Student-produced responses: fractions, decimals and negatives
About a quarter of the maths section has no choices at all — you type the answer into a box. The maths is the same; the way the box reads what you type is not.
Which entry would be scored as correct?
A student-produced response question has the answer 7/4. Which of the following entries would be scored as correct?
7/4 = 1.75 exactly, and four characters fit the box comfortably, so 1.75 scores. Typing 7/4 itself would also score — a fraction and its decimal are equally acceptable. A is a mixed number, and the box has no way to show the gap: “1 3/4” is read as the single fraction 13/4, which is 3.25. This is the most expensive habit a student brings to the test. B is 1.7, a different number; rounding is allowed only when the exact decimal will not fit, and 1.75 fits. D is the reciprocal, 4/7 ≈ 0.571.
1
About a quarter of the maths section is typed rather than clicked.
Roughly 11 of the 44 maths questions are student-produced responses. They appear in both modules, grouped at the end of each one, and they are worth exactly the same one point each.
There are no choices to work backwards from, no answer to test, and nothing to eliminate. Whatever number you produce is the number that gets scored — which is why the entry rules below cost more marks than they have any right to.
no choicesno back-solvingno partial creditno penalty for a wrong entryan answer preview under the box
The screen shows a preview of what it thinks you typed, directly under the box. Reading that preview takes one second and catches almost every entry error in this lesson. Nobody reads it.
A note about this course
Every question in the NEXUS SAT course is multiple choice, so you will never actually type an answer here. The rules below are for the real exam, and the questions in this lesson ask you which entry would be scored correct — which turns out to be a sharper test of the rules than typing them yourself.
2
The box holds about five characters, and that single fact decides most of the rules.
Five characters for a positive answer, six for a negative one — the minus sign gets a slot of its own.
The answer
What you type
Characters
3.5
3.5
3
7/4
7/4 or 1.75
3 or 4
12,500
12500
5
2/3
.6666
5
−0.625
−.625
5 of the 6 allowed
Notice what the third row does. A comma is not a character the box accepts, so twelve thousand five hundred is typed as 12500 — and the digits alone happen to fill the box exactly.
If your answer does not fit, your answer is wrong
The test is written so that every correct answer fits. So when you finish a question and find yourself holding 1,248.75 or 17/23, that is not a formatting problem — it is a signal to go back and re-read the stem, because the SAT did not intend a number that shape. Treat the box as a free check on your arithmetic.
3
A fraction or a decimal, whichever you like — but never a mixed number.
The box has no way to show the gap between a whole number and a fraction, so it closes it. Everything you type becomes one run of characters.
Entry for the answer 7/4
Read as
Scored
7/4
7/4
correct
1.75
1.75
correct
14/8
1.75
correct
1 3/4
13/4
wrong
1.7
1.7
wrong
You never have to simplify. 14/8 scores exactly as well as 7/4, so the moment you have a fraction that is right, type it and move on — cancelling it down is time spent for nothing.
The simplest rule to carry into the exam: if your answer is a fraction, type the fraction. It is the one form that can never be rounded wrongly, never be truncated too early and never be mistaken for a mixed number, because there is no whole part sitting in front of it.
4
A decimal that runs forever must fill the box — truncated or rounded, but full.
2/3 = 0.6666666… and there is no version of that which fits five characters exactly. The rule is that you give as many digits as the box will hold, and you may either cut the digits off or round the last one.
2/3 = 0.666666…
no exact decimal exists at five characters
cut it off: .6666
five characters, all of them used
or round it: .6667
also five, also accepted
0.666 and 0.667 also score
the leading zero uses a slot, so a digit gives way
.66 does not score
two slots left empty, so it is not accurate enough
The difference between .6666 and .66 is not a rounding preference. .66 is a less accurate number, and the box was still willing to hold two more digits — so it is marked wrong.
Exact value
Type either
Never
2/3
.6666 or .6667
.66, .67, 0.7
1/7
.1428 or .1429
.14, .143
5/12
.4166 or .4167
.41, .42
any of them
the fraction itself
—
Which is the argument for step 3's rule all over again. 2/3, 1/7 and 5/12 are three characters, four characters and four characters. Typing the fraction removes the whole problem.
5
Negatives get a slot; units, commas and symbols get nothing.
The box accepts digits, a decimal point, a slash and a minus sign. That is the entire alphabet.
The answer is
Type
Do not type
2,500 dollars
2500
2,500 · $2500 · 2500 dollars
12 inches
12
12 in · 12in · 12”
an increase of 45 percent
45
45% · 45 percent
−8
−8
8− · (8) · neg 8
−3/8
−3/8 or −.375
−3/−8 · 3/−8
The stem always names the unit for you — “what is the cost, in dollars” or “what is the length, in inches”. That sentence exists precisely so the box can hold a bare number. Read it, then type digits only.
4(x + 5) = x − 4
a typical one-variable stem
4x + 20 = x − 4
expand the bracket
3x = −24, so x = −8
and the minus sign must be typed
The sign is the single most dropped character
A negative answer is a correct answer typed as its opposite. Nothing about the screen warns you, the preview shows a perfectly reasonable 8, and the point is gone. When your working ends in a negative, say the word “minus” to yourself as you type it — the same discipline as checking which coordinate the calculator handed you.
6
When several values satisfy the question, any one of them scores.
The box holds one number. If the maths produces two or more, pick whichever is easiest to type and stop.
|2x − 7| = 5
“what is one possible value of x?”
2x − 7 = 5 → x = 6
the first branch
2x − 7 = −5 → x = 1
the second branch
type 6 — or type 1
either one scores; typing both scores nothing
The same applies to a range. If 12 < 4x < 20 then 3 < x < 5, and 3.5, 4 and 4.9 all score. Choose the one that is quickest to type and least likely to be mistyped — here that is 4.
“one possible value” → any one“a solution” → either solutiontwo answers typed → no scorea comma is not a separator
Typing both is the reflex to unlearn
Having found x = 6 and x = 1, it feels generous to offer both — and “6, 1” contains a comma, which the box does not accept at all. Even if it did, the entry would not match either value. One box, one number, and the question already told you one is enough.
✓
Check: read the preview before you move on.
the mixed number1 3/4 → 13/4type 7/4 or 1.75 ✓
the long decimal2/3 → .6666fill the box, or type 2/3 ✓
the negative−8 uses 2 of 6 slotsthe sign is a character ✓
the units2,500 dollars → 2500digits only ✓
two solutionsx = 6 or x = 1one of them, not both ✓
Remember the flow
Prefer the fraction · Fill the box · Keep the minus sign
If the answer will not fit, the mistake is upstream.
Now you try
Practice problem
Which entry would be scored as correct?
A student-produced response question reads: “2x² − 11x + 12 = 0. What is one possible value of x?” Which of the following entries would be scored as correct?
Factoring gives (2x − 3)(x − 4) = 0, so x = 3/2 or x = 4. “One possible value” means either one scores on its own, and 3/2 is one of them — check it: 2(1.5)² − 11(1.5) + 12 = 4.5 − 16.5 + 12 = 0. Typing 1.5 would score equally well. A offers both values, but the box takes no commas and matches no single number, so an entry that contains the right answer twice over scores nothing. C has the sign wrong: the roots of this quadratic are both positive, and 4 is a root while −4 is not. D is 5.5, which is 11/2 — the sum of the two roots, read straight off the middle coefficient instead of solved for.
Hint: solve the equation first and hold both roots in mind, then ask the entry question separately — is this string of characters one of those two numbers, written in a form the box accepts?
