The SHIFT (or 2nd) key.","correct":false,"explanation":"SHIFT accesses alternative key functions but does not itself convert a fraction answer. The conversion is carried out using the S-D, or $S \\iff D$, key."}]},{"id":"fd48cd07-af2d-95a1-2af9-7d30ffd33f8c","cardType":"basic","points":1,"front":"What is the mathematical meaning of $1.35^2$?","back":"$$1.35 \\times 1.35$ (repeated multiplication).","mcqOptions":[{"text":"$$1.35 \\times 1.35$ (repeated multiplication).","correct":true,"explanation":"An index of 2 means that the base is used as a factor twice. Therefore, squaring 1.35 means multiplying 1.35 by itself."},{"text":"$$1.35 \\times 2$ (multiplication by the power).","correct":false,"explanation":"An index is not a number by which the base is multiplied. The power 2 means using 1.35 as a factor twice: $1.35 \\times 1.35$."},{"text":"$$1.35 + 1.35$ (repeated addition).","correct":false,"explanation":"Adding the number twice calculates $2 \\times 1.35$, not its square. Squaring requires repeated multiplication, so the correct calculation is $1.35 \\times 1.35$."},{"text":"$$1.35 \\times 1.35 \\times 1.35$ (three repeated factors).","correct":false,"explanation":"Using three factors calculates $1.35^3$, which is the cube. The index 2 requires exactly two factors, giving $1.35 \\times 1.35$."}]},{"id":"a39e860d-f086-e023-ee81-3e695a8fdad5","cardType":"cloze","points":null,"front":"The little 2 in the expression $1.45^2$ is called an [ ].","back":"The little 2 in the expression $1.45^2$ is called an index.","mcqOptions":[{"text":"index","correct":true,"explanation":"An index is the small raised number that states how many times the base is used as a factor. Here, the index 2 means square the base."},{"text":"coefficient","correct":false,"explanation":"A coefficient is a number multiplying a variable, such as 3 in $3x$. The small raised 2 in $1.45^2$ is called an index."},{"text":"base","correct":false,"explanation":"The base is the number being raised to a power, which is 1.45 here. The small raised 2 is called the index."},{"text":"factor","correct":false,"explanation":"A factor is a number multiplied by another number in a product. The small raised number that indicates a power is called an index."}]},{"id":"33c25d83-8b69-a9df-3dcb-f9e8a56e669c","cardType":"basic","points":2,"front":"What is the calculator's order of operations (BIDMAS/BODMAS)?","back":"

Brackets first
Powers and roots
Multiplication and division
Addition and subtraction

","mcqOptions":[{"text":"

Brackets first
Powers and roots
Multiplication and division
Addition and subtraction

","correct":true,"explanation":"BIDMAS requires brackets first, followed by indices such as powers and roots, then multiplication and division, and finally addition and subtraction."},{"text":"

Brackets first
Multiplication and division
Powers and roots
Addition and subtraction

","correct":false,"explanation":"This places multiplication and division too early. After brackets, powers and roots must be evaluated before multiplication and division, with addition and subtraction last."},{"text":"

Powers and roots
Brackets first
Multiplication and division
Addition and subtraction

","correct":false,"explanation":"Brackets cannot come after powers because they determine which expression a power applies to. The correct order begins with brackets, then powers and roots."},{"text":"

Brackets first
Powers and roots
Addition and subtraction
Multiplication and division

","correct":false,"explanation":"This reverses the final two stages of BIDMAS. Multiplication and division must be completed before addition and subtraction, after brackets, powers and roots."}]},{"id":"eeb3c296-b9c7-d98b-7a15-cca8a4ee9495","cardType":"cloze","points":null,"front":"In the calculation $(3.20 - 0.45)^2$, the [ ] ensure the subtraction happens before the squaring.","back":"In the calculation $(3.20 - 0.45)^2$, the brackets ensure the subtraction happens before the squaring.","mcqOptions":[{"text":"brackets","correct":true,"explanation":"Brackets group $3.20 - 0.45$ into a single expression, forcing the calculator to complete that subtraction before applying the power of 2."},{"text":"decimals","correct":false,"explanation":"Decimal points specify place value but do not control calculation order. The brackets make the subtraction happen before the result is squared."},{"text":"indices","correct":false,"explanation":"Indices specify powers and would normally be evaluated before subtraction. The brackets override that usual order by requiring the subtraction to be completed first."},{"text":"subtractions","correct":false,"explanation":"The subtraction operation does not itself determine that it must happen first. The brackets group the difference, ensuring it is found before squaring."}]},{"id":"2a77c79b-9749-9ac7-8138-7ce590d0b3b4","cardType":"cloze","points":null,"front":"In the calculation $(3.20 - 0.45)^2$, the brackets ensure the subtraction happens before the [ ].","back":"In the calculation $(3.20 - 0.45)^2$, the brackets ensure the subtraction happens before the squaring.","mcqOptions":[{"text":"squaring","correct":true,"explanation":"The brackets require the difference $3.20 - 0.45$ to be calculated first. The resulting value is then squared because the index applies to the whole bracket."},{"text":"addition","correct":false,"explanation":"There is no addition operation in this expression. The brackets ensure that $3.20 - 0.45$ is evaluated before the resulting difference is squared."},{"text":"multiplication","correct":false,"explanation":"Although squaring can be interpreted as multiplying a value by itself, the named operation shown by the index 2 is squaring, which follows the bracketed subtraction."},{"text":"division","correct":false,"explanation":"No division is present in the expression. The brackets ensure the subtraction is completed first, and then the entire bracketed result is squared."}]},{"id":"bbb51105-f557-17bf-ca89-43ddc0447e43","cardType":"basic","points":2,"front":"How does the calculator process $3.20 - 0.45^2$ compared to $(3.20 - 0.45)^2$?","back":"In $3.20 - 0.45^2$, only 0.45 is squared before subtracting.","mcqOptions":[{"text":"In $3.20 - 0.45^2$, only 0.45 is squared before subtracting.","correct":true,"explanation":"Powers are evaluated before subtraction, so the index applies only to 0.45. Brackets would be needed for the entire difference to be squared."},{"text":"In $3.20 - 0.45^2$, the whole expression is squared after subtracting.","correct":false,"explanation":"Without brackets around the subtraction, the index cannot apply to the whole expression. Only 0.45 is squared, and that result is then subtracted from 3.20."},{"text":"In $3.20 - 0.45^2$, 3.20 and 0.45 are both squared before subtracting.","correct":false,"explanation":"An index applies only to the number immediately before it unless brackets indicate otherwise. Therefore, only 0.45 is squared before it is subtracted from 3.20."},{"text":"In $3.20 - 0.45^2$, 0.45 is doubled before subtracting.","correct":false,"explanation":"The index 2 means square, not multiply by 2. The calculator evaluates $0.45 \\times 0.45$ first and subtracts that result from 3.20."}]},{"id":"043fddc6-22aa-41ff-8cca-4e02e291cdd8","cardType":"cloze","points":null,"front":"The top of a fraction is the [ ] and the bottom is the denominator.","back":"The top of a fraction is the numerator and the bottom is the denominator.","mcqOptions":[{"text":"numerator","correct":true,"explanation":"The numerator is the number above the fraction bar. It gives the number of parts being considered, while the denominator below shows the total number of equal parts."},{"text":"denominator","correct":false,"explanation":"The denominator is below the fraction bar, not above it. The correct term for the number at the top of a fraction is the numerator."},{"text":"quotient","correct":false,"explanation":"A quotient is the result obtained from division, rather than the top number of a fraction. The number above the fraction bar is called the numerator."},{"text":"remainder","correct":false,"explanation":"A remainder is the amount left over after a division cannot be completed exactly. The top number in a fraction is instead called the numerator."}]},{"id":"02f3a2e5-054c-315a-efcf-2d0b97846a81","cardType":"cloze","points":null,"front":"The top of a fraction is the numerator and the bottom is the [ ].","back":"The top of a fraction is the numerator and the bottom is the denominator.","mcqOptions":[{"text":"denominator","correct":true,"explanation":"The denominator is the number below the fraction bar. It shows how many equal parts make up the whole, while the numerator shows how many are considered."},{"text":"numerator","correct":false,"explanation":"The numerator is the number above the fraction bar, not below it. The number at the bottom of a fraction is called the denominator."},{"text":"quotient","correct":false,"explanation":"A quotient is the answer produced by a division calculation, not the name of the bottom number. The bottom of a fraction is the denominator."},{"text":"divisor","correct":false,"explanation":"A divisor is a number by which another number is divided, but it is not the standard positional name used here. The bottom number is the denominator."}]},{"id":"8140d386-9f9e-a6dc-2f47-844ae2cabb02","cardType":"basic","points":1,"front":"What mathematical operation does the fraction bar represent?","back":"Division (top divided by bottom).","mcqOptions":[{"text":"Division (top divided by bottom).","correct":true,"explanation":"A fraction bar means that the numerator is divided by the denominator. For example, $\\frac{6}{3}$ represents $6 \\div 3$."},{"text":"Multiplication (top multiplied by bottom).","correct":false,"explanation":"Multiplication may be used with fractions in other calculations, but the fraction bar itself means division. The numerator is divided by the denominator."},{"text":"Subtraction (bottom subtracted from top).","correct":false,"explanation":"The vertical arrangement can make subtraction seem plausible, but a fraction bar does not mean subtracting the lower value. It represents top divided by bottom."},{"text":"Addition (top added to bottom).","correct":false,"explanation":"The two numbers in a fraction are not added merely because they appear together. The fraction bar instructs you to divide the top by the bottom."}]},{"id":"ae2cc9c9-15c4-bb61-1403-f5ccf2a6ebfa","cardType":"basic","points":2,"front":"How should you enter a long fraction if your calculator does not have a fraction template?","back":"Put the whole numerator in brackets before dividing.","mcqOptions":[{"text":"Put the whole numerator in brackets before dividing.","correct":true,"explanation":"Brackets ensure that every term in a multi-part numerator is evaluated before division occurs. Without them, the calculator may divide only the final term."},{"text":"Enter the numerator without any brackets before dividing.","correct":false,"explanation":"Leaving a multi-part numerator ungrouped allows order of operations to divide only part of it. The whole numerator must be placed in brackets before dividing."},{"text":"Put the final numerator term in brackets before dividing.","correct":false,"explanation":"Bracketing only the final term does not group the complete numerator, so earlier additions or subtractions may be handled separately. Bracket the whole numerator before dividing."},{"text":"Put the denominator before the numerator when dividing.","correct":false,"explanation":"Reversing the order calculates the reciprocal of the intended fraction. Enter the whole numerator in brackets first, followed by the division sign and denominator."}]},{"id":"971c8b80-9fc5-621a-a2dd-cc0cd5e54921","cardType":"cloze","points":null,"front":"To calculate $\\sqrt{\\frac{18.6-2.4}{4.1+2.2}}$, you must work out the [ ] before taking the square root.","back":"To calculate $\\sqrt{\\frac{18.6-2.4}{4.1+2.2}}$, you must work out the entire fraction before taking the square root.","mcqOptions":[{"text":"entire fraction","correct":true,"explanation":"The square-root sign covers the complete fraction, so both bracketed expressions must be evaluated and divided first. The square root is then taken of that quotient."},{"text":"numerator only","correct":false,"explanation":"Calculating only the numerator ignores the denominator within the square-root sign. Evaluate both numerator and denominator, divide them, and then take the square root of the entire fraction."},{"text":"denominator only","correct":false,"explanation":"Calculating only the denominator leaves the numerator unevaluated and does not produce the fraction’s value. The entire fraction must be found before applying the square root."},{"text":"numerator difference","correct":false,"explanation":"Although the subtraction in the numerator must be completed, the denominator and division must also be evaluated. Work out the entire fraction before taking its square root."}]},{"id":"5ed0bce6-1a33-91c4-5f75-6636e33041f0","cardType":"cloze","points":null,"front":"To calculate $\\sqrt{\\frac{18.6-2.4}{4.1+2.2}}$, you must work out the entire fraction before taking the [ ].","back":"To calculate $\\sqrt{\\frac{18.6-2.4}{4.1+2.2}}$, you must work out the entire fraction before taking the square root.","mcqOptions":[{"text":"square root","correct":true,"explanation":"The radical symbol $\\sqrt{\\phantom{x}}$ denotes a square root. Because it covers the whole fraction, evaluate the fraction fully and then take its square root."},{"text":"cube root","correct":false,"explanation":"A cube root is represented by a radical carrying a small $3$, which is absent here. The ordinary radical shown instructs you to take the square root."},{"text":"reciprocal","correct":false,"explanation":"Taking a reciprocal would interchange the numerator and denominator, but the radical symbol does not give that instruction. It indicates that the square root is required."},{"text":"absolute value","correct":false,"explanation":"Absolute value is normally indicated using vertical bars, not a radical sign. The expression shown requires the square root of the fully evaluated fraction."}]},{"id":"13cc348d-2d2e-3cfe-89fe-6273ba3af9ca","cardType":"basic","points":1,"front":"Where do you start counting when identifying significant figures?","back":"At the first non-zero digit.","mcqOptions":[{"text":"At the first non-zero digit.","correct":true,"explanation":"Leading zeros only locate the decimal point and are not significant. Counting begins at the first non-zero digit and continues through the required number of significant figures."},{"text":"At the first digit after the decimal point.","correct":false,"explanation":"Decimal places are counted from the decimal point, but significant figures are not. For significant figures, begin at the first non-zero digit wherever it occurs."},{"text":"At the first digit including zero.","correct":false,"explanation":"Leading zeros are placeholders and do not count as significant figures. Counting must start at the first non-zero digit rather than automatically including an initial zero."},{"text":"At the last non-zero digit.","correct":false,"explanation":"Starting at the final non-zero digit reverses the required counting direction and misses earlier significant digits. Begin at the first non-zero digit and count from left to right."}]},{"id":"7d3b2074-cfe7-9b77-7164-7be335fa65ce","cardType":"basic","points":2,"front":"What is the difference between rounding to 2 decimal places vs 2 significant figures for the number 0.587?","back":"

2dp: 0.59 (digits after decimal point)
2sf: 0.59 (digits from first non-zero)

","mcqOptions":[{"text":"

2dp: 0.59 (digits after decimal point)
2sf: 0.59 (digits from first non-zero)

","correct":true,"explanation":"Two decimal places keeps two digits after the decimal point, while two significant figures starts at $5$. In both cases, the next digit is $7$, so $0.58$ rounds to $0.59$."},{"text":"

2dp: 0.58 (digits after decimal point)
2sf: 0.58 (digits from first non-zero)

","correct":false,"explanation":"This truncates the number rather than rounding it. In each method, the next digit is $7$, so the retained $8$ must round up and both answers are $0.59$."},{"text":"

2dp: 0.59 (digits after decimal point)
2sf: 0.58 (digits from first non-zero)

","correct":false,"explanation":"The decimal-place result is rounded correctly, but the significant-figure result is truncated. The third significant digit is $7$, so the second significant digit rounds up to give $0.59$."},{"text":"

2dp: 0.587 (digits after decimal point)
2sf: 0.59 (digits from first non-zero)

","correct":false,"explanation":"Keeping $0.587$ leaves three decimal places rather than two. The third decimal digit is $7$, so the hundredths digit rounds up and both required results are $0.59$."}]},{"id":"90f64764-9c3e-513a-9d1d-257ff237bc7b","cardType":"basic","points":2,"front":"If an answer to 2 decimal places is 1.60, why must you include the final zero?","back":"It proves the value has been rounded to that specific degree of accuracy.","mcqOptions":[{"text":"It proves the value has been rounded to that specific degree of accuracy.","correct":true,"explanation":"Writing 1.60 shows that the result was rounded to two decimal places. Without the final zero, 1.6 would communicate only one decimal place."},{"text":"It proves the value has been rounded to one decimal place.","correct":false,"explanation":"One decimal place would be written as 1.6, not 1.60. The final zero proves that the value has been rounded to two decimal places."},{"text":"It proves the value has been rounded up rather than rounded down.","correct":false,"explanation":"A final zero does not reveal whether rounding increased or decreased the original value. It shows the specific degree of accuracy, which here is two decimal places."},{"text":"It proves the value has been entered exactly as shown on the calculator.","correct":false,"explanation":"Calculator displays do not necessarily indicate the required accuracy. The final zero is included to show that the answer has been rounded specifically to two decimal places."}]},{"id":"b67aeac9-2d36-de59-6b37-23f56dffa8b5","cardType":"basic","points":1,"front":"Which calculator mode must be active for GCSE trigonometry (sin, cos, tan) questions?","back":"DEG (degrees) mode.","mcqOptions":[{"text":"DEG (degrees) mode.","correct":true,"explanation":"GCSE trigonometry questions normally give angles in degrees, so the calculator must interpret inputs for sin, cos and tan using DEG mode."},{"text":"RAD (radians) mode.","correct":false,"explanation":"RAD mode interprets angles as radians, producing different trigonometric values. GCSE questions normally use degrees, so the calculator must be set to DEG mode."},{"text":"GRAD (gradians) mode.","correct":false,"explanation":"GRAD mode divides a full turn into 400 gradians rather than 360 degrees. Standard GCSE trigonometry requires DEG mode unless another angle unit is explicitly stated."},{"text":"SCI (scientific notation) mode.","correct":false,"explanation":"SCI controls how numbers are displayed in standard form; it does not set the angle unit. GCSE trigonometry normally requires DEG mode."}]},{"id":"a10af574-3983-2954-4426-847039e614d0","cardType":"cloze","points":null,"front":"If your calculator shows [ ] instead of DEG while using $sin$, $cos$ or $tan$, your answer will be incorrect.","back":"If your calculator shows RAD instead of DEG while using $sin$, $cos$ or $tan$, your answer will be incorrect.","mcqOptions":[{"text":"RAD","correct":true,"explanation":"RAD means radians, so the calculator interprets entered angles in radians rather than degrees. This gives incorrect values when a GCSE question provides angles in degrees."},{"text":"GRAD","correct":false,"explanation":"GRAD is another angle mode, but the named warning here is about RAD appearing instead of DEG. RAD interprets angles in radians and causes the error."},{"text":"FIX","correct":false,"explanation":"FIX controls the number of decimal places displayed, not the angle unit used in trigonometry. RAD is the mode that must be changed to DEG."},{"text":"SCI","correct":false,"explanation":"SCI changes numerical display to scientific notation and does not determine whether angles are degrees or radians. RAD is the incorrect angle mode described here."}]},{"id":"561ec4cb-8321-768c-a308-8a732dc6442d","cardType":"cloze","points":null,"front":"If your calculator shows RAD instead of DEG while using $sin$, $cos$ or $tan$, your answer will be [ ].","back":"If your calculator shows RAD instead of DEG while using $sin$, $cos$ or $tan$, your answer will be incorrect.","mcqOptions":[{"text":"incorrect","correct":true,"explanation":"RAD mode treats the entered angle as a number of radians rather than degrees. Therefore, sin, cos or tan produces the wrong value for a degree-based question."},{"text":"correct","correct":false,"explanation":"RAD mode does not correctly interpret angles given in degrees. The answer will be incorrect unless the calculator is changed to DEG mode or the angle is converted."},{"text":"unaffected","correct":false,"explanation":"Changing between RAD and DEG changes how the calculator interprets the angle, so trigonometric results are affected. For degree-based GCSE questions, RAD produces an incorrect answer."},{"text":"exact","correct":false,"explanation":"Exactness is not the issue: RAD mode uses the wrong angle unit for a degree-based question. The resulting trigonometric answer will therefore be incorrect."}]},{"id":"678736a7-82ca-cc19-57a4-9a13ea9232ee","cardType":"basic","points":1,"front":"What is the rule for rounding up a digit?","back":"If the next digit is 5 or more, round up.","mcqOptions":[{"text":"If the next digit is 5 or more, round up.","correct":true,"explanation":"When the digit immediately after the rounding position is 5, 6, 7, 8 or 9, the retained digit increases by one."},{"text":"If the next digit is 4 or more, round up.","correct":false,"explanation":"Treating 4 as the threshold rounds too many values upwards. The retained digit increases only when the next digit is 5 or more."},{"text":"If the next digit is exactly 5, round up.","correct":false,"explanation":"Digits above 5 also require rounding up, so limiting the rule to exactly 5 is incomplete. Round up whenever the next digit is 5 or more."},{"text":"If the next digit is 6 or more, round up.","correct":false,"explanation":"Using 6 as the threshold incorrectly rounds values followed by 5 downwards. The standard rule is to round up when the next digit is 5 or more."}]},{"id":"4c982fb7-1d77-c91e-867d-0ec76edad590","cardType":"basic","points":1,"front":"When should you perform rounding in a multi-step calculator problem?","back":"Only at the very end of the calculation.","mcqOptions":[{"text":"Only at the very end of the calculation.","correct":true,"explanation":"Keeping the full calculator value throughout prevents small rounding errors from accumulating. Round only the final result to the accuracy requested in the question."},{"text":"Only at the very start of the calculation.","correct":false,"explanation":"Rounding an initial value can introduce an error that is magnified by later operations. Keep full precision and round only at the very end."},{"text":"After every step of the calculation.","correct":false,"explanation":"Repeated rounding causes errors to accumulate across the calculation, potentially changing the final answer. Retain full calculator values and round only at the very end."},{"text":"Whenever the calculator shows a decimal in the calculation.","correct":false,"explanation":"A decimal display is not a signal to round, because later steps may need its full precision. Rounding should occur only at the very end."}]},{"id":"4da986eb-937b-526f-2f56-85521e47dcac","cardType":"basic","points":1,"front":"In the expression $\\sqrt{1.44} = 1.2$, what is the relationship between 1.2 and 1.44?","back":"$$1.2 \\times 1.2 = 1.44$.","mcqOptions":[{"text":"$$1.2 \\times 1.2 = 1.44$.","correct":true,"explanation":"A square root is a number that multiplies by itself to produce the original value. Squaring 1.2 gives 1.44, so its square root is 1.2."},{"text":"$$1.2 + 1.2 = 1.44$.","correct":false,"explanation":"This confuses squaring with doubling by addition, and the sum is actually 2.4. The square-root relationship is $1.2 \\times 1.2 = 1.44$."},{"text":"$$1.44 \\times 1.44 = 1.2$.","correct":false,"explanation":"This reverses the relationship and squares the original number instead of the root. A square root satisfies $1.2 \\times 1.2 = 1.44$."},{"text":"$$1.2 \\times 2 = 1.44$.","correct":false,"explanation":"Multiplying by 2 doubles a number rather than squaring it, and gives 2.4. The correct relationship is $1.2 \\times 1.2 = 1.44$."}]}]}],"examCountdown":null,"heading":"Using a Calculator","title":"Using a Calculator Flashcards","topbar":{"backHref":"/gcse/maths/ccea/flashcards"},"topicSidebar":"$L37"}]}],"topicId":"5be91c51-34a1-144d-0927-ebe0e0e22cdf","walled":"$L38"}],"$L39","$L3a"]