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fixed and unchanging value.","correct":false,"explanation":"A fixed, unchanging number is a constant, not a variable. A variable is a letter representing an unknown or changing number."},{"text":"A number placed before a letter to show multiplication.","correct":false,"explanation":"The number multiplying a variable is its coefficient. The variable itself is the letter that represents an unknown or changing number."},{"text":"A symbol that shows an algebraic operation between numbers.","correct":false,"explanation":"Symbols such as $+$ and $-$ are operators, not variables. 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The described combination without an equals sign is an expression."},{"text":"inequality","correct":false,"explanation":"An inequality compares expressions using a sign such as $<$ or $>$. A combination of numbers, variables and operations alone is an expression."}]},{"id":"44b184ba-bff3-4f4c-96a8-ebd6b0f2c0a2","cardType":"basic","points":2,"front":"What is the key difference between an expression and a formula?","back":"A formula contains an equals sign ($=$) to link variables, whereas an expression does not.","mcqOptions":[{"text":"A formula contains an equals sign ($=$) to link variables, whereas an expression does not.","correct":true,"explanation":"A formula states a relationship between variables using an equals sign, while an expression is only a combination of terms and operations."},{"text":"An expression contains an equals sign ($=$) to link variables, whereas a formula does not.","correct":false,"explanation":"This reverses the definitions. 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Their distinguishing feature is an equals sign linking variables, which an expression does not have."}]},{"id":"b4a4f77f-6b83-4542-b2cc-95771c10addd","cardType":"cloze","points":null,"front":"A [ ] is the number that multiplies a variable.","back":"A coefficient is the number that multiplies a variable.","mcqOptions":[{"text":"coefficient","correct":true,"explanation":"A coefficient is the numerical factor multiplying a variable, such as $7$ in the term $7x$."},{"text":"constant","correct":false,"explanation":"A constant is a fixed value that appears independently of a variable. The number multiplying a variable is called its coefficient."},{"text":"exponent","correct":false,"explanation":"An exponent shows the power to which a variable or number is raised. The number that multiplies a variable is its coefficient."},{"text":"variable","correct":false,"explanation":"A variable is the letter representing an unknown or changing value. 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The product of $5$ and $x$ is written as $5x$."}]},{"id":"84a98bf4-ff78-433f-b808-d9e313a80353","cardType":"basic","points":1,"front":"How is '4 fewer than $m$' written as an algebraic expression?","back":"$$m - 4$","mcqOptions":[{"text":"$$m - 4$","correct":true,"explanation":"The phrase “4 fewer than $m$” means start with $m$ and reduce it by $4$, giving $m-4$."},{"text":"$$4 - m$","correct":false,"explanation":"This reverses the order of subtraction and means “$m$ fewer than 4”. For “4 fewer than $m$”, start with $m$ and subtract $4$."},{"text":"$$m + 4$","correct":false,"explanation":"Adding $4$ gives “4 more than $m$”, not “4 fewer than $m$”. Fewer indicates subtraction, so the expression is $m-4$."},{"text":"$$4m$","correct":false,"explanation":"Placing $4$ beside $m$ means multiplication, giving “four times $m$”. The word “fewer” requires subtraction, so the expression is $m-4$."}]},{"id":"b6473808-4d4d-4c7d-a91b-87f5911f2eda","cardType":"basic","points":2,"front":"Why is '4 fewer than $m$' written as $m-4$ and not $4-m$?","back":"Because 'fewer than' means starting with $m$ and subtracting 4 from it.","mcqOptions":[{"text":"Because 'fewer than' means starting with $m$ and subtracting 4 from it.","correct":true,"explanation":"The quantity following “than” is the starting value. Therefore, “4 fewer than $m$” means begin with $m$ and subtract $4$."},{"text":"Because 'fewer than' means starting with 4 and subtracting $m$ from it.","correct":false,"explanation":"This reverses the order and produces $4-m$, meaning “$m$ fewer than 4”. The correct interpretation starts with $m$ and subtracts $4$."},{"text":"Because 'fewer than' means starting with $m$ and adding 4 to it.","correct":false,"explanation":"Adding gives “4 more than $m$”, not “4 fewer than $m$”. The word “fewer” signals subtraction, producing $m-4$."},{"text":"Because subtraction is commutative, so $m-4$ and $4-m$ are equivalent.","correct":false,"explanation":"Subtraction is not commutative, so changing the order generally changes the value. “4 fewer than $m$” specifically means $m-4$."}]},{"id":"271eae7d-b0dd-4cdf-a8f9-15bd63c05846","cardType":"basic","points":1,"front":"Write an expression for a junior ticket price if it is half of the adult price ($x$).","back":"$$\\frac{x}{2}$","mcqOptions":[{"text":"$$\\frac{x}{2}$","correct":true,"explanation":"Half of a quantity is found by dividing it by 2, so half of the adult ticket price $x$ is $\\frac{x}{2}$."},{"text":"$$2x$","correct":false,"explanation":"Multiplying by 2 gives double the adult price, not half of it. Half of $x$ is found by dividing by 2, giving $\\frac{x}{2}$."},{"text":"$$x - 2$","correct":false,"explanation":"Subtracting 2 makes the junior ticket £2 cheaper rather than half-price. To find half of the adult price, divide $x$ by 2."},{"text":"$$\\frac{x}{4}$","correct":false,"explanation":"Dividing by 4 finds one quarter of the adult price. A junior ticket costing half the adult price is represented by $\\frac{x}{2}$."}]},{"id":"23e96ac3-6583-4041-8107-00fcb7d1c96d","cardType":"basic","points":1,"front":"A tutor earns $p$ pounds per hour. Write an expression for their total pay after 12 hours.","back":"$$12p$","mcqOptions":[{"text":"$$12p$","correct":true,"explanation":"Total pay equals the hourly rate multiplied by the number of hours. At $p$ pounds per hour for 12 hours, the pay is $12 \\times p = 12p$."},{"text":"$$p + 12$","correct":false,"explanation":"Adding the hours to the hourly rate mixes different quantities and does not calculate total pay. The rate must be multiplied by 12, giving $12p$."},{"text":"$$\\frac{p}{12}$","correct":false,"explanation":"Dividing the hourly rate by 12 would produce a smaller rate, not the total earned. Multiply $p$ by the 12 hours to obtain $12p$."},{"text":"$$p^{12}$","correct":false,"explanation":"Raising $p$ to the power 12 means multiplying twelve copies of $p$ together. Total pay requires multiplying $p$ by 12, which gives $12p$."}]},{"id":"9b4db4a0-94d4-45f8-96bd-8284d5085951","cardType":"basic","points":2,"front":"Why is 12 hours at $p$ pounds per hour written as $12p$ instead of $p+12$?","back":"Because 'per hour' means you must multiply the number of hours by the rate.","mcqOptions":[{"text":"Because 'per hour' means you must multiply the number of hours by the rate.","correct":true,"explanation":"A rate of $p$ pounds for each hour is repeated 12 times, so total pay is calculated as $12 \\times p = 12p$."},{"text":"Because 'per hour' means you must add the number of hours to the rate.","correct":false,"explanation":"Adding 12 to $p$ incorrectly combines a number of hours with a rate in pounds per hour. Total pay is hours multiplied by the rate, giving $12p$."},{"text":"Because 'per hour' means you must divide the number of hours by the rate.","correct":false,"explanation":"Division is used to recover a rate or quantity from a known total, not to calculate total pay. Here, 12 hours must be multiplied by $p$."},{"text":"Because 'per hour' means you must subtract the number of hours from the rate.","correct":false,"explanation":"Subtraction would represent a decrease and mixes the number of hours with the hourly rate. Total earnings are found by multiplying 12 by $p$."}]},{"id":"8b7c395a-6c56-4309-bad7-dd4f7fb433f3","cardType":"basic","points":1,"front":"A juice costs $j$ pounds and a sandwich costs $s$ pounds. Write an expression for the total cost of 4 juices and 3 sandwiches.","back":"$$4j + 3s$","mcqOptions":[{"text":"$$4j + 3s$","correct":true,"explanation":"Four juices cost $4j$ and three sandwiches cost $3s$. Adding these separate costs gives the total expression $4j + 3s$."},{"text":"$$4j + 4s$","correct":false,"explanation":"This counts four sandwiches instead of three, so the sandwich cost is too large. Three sandwiches contribute $3s$, making the correct total $4j + 3s$."},{"text":"$$3j + 4s$","correct":false,"explanation":"The coefficients have been swapped, representing three juices and four sandwiches. The stated quantities are four juices and three sandwiches, so the total is $4j + 3s$."},{"text":"$$12js$","correct":false,"explanation":"Multiplying the quantities and prices together does not combine the costs of two different item types. Calculate each cost separately and add them to get $4j + 3s$."}]},{"id":"48d627f9-1352-4520-9463-7406171fec44","cardType":"cloze","points":null,"front":"To write an expression for a total containing two different types of items, you should build the expression in [ ] first, then [ ] them.","back":"To write an expression for a total containing two different types of items, you should build the expression in individual chunks first, then add them.","mcqOptions":[{"text":"To write an expression for a total containing two different types of items, you should build the expression in individual chunks first, then add them.","correct":true,"explanation":"Each item type has its own quantity and price, so its cost should be formed separately. Because the question asks for a total, those individual costs are then added."},{"text":"To write an expression for a total containing two different types of items, you should build the expression in separate equations first, then add them.","correct":false,"explanation":"An expression does not require separate equations, because equations contain equals signs. Build one cost term for each item type as individual chunks, then add those terms."},{"text":"To write an expression for a total containing two different types of items, you should build the expression in individual chunks first, then multiply them.","correct":false,"explanation":"Multiplying the chunks combines different item costs as factors rather than finding their total. After forming each item type's cost separately, add the individual chunks together."},{"text":"To write an expression for a total containing two different types of items, you should build the expression in matching factors first, then subtract them.","correct":false,"explanation":"Different item types do not need matching factors, and subtraction finds a difference rather than a total. Form individual cost chunks and add them together."}]},{"id":"8f911984-f16c-4103-a036-8232f8808d70","cardType":"basic","points":1,"front":"Concert tickets cost £4 each. If the total money collected is $y$ pounds, write an expression for the number of tickets sold.","back":"$$\\frac{y}{4}$","mcqOptions":[{"text":"$$\\frac{y}{4}$","correct":true,"explanation":"The total money equals the number of tickets multiplied by £4. Dividing the total $y$ by the price per ticket gives $\\frac{y}{4}$ tickets."},{"text":"$$4y$","correct":false,"explanation":"Multiplying the total money by £4 makes the result larger and does not recover the number sold. Divide $y$ by the £4 ticket price to get $\\frac{y}{4}$."},{"text":"$$y - 4$","correct":false,"explanation":"Subtracting £4 removes the price of one ticket from the total rather than finding how many tickets were sold. The correct operation is $y \\div 4$."},{"text":"$$\\frac{y}{2}$","correct":false,"explanation":"Dividing by 2 incorrectly treats each ticket as costing £2. Since every ticket costs £4, the number sold is the total divided by 4, or $\\frac{y}{4}$."}]},{"id":"5fbaed22-fb3e-4ed4-a066-7790bbe66997","cardType":"basic","points":1,"front":"Lina is $n$ years old. Her brother is 6 years older than Lina. Write an expression for her brother's age.","back":"$$n + 6$","mcqOptions":[{"text":"$$n + 6$","correct":true,"explanation":"Being 6 years older means the brother's age is 6 more than Lina's age. Adding 6 to $n$ gives $n + 6$."},{"text":"$$n - 6$","correct":false,"explanation":"Subtracting 6 would make the brother 6 years younger than Lina. Since he is older, 6 must be added to $n$, giving $n + 6$."},{"text":"$$6n$","correct":false,"explanation":"Multiplying by 6 would mean the brother is six times Lina's age, not 6 years older. A fixed age difference is represented by $n + 6$."},{"text":"$$\\frac{n}{6}$","correct":false,"explanation":"Dividing by 6 makes the brother a fraction of Lina's age and does not represent a six-year difference. Six years older is written as $n + 6$."}]},{"id":"362c7dde-e341-4f1a-94b9-08c5b97dee76","cardType":"cloze","points":null,"front":"In algebra, [ ] have the same variable part and can be collected together.","back":"In algebra, like terms have the same variable part and can be collected together.","mcqOptions":[{"text":"like terms","correct":true,"explanation":"Like terms have identical variable parts, including the same variables raised to the same powers. Their numerical coefficients can therefore be added or subtracted."},{"text":"unlike terms","correct":false,"explanation":"Unlike terms have different variable parts, so they cannot be collected directly. Terms sharing the same variables and powers are called like terms."},{"text":"constant terms","correct":false,"explanation":"Constant terms contain no variables, although constants can be collected with other constants. The general name for terms with the same variable part is like terms."},{"text":"algebraic factors","correct":false,"explanation":"Factors are quantities multiplied together within a term, not terms grouped by matching variable parts. Terms that can be collected together are called like terms."}]},{"id":"1477c10e-9f42-4b60-bdd2-8b6b6ef57b9e","cardType":"basic","points":2,"front":"Simplify the age total expression $n + (n + 6) + (n - 3)$ by collecting like terms.","back":"$$3n + 3$","mcqOptions":[{"text":"$$3n + 3$","correct":true,"explanation":"The three $n$ terms combine to give $3n$, while the constants combine as $6 - 3 = 3$. Therefore the simplified expression is $3n + 3$."},{"text":"$$3n + 9$","correct":false,"explanation":"This comes from treating the subtraction of 3 as addition. The constants must combine as $6 - 3 = 3$, while the variable terms give $3n$, so the answer is $3n + 3$."},{"text":"$$2n + 3$","correct":false,"explanation":"This misses one of the three $n$ terms in the original expression. All three combine to make $3n$, and the constants give $6 - 3 = 3$, so the answer is $3n + 3$."},{"text":"$$3n - 3$","correct":false,"explanation":"This keeps only the negative constant and overlooks the positive 6. The constants combine to give $6 - 3 = 3$, so after collecting the three $n$ terms the answer is $3n + 3$."}]},{"id":"10cdf00f-a0c5-4e36-8bde-519db9fc15b1","cardType":"basic","points":1,"front":"A shop has $s$ small boxes and $l$ large boxes. Write an expression for the total number of boxes.","back":"$$s + l$","mcqOptions":[{"text":"$$s + l$","correct":true,"explanation":"There are $s$ small boxes and $l$ large boxes, so adding the two quantities gives the total number of boxes: $s + l$."},{"text":"$$sl$","correct":false,"explanation":"Multiplication would count combinations or form a product, not combine two groups of boxes. The total is found by adding the small and large box counts, giving $s + l$."},{"text":"$$2s + l$","correct":false,"explanation":"This incorrectly counts every small box twice. Each small and large box is counted once, so the two quantities should simply be added to give $s + l$."},{"text":"$$s + 2l$","correct":false,"explanation":"This incorrectly counts every large box twice. Each box contributes one to the total, so adding the two given numbers produces the expression $s + l$."}]},{"id":"6c6cf27b-54a3-4c35-82c3-7035aa700493","cardType":"basic","points":1,"front":"A shop has $s$ small boxes containing 6 pencils each, and $l$ large boxes containing 10 pencils each. Write an expression for the total number of pencils.","back":"$$6s + 10l$","mcqOptions":[{"text":"$$6s + 10l$","correct":true,"explanation":"The $s$ small boxes contain $6s$ pencils altogether, and the $l$ large boxes contain $10l$ pencils. Adding these amounts gives $6s + 10l$."},{"text":"$$10s + 6l$","correct":false,"explanation":"This swaps the numbers of pencils in the two box sizes. Small boxes contribute $6s$ pencils and large boxes contribute $10l$ pencils, so the correct total is $6s + 10l$."},{"text":"$$6s + l$","correct":false,"explanation":"This counts each large box as containing only one pencil. Since every large box contains 10 pencils, its contribution is $10l$, making the total $6s + 10l$."},{"text":"$$s + 10l$","correct":false,"explanation":"This counts each small box as containing only one pencil. Since every small box contains 6 pencils, its contribution is $6s$, making the total $6s + 10l$."}]},{"id":"dbda2daf-bc6a-4c3f-a43b-9c536ccb4323","cardType":"basic","points":2,"front":"Muffins cost 40p each and juice cartons cost 65p each. Write a formula for the total cost, $C$ pence, of $m$ muffins and $j$ juice cartons.","back":"$$C = 40m + 65j$","mcqOptions":[{"text":"$$C = 40m + 65j$","correct":true,"explanation":"The muffins cost $40m$ pence altogether and the juice cartons cost $65j$ pence. Adding these costs gives the formula $C = 40m + 65j$."},{"text":"$$C = 65m + 40j$","correct":false,"explanation":"This assigns the prices to the wrong products. Each muffin costs 40p and each juice carton costs 65p, so the correct formula is $C = 40m + 65j$."},{"text":"$$C = 0.40m + 0.65j$","correct":false,"explanation":"These coefficients express the prices in pounds, but $C$ is defined in pence. Using 40 and 65 as the pence prices gives $C = 40m + 65j$."},{"text":"$$C = 105(m + j)$","correct":false,"explanation":"This adds the two different prices and charges 105p for every item. Muffins and juice cartons must be costed separately, giving $C = 40m + 65j$."}]}]}],"examCountdown":null,"heading":"Writing an Expression","title":"Writing an Expression Flashcards","topbar":{"backHref":"/igcse/maths/cie/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"6b994104-a005-459f-841e-936de36ba5ba","walled":"$L39"}],"$L3a","$L3b"]