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Letters such as $x$, $n$, and $p$ are commonly used as variables."},{"text":"A number that has the same value in every calculation.","correct":false,"explanation":"A value that stays fixed is a constant, not a variable. A variable is a letter that represents an unknown or changing number."},{"text":"A letter that tells you which operation to perform.","correct":false,"explanation":"Operation symbols such as $+$ and $-$ indicate what calculation to perform. A variable is a letter standing for an unknown or changing number."},{"text":"A number written directly in front of a letter.","correct":false,"explanation":"A number multiplying a variable is called a coefficient. The variable itself is the letter representing an unknown or changing number."}]},{"id":"5de57ea0-2501-3177-3707-5b347ad11941","cardType":"cloze","points":null,"front":"A mathematical phrase made from numbers, variables, and operations, but with no equals sign, is called an [ ].","back":"A mathematical phrase made from numbers, variables, and operations, but with no equals sign, is called an expression.","mcqOptions":[{"text":"expression","correct":true,"explanation":"An expression combines numbers, variables, and operations without stating that two quantities are equal. For example, $3x + 5$ is an expression."},{"text":"equation","correct":false,"explanation":"An equation includes an equals sign connecting two equal expressions. A mathematical phrase with operations and variables but no equals sign is an expression."},{"text":"inequality","correct":false,"explanation":"An inequality compares quantities using a sign such as $<$ or $>$. With no comparison or equals sign, the mathematical phrase is an expression."},{"text":"coefficient","correct":false,"explanation":"A coefficient is a number multiplying a variable, such as $4$ in $4x$. The whole mathematical phrase without an equals sign is an expression."}]},{"id":"973d2dd0-eb7b-1569-95c8-2e4130a6a6f5","cardType":"basic","points":1,"front":"What does a question mean when it asks for an answer in terms of $t$?","back":"The final answer must use the letter $t$.","mcqOptions":[{"text":"The final answer must use the letter $t$.","correct":true,"explanation":"An answer in terms of $t$ must express the required quantity using $t$. The letter remains in the final algebraic expression rather than being evaluated."},{"text":"The final answer must replace the letter $t$.","correct":false,"explanation":"Replacing $t$ would require a numerical value, which has not necessarily been supplied. In terms of $t$ means the final answer must still use $t$."},{"text":"The final answer must equal the letter $t$.","correct":false,"explanation":"The required quantity does not have to equal $t$; it may be an expression such as $2t+3$. The final answer simply needs to use $t$."},{"text":"The final answer must define the letter $t$.","correct":false,"explanation":"The instruction is not asking for a definition of the variable. It requires the answer to be written as an expression that uses $t$."}]},{"id":"035bee77-1b17-50cb-3014-ab6b3b154089","cardType":"basic","points":1,"front":"What is the standard algebraic notation for half of price $p$?","back":"$$\\frac{p}{2}$","mcqOptions":[{"text":"$$\\frac{p}{2}$","correct":true,"explanation":"Finding half means dividing by $2$. Therefore, half of a price represented by $p$ is written as $\\frac{p}{2}$."},{"text":"$$\\frac{p}{4}$","correct":false,"explanation":"Dividing by $4$ finds one quarter, not one half. Half of the price is found by dividing $p$ by $2$, giving $\\frac{p}{2}$."},{"text":"$$2p$","correct":false,"explanation":"Multiplying by $2$ doubles the price rather than halves it. Half of $p$ is found by dividing by $2$, so it is $\\frac{p}{2}$."},{"text":"$$p - 2$","correct":false,"explanation":"Subtracting $2$ reduces the price by a fixed amount rather than finding half. Half of any value $p$ is $\\frac{p}{2}$."}]},{"id":"356002cf-0ef3-3c9c-a8da-cf19209c2fcf","cardType":"cloze","points":null,"front":"Words like more than or longer than usually indicate the operation of [ ].","back":"Words like more than or longer than usually indicate the operation of addition.","mcqOptions":[{"text":"addition","correct":true,"explanation":"Phrases such as “more than” and “longer than” describe an increase from an original amount, so they usually translate into addition."},{"text":"subtraction","correct":false,"explanation":"Subtraction is usually indicated by phrases such as “less than” or “shorter than”. “More than” and “longer than” indicate an increase, so addition is used."},{"text":"multiplication","correct":false,"explanation":"Multiplication is indicated by wording such as “times as many” or “double”. “More than” and “longer than” normally mean that an amount is added."},{"text":"division","correct":false,"explanation":"Division is indicated by phrases such as “shared equally” or “half of”. “More than” and “longer than” describe an increase and therefore indicate addition."}]},{"id":"a0ab67a9-2c4c-6f5d-6b1a-4920aea76af7","cardType":"cloze","points":null,"front":"Words like fewer than or gives away usually indicate the operation of [ ].","back":"Words like fewer than or gives away usually indicate the operation of subtraction.","mcqOptions":[{"text":"subtraction","correct":true,"explanation":"“Fewer than” describes a smaller amount, while “gives away” means an amount is removed. Both phrases therefore usually translate into subtraction."},{"text":"addition","correct":false,"explanation":"Addition would increase the original amount, which conflicts with having fewer items or giving some away. These phrases indicate subtraction because an amount is removed."},{"text":"multiplication","correct":false,"explanation":"Multiplication applies to repeated groups or phrases such as “times as many”. Having fewer items or giving items away means subtracting from the original amount."},{"text":"division","correct":false,"explanation":"Division involves sharing or splitting an amount into equal parts. “Fewer than” and “gives away” instead describe removing an amount, so they indicate subtraction."}]},{"id":"b8adcec8-cebd-31d1-d7bc-c54456ba5f04","cardType":"basic","points":1,"front":"Write an expression for \"13 years younger than $n$\".","back":"$$n - 13$","mcqOptions":[{"text":"$$n - 13$","correct":true,"explanation":"“13 years younger than $n$” means starting with the age $n$ and reducing it by $13$. This gives the expression $n-13$."},{"text":"$$n + 13$","correct":false,"explanation":"Adding $13$ gives an age that is older than $n$, not younger. A person $13$ years younger than $n$ has age $n-13$."},{"text":"$$13 - n$","correct":false,"explanation":"This reverses the order of the subtraction and can produce a negative age. Start with the original age $n$ and subtract $13$, giving $n-13$."},{"text":"$$13n$","correct":false,"explanation":"Writing two quantities together means multiplication, so this represents thirteen times the age. “13 years younger” requires subtracting $13$ from $n$, giving $n-13$."}]},{"id":"41c9ab3a-f426-1e05-78fb-a5e726313c8b","cardType":"basic","points":2,"front":"Why is \"13 years younger than $n$\" written as $n - 13$ rather than $13 - n$?","back":"You must start with the original age and then take the 13 years away.","mcqOptions":[{"text":"You must start with the original age and then take the 13 years away.","correct":true,"explanation":"The age $n$ is the starting quantity, and “13 years younger” means subtracting $13$ from it. Subtraction order matters, so the expression is $n-13$."},{"text":"You must start with the difference in ages and then take the original age away.","correct":false,"explanation":"This reverses the subtraction by treating $13$ as the starting quantity. The original age is $n$, so taking $13$ years away gives $n-13$."},{"text":"You must start with the original age and then add the 13 years on.","correct":false,"explanation":"Adding $13$ would represent someone older than $n$. The word “younger” means the age is reduced, so $13$ must be subtracted from $n$."},{"text":"You must start with the original age and then multiply it by 13.","correct":false,"explanation":"Multiplication would mean thirteen times the original age, not an age difference of thirteen years. “13 years younger” requires $13$ to be subtracted from $n$."}]},{"id":"373e90d6-ad11-40ae-1ff1-c1304dfe1356","cardType":"basic","points":1,"front":"What is the neat algebraic way to write $16 \\times w$?","back":"$$16w$","mcqOptions":[{"text":"$$16w$","correct":true,"explanation":"A number placed directly beside a variable represents multiplication, so $16 \\times w$ is written neatly as $16w$."},{"text":"$$16 + w$","correct":false,"explanation":"This changes multiplication into addition. Algebra omits the multiplication sign between a number and a variable, so $16 \\times w$ is written as $16w$."},{"text":"$$\\frac{16}{w}$","correct":false,"explanation":"This represents 16 divided by $w$, not 16 multiplied by $w$. The required algebraic expression is $16w$."},{"text":"$$\\frac{w}{16}$","correct":false,"explanation":"This represents $w$ divided by 16, reversing the required operation. Multiplication of 16 and $w$ is written as $16w$."}]},{"id":"07c0d5cc-9c57-2eb6-e14a-38970af6329e","cardType":"basic","points":1,"front":"Write an expression for the age of a cousin who is twice as old as Noah (age $a$).","back":"$$2a$","mcqOptions":[{"text":"$$2a$","correct":true,"explanation":"Twice Noah’s age means multiplying his age $a$ by 2, giving the cousin’s age as $2a$."},{"text":"$$a + 2$","correct":false,"explanation":"Adding 2 would make the cousin two years older than Noah, not twice as old. Twice the age $a$ is $2a$."},{"text":"$$\\frac{a}{2}$","correct":false,"explanation":"Dividing $a$ by 2 gives half Noah’s age, which reverses the relationship. A cousin twice as old has age $2a$."},{"text":"$$a^2$","correct":false,"explanation":"Squaring $a$ means multiplying the age by itself, not doubling it. Twice Noah’s age is found by calculating $2 \\times a = 2a$."}]},{"id":"80c18326-d49b-6e49-ac80-538a0f0cdf4d","cardType":"cloze","points":null,"front":"In algebra, the word per (e.g. pounds per hour) usually indicates the operation of [ ].","back":"In algebra, the word per (e.g. pounds per hour) usually indicates the operation of multiplication.","mcqOptions":[{"text":"multiplication","correct":true,"explanation":"When a per-unit amount is used to calculate a total, the rate is multiplied by the number of units, so the intended operation here is multiplication."},{"text":"addition","correct":false,"explanation":"Addition combines separate quantities rather than applying a per-unit rate. To calculate a total from a rate and a number of units, the intended operation is multiplication."},{"text":"subtraction","correct":false,"explanation":"Subtraction finds a difference and does not apply a rate to a quantity. The intended operation for using a per-unit amount to find a total is multiplication."},{"text":"exponentiation","correct":false,"explanation":"Exponentiation repeatedly multiplies a quantity by itself and is not used for an ordinary per-unit calculation. The intended operation here is multiplication."}]},{"id":"31aa523d-8bdb-ddfa-1db9-f756498ef597","cardType":"basic","points":2,"front":"If total money taken is $R$ and each ticket costs £5, how is the number of tickets calculated?","back":"Divide the total money by the cost of one ticket: $\\frac{R}{5}$.","mcqOptions":[{"text":"Divide the total money by the cost of one ticket: $\\frac{R}{5}$.","correct":true,"explanation":"The number sold equals total revenue divided by the price of each ticket. Since each ticket costs £5, the number is $R \\div 5 = \\frac{R}{5}$."},{"text":"Multiply the total money by the cost of one ticket: $5R$.","correct":false,"explanation":"Multiplying revenue by £5 does not recover the number of tickets. The number sold is total revenue divided by the price per ticket, giving $\\frac{R}{5}$."},{"text":"Add the cost of one ticket to the total money: $R + 5$.","correct":false,"explanation":"Adding £5 changes the revenue rather than finding how many £5 tickets produced it. Divide the total $R$ by £5 to obtain $\\frac{R}{5}$."},{"text":"Subtract the cost of one ticket from the total money: $R - 5$.","correct":false,"explanation":"Subtracting one ticket price only removes £5 from the revenue. Finding the number of equal £5 groups requires division, so the answer is $\\frac{R}{5}$."}]},{"id":"bc1356cc-3e80-c96b-58c1-fb8cd3737cf3","cardType":"basic","points":1,"front":"What is a term in an expression?","back":"A single part of the expression separated by plus or minus signs.","mcqOptions":[{"text":"A single part of the expression separated by plus or minus signs.","correct":true,"explanation":"Terms are the individual parts joined by addition or subtraction. For example, $3x$ and $2y$ are the two terms in $3x + 2y$."},{"text":"A single letter of the expression separated by multiplication or division signs.","correct":false,"explanation":"A term can contain numbers, letters and multiplication, so it is not necessarily a single letter. Terms are separated by plus or minus signs."},{"text":"A single number of the expression separated by equals or inequality signs.","correct":false,"explanation":"Terms can include variables as well as numbers, and equals signs separate sides of equations rather than terms. Terms are separated by plus or minus signs."},{"text":"A complete expression made from numbers or letters only.","correct":false,"explanation":"A term is one part of an expression, not necessarily the entire expression. Its boundary is identified by the plus or minus signs separating it from other terms."}]},{"id":"d0183493-45ab-e3ff-cee4-384a4259b23e","cardType":"basic","points":1,"front":"Identify the terms in the expression $3x + 2y$.","back":"

$3x$
$2y$

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

$3x$
$2y$

","correct":true,"explanation":"Terms are separated by plus or minus signs. The plus sign divides this expression into the two complete terms $3x$ and $2y$."},{"text":"

","correct":false,"explanation":"These are only the numerical coefficients, not the complete terms. Each coefficient remains attached to its variable, so the terms are $3x$ and $2y$."},{"text":"

","correct":false,"explanation":"These are only the variables, with their coefficients omitted. The full parts separated by the plus sign are $3x$ and $2y$."},{"text":"

$3x + 2$
$y$

","correct":false,"explanation":"A plus sign separates terms, so it cannot be included inside the first term here. The expression divides into $3x$ and $2y$."}]},{"id":"0fbce2f3-0cff-5d18-1643-768bba6a207b","cardType":"basic","points":2,"front":"A juice costs $j$ and a chocolate costs $h$. Write an expression for the total cost of 4 juices and 3 chocolates.","back":"$$4j + 3h$","mcqOptions":[{"text":"$$4j + 3h$","correct":true,"explanation":"Four juices cost $4j$ and three chocolates cost $3h$. Adding these two costs gives the total expression $4j + 3h$."},{"text":"$$3j + 4h$","correct":false,"explanation":"This swaps the quantities of juices and chocolates. Four items at cost $j$ and three at cost $h$ give $4j + 3h$."},{"text":"$$4j \\times 3h$","correct":false,"explanation":"Multiplying the two group costs does not produce the total shopping cost. The costs must be added, giving $4j + 3h$."},{"text":"$$j + h + 7$","correct":false,"explanation":"The quantities 4 and 3 must multiply the respective item prices, not be added as seven pounds. The correct total is $4j + 3h$."}]},{"id":"aab0a35c-dd23-4b00-8421-e58dbe7806a5","cardType":"basic","points":2,"front":"A shop has $s$ small packs (4 pens each) and $b$ big packs (10 pens each). Write an expression for the total number of pens.","back":"$$4s + 10b$","mcqOptions":[{"text":"$$4s + 10b$","correct":true,"explanation":"The small packs contain $4s$ pens altogether and the big packs contain $10b$ pens. Adding both groups gives $4s + 10b$."},{"text":"$$10s + 4b$","correct":false,"explanation":"This assigns the pack sizes to the wrong variables. Small packs contain 4 pens and big packs contain 10, so the total is $4s + 10b$."},{"text":"$$4s \\times 10b$","correct":false,"explanation":"The numbers of pens from the two pack types should be added, not multiplied together. Their combined total is $4s + 10b$."},{"text":"$$14sb$","correct":false,"explanation":"Adding 4 and 10 and multiplying both variables incorrectly combines unlike terms. Count each pack type separately, then add them to obtain $4s + 10b$."}]},{"id":"e6698d45-9b0e-2637-b2de-11ff606cedb2","cardType":"cloze","points":null,"front":"A [ ] is an equation that connects variables and includes an equals sign.","back":"A formula is an equation that connects variables and includes an equals sign.","mcqOptions":[{"text":"formula","correct":true,"explanation":"A formula uses an equals sign to show a mathematical relationship between variables, such as the relationship between distance, speed and time."},{"text":"expression","correct":false,"explanation":"An expression contains numbers, variables and operations but does not include an equals sign. The correct term is formula because it states an equality relating variables."},{"text":"inequality","correct":false,"explanation":"An inequality compares quantities using symbols such as $<$ or $>$, rather than stating an equality. A formula uses an equals sign to connect variables."},{"text":"coefficient","correct":false,"explanation":"A coefficient is a number multiplying a variable, such as $3$ in $3x$. The equation connecting variables is called a formula."}]},{"id":"e90a394c-b11e-10cd-a09c-42a04822da45","cardType":"basic","points":2,"front":"Write a formula for total cost $C$ if muffins are 80p and cookies are 50p, using variables $m$ and $k$.","back":"$$C = 80m + 50k$","mcqOptions":[{"text":"$$C = 80m + 50k$","correct":true,"explanation":"Each of the $m$ muffins costs 80p, giving $80m$, and each of the $k$ cookies costs 50p, giving $50k$. Their sum is the total cost."},{"text":"$$C = 50m + 80k$","correct":false,"explanation":"This swaps the two prices, charging 50p per muffin and 80p per cookie. Matching each price to its item gives $C = 80m + 50k$."},{"text":"$$C = 130m + 130k$","correct":false,"explanation":"This adds the prices first and then incorrectly charges 130p for every item. The separate item costs must remain separate, giving $C = 80m + 50k$."},{"text":"$$C = 80 + m + 50 + k$","correct":false,"explanation":"This adds each price to the number bought instead of multiplying them. Cost equals price times quantity, so the formula is $C = 80m + 50k$."}]},{"id":"b890b6b5-e99a-6856-0127-ec0fe810ed89","cardType":"cloze","points":null,"front":"Terms that have the same variable part (e.g. $n$ and $3n$) are known as [ ].","back":"Terms that have the same variable part (e.g. $n$ and $3n$) are known as like terms.","mcqOptions":[{"text":"like terms","correct":true,"explanation":"Like terms have exactly the same variable part, including matching powers. Their numerical coefficients may differ, so $n$ and $3n$ are like terms."},{"text":"unlike terms","correct":false,"explanation":"Unlike terms have different variable parts, such as $n$ and $n^2$. Since $n$ and $3n$ share the same variable part, they are like terms."},{"text":"equivalent terms","correct":false,"explanation":"Equivalent expressions have the same value, but $n$ and $3n$ are not generally equal. Terms sharing the same variable part are called like terms."},{"text":"constant terms","correct":false,"explanation":"Constant terms contain no variables, whereas $n$ and $3n$ both contain $n$. Because their variable parts match, they are called like terms."}]},{"id":"f0840bf0-a427-97f3-8ef9-8019cc920bbd","cardType":"basic","points":3,"front":"Ben is $n$. Cara is 9 years older ($n+9$). Dan is 4 years younger ($n-4$). Write a simplified expression for their total age.","back":"$$3n + 5$","mcqOptions":[{"text":"$$3n + 5$","correct":true,"explanation":"Adding the ages gives $n+(n+9)+(n-4)$. The three $n$ terms make $3n$, while the constants give $9-4=5$, so the total is $3n+5$."},{"text":"$$3n + 13$","correct":false,"explanation":"This treats Dan’s 4-year difference as positive instead of negative. The constants combine as $9-4=5$, so the simplified total is $3n+5$."},{"text":"$$n + 5$","correct":false,"explanation":"This combines the constants correctly but fails to add all three $n$ terms. Since each person’s age contains one $n$, the total is $3n+5$."},{"text":"$$3n - 5$","correct":false,"explanation":"This reverses the sign of the constant total. Cara adds 9 years and Dan subtracts 4 years, so the net change is $+5$ and the answer is $3n+5$."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Unit 1"},"heading":"Writing an Expression","title":"Writing an Expression Flashcards","topbar":{"backHref":"/gcse/maths/wjec/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"494871bd-4e80-27d1-509d-e3a9775285e8","walled":"$L39"}],"$L3a","$L3b"]