Practice
Variables and Expressions Practice
Fifty original questions covering the complete variables and expressions lesson, with explanations and SAT-focused strategy.
- Answered
- 0 / 50
- Correct
- 0
- Incorrect
- 0
- Accuracy
- 0%
Question 1
Explanation
The skill is translating addition language. A sum means addition, so the expression is \(x+9\). Do not treat ‘sum’ as multiplication.
Question 2
Explanation
‘More than’ adds the stated amount to the reference quantity: \(n+6\). The order does not change the sum, but it matters for subtraction phrases.
Question 3
Explanation
The difference of the first quantity and the second is \(p-4\). Reversing the order gives a different value.
Question 4
Explanation
‘Five less than \(t\)’ starts with \(t\) and removes \(5\), giving \(t-5\). This is the classic word-order trap.
Question 5
Explanation
The word ‘minus’ keeps the spoken order: start with \(8\), then subtract \(y\). Thus \(8-y\).
Question 6
Explanation
A product is a multiplication result. Algebra writes \(7\cdot m\) compactly as \(7m\).
Question 7
Explanation
‘Of’ signals multiplication: \(\frac13\cdot q=\frac q3\). The correct expression is \(q/3\).
Question 8
Explanation
The quotient of the first quantity and the second is \(r\div12=r/12\). Division order cannot be reversed.
Question 9
Explanation
The total combines the variable charge and fixed fee: \(d+4\). Multiplication would incorrectly make the fee depend on \(d\).
Question 10
Explanation
Equal groups use multiplication: \(k\) rows times \(6\) markers per row gives \(6k\).
Question 11
Explanation
‘Decreased by’ subtracts from the original: \(L-2.5\). Reversing the order changes the meaning.
Question 12
Explanation
The entire sum \(b+3\) is the divisor, so grouping is required: \(\frac{a}{b+3}\). Without parentheses, only \(b\) divides \(a\).
Question 13
Explanation
First form the difference \(x-5\), then multiply the whole difference by \(2\): \(2(x-5)\).
Question 14
Explanation
The sum is one grouped quantity, so squaring it gives \((u+v)^2\). Squaring each term separately is not equivalent.
Question 15
Explanation
A constant term has no variable. In \(14-3z\), \(14\) is the constant; \(-3\) is the coefficient of \(z\).
Question 16
Explanation
Substitute \(5\): \(3(5)+2=15+2=17\). A common error is to add \(3+5\) instead of multiplying.
Question 17
Explanation
Substitute the negative value carefully: \(4-(-3)=4+3=7\). Subtracting a negative becomes addition.
Question 18
Explanation
Substitute both values: \(5(2)-7=10-7=3\). The correct answer is \(3\).
Question 19
Explanation
The constant does not change with mileage, so \(6\) is the fixed starting charge. The coefficient \(3.25\) is the per-mile rate.
Question 20
Explanation
The notebooks cost \(2.40n\); subtract the fixed coupon to get \(2.40n-5\). The coupon is not a number of notebooks.
Question 21
Explanation
The parentheses make \(x+2\) one quantity subtracted from \(7\): seven minus the sum of \(x\) and \(2\).
Question 22
Explanation
Perimeter is twice each dimension: \(2(x+3)+2x\). The product \(x(x+3)\) would be area.
Question 23
Explanation
The product \(48h\) is total production, and subtracting \(12\) removes twelve parts. It represents usable parts after 12 are discarded.
Question 24
Explanation
‘The quantity \(y\) increased by \(4\)’ is \(y+4\); three times that whole quantity is \(3(y+4)\).
Question 25
Explanation
The coefficient multiplying \(x\) is \(2\). The expression has two terms, its variable is \(x\), and its constant is \(9\).
Question 26
Explanation
‘Four fewer than twice \(n\)’ subtracts \(4\) from \(2n\), so \(2n-4\). The student reversed the subtraction order.
Question 27
Explanation
First divide the original quantity: \(w/5\). Then add \(2\) to each share, giving \(w/5+2\).
Question 28
Explanation
Distribution gives \(a(b+c)=ab+ac\). The expression \(ab+c\) fails to multiply \(c\) by \(a\).
Question 29
Explanation
Dividing liters by bottles gives liters per bottle. Unit analysis confirms both the operation and the order.
Question 30
Explanation
An average is the sum of all three values divided by the number of values: \((x+y+10)/3\). Parentheses keep the entire sum in the numerator.
Question 31
Explanation
After the rise, the temperature is \(T+8\). Doubling that new amount gives \(2(T+8)\). \(2T+8\) doubles only the original temperature.
Question 32
Explanation
Each box retains \(24-3=21\) pencils, so \(21b\). Subtracting only \(3\) would ignore the other boxes.
Question 33
Explanation
The first named quantity is the complete difference \(x-4\); divide it by \(3\): \((x-4)/3\).
Question 34
Explanation
Evaluate each candidate. \(5-3(-2)=5+6=11\); the others give \(-1,3,6\). Parentheses prevent a sign error.
Question 35
Explanation
Each guest adds \(18\) dollars. Two additional guests add \(2(18)=36\); the fixed \(75\) does not change.
Question 36
Explanation
To divide by the entire quantity \(6-2\), it must be grouped: \(x/(6-2)\). Otherwise the subtraction occurs after division.
Question 37
Explanation
The base cost is \(12n\); \(0.08(12n)\) is 8 percent of that base. Their sum is the price plus tax.
Question 38
Explanation
Add \(7\) to the entire expression: \((4x-1)+7=4x+6\). The difference between \(4x+6\) and \(4x-1\) is exactly \(7\).
Question 39
Explanation
Area of a square is side squared, so \((s-1)^2\). \(4(s-1)\) is perimeter, and \(s^2-1\) does not square the binomial.
Question 40
Explanation
Batch use is rate times batches: \(\frac34b\). Add the separate topping amount to get \(\frac{3b}{4}+\frac12\).
Question 41
Explanation
The inner difference is \(x-2\), it is multiplied by \(5\), then increased by \(1\). This exactly matches choice A.
Question 42
Explanation
Parentheses make the entire sum the numerator. Without them, division applies only to \(q\), so the new expression is \(p+(q/2)\).
Question 43
Explanation
Substitute: \(2(4-(-1))+3(-1)=2(5)-3=7\). The nested subtraction and negative coefficient both require care.
Question 44
Explanation
The increase is \(0.15f\), so the new total is \(f+0.15f=1.15f\). Choice B gives only the increase.
Question 45
Explanation
Draining one quarter leaves three quarters: \(v-\frac14v=\frac34v\). Then add \(6\), giving \(3v/4+6\).
Question 46
Explanation
The integers are \(n,n+1,n+2\). Their entire sum must be grouped before multiplying by one half: \((n+(n+1)+(n+2))/2\).
Question 47
Explanation
There is one first-month charge and \(m-1\) later charges, so total cost is \(25+r(m-1)\).
Question 48
Explanation
Distance cannot be negative, so it is the absolute difference \(|x-7|\). Either subtraction order inside absolute value gives the same distance.
Question 49
Explanation
Juxtaposition means multiplication: \(3(x+4)\) is three times the sum, not three more than it. ‘Three more’ would be \(x+4+3\).
Question 50
Explanation
Each of the \(k\) bundles contains the whole sum \(a+b\), producing \(k(a+b)\); add \(c\) loose objects.
Keyboard: use Tab to move, arrow keys to change answer choices, and Enter to check an answer.
Your practice summary
Use the results to decide what to review before your next attempt.
- Correct
- 0
- Incorrect
- 0
- Completed
- 50 / 50
Questions to review
No mistakes this time. Excellent work.
- Question 1Translate verbal expressionsEasy
- Question 2Addition languageEasy
- Question 3Subtraction languageEasy
- Question 4Word-order trapsEasy
- Question 5Subtraction languageEasy
- Question 6Multiplication languageEasy
- Question 7Fractional expressionsEasy
- Question 8Division languageEasy
- Question 9Model expressionsEasy
- Question 10Model multiplicationEasy
- Question 11Decimal expressionsEasy
- Question 12Grouping symbolsEasy
- Question 13Nested translationEasy
- Question 14Grouping symbolsEasy
- Question 15Identify constantsEasy
- Question 16Evaluate expressionsMedium
- Question 17Negative substitutionMedium
- Question 18Multiple substitutionMedium
- Question 19Interpret expressionsMedium
- Question 20Real-world modelingMedium
- Question 21Interpret groupingMedium
- Question 22Model geometryMedium
- Question 23Interpret expressionsMedium
- Question 24Nested translationMedium
- Question 25Expression vocabularyMedium
- Question 26Error analysisMedium
- Question 27Multi-step modelingMedium
- Question 28Equivalent expressionsMedium
- Question 29Unit analysisMedium
- Question 30Average expressionsMedium
- Question 31Sequential modelingMedium
- Question 32Repeated-group modelingMedium
- Question 33Complex quotient translationMedium
- Question 34Reverse evaluationMedium
- Question 35Interpret coefficientMedium
- Question 36Grouping and ambiguityMedium
- Question 37Percent expressionsMedium
- Question 38Compare expressionsMedium
- Question 39Model geometryMedium
- Question 40Fractional modelingMedium
- Question 41Reverse translationHard
- Question 42Grouping error analysisHard
- Question 43Multi-variable evaluationHard
- Question 44Percent modelingHard
- Question 45Multi-step modelingHard
- Question 46Consecutive integer modelingHard
- Question 47Piecewise verbal modelingHard
- Question 48Absolute-value expressionsHard
- Question 49Notation interpretationHard
- Question 50Complex groupingHard