December 2026 SAT Math Prediction: Rules, Steps and Formulas to Know

Our December 2026 SAT Math prediction is a ranking of skills. We built it from 4,159 questions in 22 Math question banks on our site. Study linear functions first, then linear equations, exponential functions, polynomials and systems of equations. Those five skills made up about 42% of the 759 Math questions in our fall 2026 banks.

This is a prediction. It is not a leak, and it is not a guarantee. Most of what appears on a test date will not be in any prediction bank, and results swing from date to date. This page updates our earlier November and December 2026 SAT Math page with two new things: the score of our November prediction, and a new model that we re-fit after every test date. You can browse every monthly bank in our SAT question bank hub. The full method is on our SAT predictions 2026 page.

What is the December 2026 SAT Math prediction?

It is a study order for the December SAT. Our model scores every question in our 22 Math banks, which run from March 2024 to November 2026. Then we rank the skills behind the questions it scores highest. It names skills, rules and formulas. It does not name questions.

• Skills first. Linear functions lead our fall 2026 banks at 14.9%. Linear equations follow at 8.3%, then exponential functions at 6.6%.
• A 200-question bank. The model ranked 1,978 candidates for December. We built the 200-question December 2026 Math prediction bank from the top of that ranking.
• A measured hit rate. In back-tests, 11.4% of a 200-question bank came back on an average 2026 test date. On the worst 2026 date it was 2.0%. On the best it was 25.0%.

When is the December SAT, and what is on the Math section?

The December SAT is on Saturday, December 5, 2026. The registration deadline is November 20, 2026. The late registration deadline is November 24, 2026. Both dates come from College Board's SAT dates and deadlines page and its December 5 test date page. Our December 2026 SAT date and deadline guide covers score release too.

The Math section has 44 questions in 70 minutes. It has two 35-minute modules. Each module has 20 operational questions and 2 pretest questions, per the College Board Math specifications. Your result on the first module decides whether the second module is harder or easier, per College Board's test structure page.

College Board's Math section overview lists four question categories:

• Algebra: 13 to 15 questions
• Advanced Math: 13 to 15 questions
• Problem-Solving and Data Analysis: 5 to 7 questions
• Geometry and Trigonometry: 5 to 7 questions

About 30% of the questions are set in a real-world context, per the same overview. For every topic inside each category, see our guide to what math is on the SAT.

How did our November SAT Math prediction do?

It caught too little. The November Math prediction bank used one rule: pick questions that had already repeated across test dates. It held 53 questions. After the November test date, we checked it against our November 2026 Math bank. 4 of the 53 came back as the same or a reworked question. That is 7.5%.

The test date itself repeated far more than that. 107 of the 170 questions in our November 2026 Math question bank repeated or reworked a question from an earlier bank on our site. That is 62.9%. So repeats were there to find, and one simple rule missed most of them. Our November 2026 SAT prediction is the page that used the old rule.

For December we replaced the rule with a model. We re-fit it after every test date. It scores each question on five things:

• how many test dates the question has appeared on
• how many times it appeared this year
• how long ago it appeared, and in which season
• how often its setup has come back
• how often its skill comes back

Each question gets two scores. One is the chance that the question returns. The other is the chance that its setup returns with a different question.

We then back-tested the model. For each earlier test date, we rebuilt the bank using only the banks that existed before that date. Across the 2026 test dates, an average of 11.4% of the 200 questions came back. For 14.0%, the setup came back. On November 2026, this model would have scored 12.5% on questions and 16.5% on setups. The old rule scored 7.5%.

The range runs from 2.0% on the worst 2026 date to 25.0% on the best. Treat the bank as extra practice on likely skills. Do not treat it as an answer key. The English side of this study is in our guides to December 2026 SAT vocabulary and December 2026 SAT reading question types.

Which SAT Math questions come back most often?

The SAT Math questions that come back most are the ones that have already appeared on several test dates. In our 2026 checks, a question seen on one earlier date came back 3.8% of the time. A question seen on five or more dates came back 28.3% of the time.

Each check is one earlier question tested against one 2026 test date, March through November. The same pattern shows inside a single year. A question already seen twice in the same year came back 10.3% of the time (23 of 223 checks). A question seen three or more times that year came back 31.0% of the time (13 of 42 checks). Those last two counts are small, so expect them to move.

Which item types have appeared on the most test dates?

An item type is a family of questions that our matching links as versions of one question. The table lists the 40 item types seen on the most test dates in our banks, grouped by skill. We name the skill only. We do not reproduce any question.

Algebra owns 23 of the 40. Advanced Math has 11. Problem-Solving and Data Analysis has 3, and Geometry and Trigonometry has 3. One systems of equations item type has shown up on 19 test dates in 56 versions. Our matching links exact copies, near copies and reworked versions. Learn the method. Do not memorize an answer.

What should you study first for SAT Math in December 2026?

Study the skills in the order of this table. It ranks skills by their share of our fall 2026 banks (August to November, 759 questions). The most common SAT Math questions in those banks test linear functions, linear equations and exponential functions. The last two columns show how often each skill's questions came back in 2026 and how many of its questions sit in the December prediction bank.

The ten largest shares in the table add up to 67.0%.

• December leans toward Advanced Math in our banks. Our two earlier December banks (2024 and 2025, 326 questions) were 40.2% Advanced Math. Fall 2026 was 33.7%. Exponential functions were 10.1% of those December banks and 6.6% of fall 2026. Two test dates is a small sample, so treat this as a lean.
• Small skills can repeat often. Percentages are 4.5% of fall 2026, but their questions came back 8.1% of the time in 2026. That is the highest rate in the table. Triangles came back 2.8% of the time.

Rules, steps and worked examples for the top SAT Math skills

Each section gives the rule, the steps and one worked example. Every example is our own invented problem. None comes from a question bank. The percent in each heading is the skill's share of our fall 2026 banks.

Eight practice questions sit inside the sections, in study-first order. We wrote them for this page, in the style of each question type. None is from a test, and none is from a question bank. Two of them are typed-answer questions.

1. Linear functions, lines and models (14.9%)

• Slope: \( m = \dfrac{y_2 - y_1}{x_2 - x_1} \)
• Slope-intercept form: \( y = mx + b \). In a word problem, \(b\) is the starting value and \(m\) is the change per unit.
• Standard form \( Ax + By = C \) has slope \( -\dfrac{A}{B} \).
• Parallel lines have equal slopes. Perpendicular slopes multiply to \(-1\).

1. Find two points, or find the rate and the starting value.
2. Compute the slope.
3. Plug in one point to find \(b\).
4. Answer what the question asks: a value, the slope or the meaning of a number.

Worked example. A bike shop charges a flat fee plus an hourly rate. A 2-hour rental costs 19 dollars. A 5-hour rental costs 34 dollars. The slope is \( \dfrac{34 - 19}{5 - 2} = 5 \). Then \( 19 = 5(2) + b \), so \( b = 9 \). The model is \( C = 5h + 9 \). The flat fee is 9 dollars and each hour costs 5 dollars. Check: \( 5(5) + 9 = 34 \).

In our data: 26 of the 200 prediction bank questions. Practice with the lines and linear relationships drill and the interpreting linear models drill.

2. Linear equations and solving (8.3%)

• Do the same operation to both sides. Distribute first, then combine like terms.
• For \( ax + b = cx + d \): one solution when \( a \ne c \). No solution when \( a = c \) and \( b \ne d \). Infinitely many solutions when \( a = c \) and \( b = d \).

1. Clear parentheses and fractions.
2. Move the variable terms to one side and the numbers to the other.
3. Divide by the coefficient.
4. Plug your answer back in to check.

Worked example. Solve \( 3(2x - 5) = 4x + 7 \). Distribute: \( 6x - 15 = 4x + 7 \). Subtract \(4x\) and add 15: \( 2x = 22 \), so \( x = 11 \). Check: the left side is \( 3(17) = 51 \) and the right side is \( 44 + 7 = 51 \).

In our data: 13 of the 200 prediction bank questions, and 8 of the 40 most recurring item types. Practice with the linear equations drill.

3. Exponential growth and functions (6.6%)

• General form: \( y = a \cdot b^{x} \). Here \(a\) is the starting value and \(b\) is the growth factor.
• Percent growth: \( y = a(1 + r)^{t} \). Percent decay: \( y = a(1 - r)^{t} \).
• If the amount is multiplied by \(b\) every \(k\) time units: \( y = a \cdot b^{t/k} \).
• A linear model adds the same amount each step. An exponential model multiplies by the same factor each step.

1. Find the starting value \(a\).
2. Turn the percent into a factor. A 5% increase is a factor of 1.05.
3. Match the exponent to the time unit in the question.

Worked example. A town has 8,000 people and grows 5% each year. The model is \( P = 8000(1.05)^{t} \). After 2 years, \( P = 8000(1.1025) = 8820 \). A second case: a culture starts at 200 cells and doubles every 6 hours, so \( N = 200 \cdot 2^{t/6} \). After 18 hours, \( N = 200 \cdot 2^{3} = 1600 \).

In our data: 18 of the 200 prediction bank questions. Practice with the growth factors and exponential models drill.

4. Expressions and polynomials (6.5%)

• Difference of squares: \( a^2 - b^2 = (a - b)(a + b) \)
• Perfect squares: \( (a + b)^2 = a^2 + 2ab + b^2 \) and \( (a - b)^2 = a^2 - 2ab + b^2 \)
• Exponent rules: \( x^{a} \cdot x^{b} = x^{a+b} \) and \( (x^{a})^{b} = x^{ab} \)

1. Expand each product.
2. Distribute any minus sign across the whole bracket.
3. Combine like terms.
4. Test your result with an easy number such as \( x = 1 \).

Worked example. Simplify \( (3x - 2)^2 - (x - 2)(x + 2) \). The first part is \( 9x^2 - 12x + 4 \). The second part is \( x^2 - 4 \). Subtract: \( 9x^2 - 12x + 4 - x^2 + 4 = 8x^2 - 12x + 8 \). Check with \( x = 1 \): the original gives \( 1 - (-3) = 4 \), and the result gives \( 8 - 12 + 8 = 4 \).

In our data: 12 of the 200 prediction bank questions. One item type in this skill has appeared on 14 test dates. Practice with the expressions drill.

5. Systems of equations (5.8%)

• Elimination: add or subtract the equations to remove one variable.
• Substitution: solve one equation for a variable and plug it into the other.
• For \( a_1x + b_1y = c_1 \) and \( a_2x + b_2y = c_2 \): there is no solution when \( \dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \ne \dfrac{c_1}{c_2} \). There are infinitely many solutions when all three ratios are equal.

1. Line up the equations in the same form.
2. Pick the variable that cancels with the least work.
3. Solve for one variable, then the other.
4. Check the pair in both equations.

Worked example. Solve \( 2x + 3y = 18 \) and \( 4x - 3y = 0 \). Add the equations: \( 6x = 18 \), so \( x = 3 \). Then \( 6 + 3y = 18 \), so \( y = 4 \). Check the second equation: \( 12 - 12 = 0 \). A second case: \( 3x + ky = 5 \) and \( 6x + 8y = 7 \) have no solution when \( \dfrac{3}{6} = \dfrac{k}{8} \), so \( k = 4 \). The constants 5 and 7 are in a different ratio, so the lines never meet.

In our data: 19 of the 200 prediction bank questions, and a 7.7% come-back rate in 2026. Practice with the systems of two linear equations drill.

6. Quadratic equations (5.5%)

• Quadratic formula: \( x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)
• Discriminant: \( D = b^2 - 4ac \). Two real solutions when \( D > 0 \), one when \( D = 0 \), none when \( D < 0 \).
• Sum of solutions formula: \( -\dfrac{b}{a} \)
• Product of solutions formula: \( \dfrac{c}{a} \)

1. Write the equation as \( ax^2 + bx + c = 0 \).
2. Try to factor. If that is slow, use the quadratic formula.
3. If the question asks only for the sum or the product of the solutions, use the shortcut and stop.

Worked example. Solve \( 2x^2 - 7x + 3 = 0 \). The discriminant is \( 49 - 24 = 25 \). So \( x = \dfrac{7 \pm 5}{4} \), which gives \( x = 3 \) or \( x = \dfrac{1}{2} \). The sum is \( \dfrac{7}{2} \), which matches \( -\dfrac{b}{a} \). The product is \( \dfrac{3}{2} \), which matches \( \dfrac{c}{a} \). A second case: \( x^2 + kx + 9 = 0 \) has exactly one real solution when \( k^2 - 36 = 0 \), so \( k = 6 \) or \( k = -6 \).

For more on the two shortcuts, see our pages on the sum of solutions and the product of roots. In our data: 14 of the 200 prediction bank questions. Practice with the quadratic equations drill.

7. Quadratic and nonlinear functions (5.5%)

• Standard form \( y = ax^2 + bx + c \): the y-intercept is \(c\). The graph opens up when \( a > 0 \) and down when \( a < 0 \).
• Vertex form \( y = a(x - h)^2 + k \): the vertex is \( (h, k) \).
• Factored form \( y = a(x - p)(x - q) \): the x-intercepts are \(p\) and \(q\).
• Axis of symmetry: \( x = -\dfrac{b}{2a} \)

1. Decide what the question wants: a vertex, an intercept or a value.
2. Use the form that shows it. For a maximum or minimum, find the vertex.
3. Plug the x-value back in to get the y-value.

Worked example. A ball's height in meters is \( h = -5t^2 + 20t + 3 \), with \(t\) in seconds. The peak is at \( t = -\dfrac{20}{2(-5)} = 2 \). The height there is \( -5(4) + 20(2) + 3 = 23 \) meters. Check by symmetry: at \( t = 1 \) and at \( t = 3 \) the height is 18 meters.

In our data: 10 of the 200 prediction bank questions. Practice with the quadratic functions drill.

8. Inequalities (4.7%)

• Solve an inequality like an equation, with one extra rule: flip the sign when you multiply or divide by a negative number.
• "At least" means \( \ge \). "At most" means \( \le \).
• For a system of inequalities, a point is a solution only if it makes every inequality true.

1. Write the inequality from the words.
2. Isolate the variable.
3. Flip the sign if you divided by a negative.
4. Test one number from your answer.

Worked example. Solve \( -3x + 4 \le 19 \). Subtract 4: \( -3x \le 15 \). Divide by \(-3\) and flip the sign: \( x \ge -5 \). Check with \( x = 0 \): \( 4 \le 19 \) is true. A word case: tickets cost 12 dollars each, plus an 8-dollar fee, and you can spend at most 80 dollars. Then \( 12t + 8 \le 80 \), so \( t \le 6 \).

In our data: 6 of the 200 prediction bank questions. Practice with the linear inequalities drill.

9. Area, perimeter and volume (4.7%)

• The reference sheet gives the area and volume formulas, such as \( A = \pi r^2 \) and \( V = \pi r^2 h \).
• Scale factor rule, which the sheet does not give: if every length is multiplied by \(k\), areas are multiplied by \(k^2\) and volumes by \(k^3\).

1. Name the shape and open the reference sheet.
2. Label every length with its unit.
3. Plug in, and keep \( \pi \) as a symbol unless the question asks for a decimal.

Worked example. A cylinder has radius 3 and height 10. Its volume is \( \pi (3)^2 (10) = 90\pi \). Now double every length. The volume is multiplied by \( 2^3 = 8 \), which gives \( 720\pi \). Check: \( \pi (6)^2 (20) = 720\pi \).

In our data: 9 of the 200 prediction bank questions. Practice with the area, perimeter and volume drill.

10. Percentages (4.5%)

• Percent change: \( \dfrac{\text{new} - \text{old}}{\text{old}} \times 100 \)
• A \(p\) percent increase multiplies by \( 1 + \dfrac{p}{100} \). A \(p\) percent decrease multiplies by \( 1 - \dfrac{p}{100} \).
• To undo a percent change, divide by the same multiplier.

1. Turn each percent into a multiplier.
2. Decide the direction: multiply to go forward, divide to go back.
3. Chain the multipliers when there are two changes.

Worked example. A jacket's price rose 25% to 60 dollars. The original price was \( \dfrac{60}{1.25} = 48 \) dollars. Now take 20% off the 60 dollars: \( 60(0.80) = 48 \) dollars. The two changes cancel because \( 1.25 \times 0.80 = 1 \). A 25% increase is not undone by a 25% decrease.

In our data: 13 of the 200 prediction bank questions, and an 8.1% come-back rate in 2026. Practice with the percent change drill and our percent change practice page.

11. Functions (4.0%)

• \( f(a) \) means: replace every \(x\) with \(a\).
• Composition: for \( f(g(x)) \), find \( g(x) \) first, then put that result into \(f\).
• To solve \( f(x) = c \), set the rule equal to \(c\) and solve for \(x\).

1. Work from the inside out.
2. Use parentheses every time you substitute.
3. Check whether the question asks for an input or an output.

Worked example. Let \( f(x) = 2x^2 - 3 \) and \( g(x) = x + 4 \). Then \( g(1) = 5 \) and \( f(5) = 2(25) - 3 = 47 \), so \( f(g(1)) = 47 \). To solve \( f(x) = 15 \): \( 2x^2 = 18 \), so \( x = 3 \) or \( x = -3 \).

In our data: 14 of the 200 prediction bank questions, and a 7.3% come-back rate in 2026. One item type in this skill has appeared on 14 test dates.

Rules for the next skills

• Triangles (4.0%). The angles add to \( 180^\circ \). The reference sheet gives \( c^2 = a^2 + b^2 \) and both special right triangles. Similar triangles have equal ratios of matching sides. Practice: triangles drill.
• Ratios, rates and units (3.2%). Write the units in every step and cancel them like fractions. Example: 90 miles in 1.5 hours is \( \dfrac{90}{1.5} = 60 \) miles per hour.
• Circles (3.0%). The circle equation is \( (x - h)^2 + (y - k)^2 = r^2 \), with center \( (h, k) \). Example: \( x^2 + y^2 - 6x + 4y = 12 \) becomes \( (x - 3)^2 + (y + 2)^2 = 25 \). The center is \( (3, -2) \) and the radius is 5. Practice: circles drill.
• Right-triangle trigonometry (2.9%). \( \sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}} \), \( \cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}} \), \( \tan\theta = \dfrac{\text{opposite}}{\text{adjacent}} \). Also \( \sin x^\circ = \cos(90^\circ - x^\circ) \).
• Number of solutions and extraneous solutions (2.5%). Plug every answer back into the original equation. A value that fails is extraneous. Example: \( \sqrt{x + 2} = x \) gives \( x = 2 \) or \( x = -1 \), and only \( x = 2 \) works. Practice: solution counts drill.

SAT Math formulas: what the SAT reference sheet gives you

The SAT reference sheet gives you area, volume and right-triangle facts. It does not give you algebra formulas. Bluebook shows the sheet on every test with math questions, per College Board's Bluebook testing tools page. We read its contents from Appendix D of College Board's Assessment Framework for the Digital SAT Suite.

The table marks which SAT Math formulas are on the SAT Math reference sheet and which are not. The rows marked "No" are the math formulas to know for the SAT by heart.

If you want one page to print, treat the "No" rows as your own SAT Math formula sheet. Our SAT Math formulas page has the reference sheet plus 54 more SAT Math formulas to memorize.

What are the hardest SAT Math question types?

This page sizes the hard questions. A separate guide ranks the types. In our fall 2026 banks, we tagged 36.8% of Math questions Hard, 34.9% Intermediate and 28.3% Easy. Those are our own difficulty tags, not College Board's.

• The prediction bank leans hard. We tagged 77 of its 200 questions Hard, 82 Intermediate and 41 Easy.
• Typed answers are growing in our banks. Questions where you type the answer were 22.8% of our fall 2026 banks. Across all 22 banks they are 15.4%. Practice finishing a problem with no choices to check against.
• Train for length. When you practice the hardest SAT Math questions, write every step. Then check each step against the rules on this page.

Our guide to the hardest SAT Math question types ranks them with data. For method, read how to solve hard Module 2 SAT Math questions. Then try the five problems in our hard SAT Math questions set.

How to study for SAT Math before the December 5 test

Work from the top of the priority table down, then switch to timed practice in the last week. The plan starts on November 10 and uses the 25 days before the test. If you start later, keep the order and shorten each block.

For timed sets, use the November 2026 Math question bank or the December 2025 Math question bank. After each set, turn your raw score into an estimate with our Digital SAT score calculator. For a longer schedule, see how to build a Digital SAT Math study plan, or use our SAT study plan generator for a free week-by-week plan.

Keep some days for Reading and Writing. On those days, use our December 2026 SAT grammar rules guide and our December 2026 SAT transitions and notes guide.

What is in the December 2026 SAT Math prediction bank?

The December 2026 Math prediction bank holds 200 questions from the top of our model's December ranking. Every one of the 200 has appeared on two or more test dates in our banks. It costs $99.99.

• By section: 75 Advanced Math, 64 Algebra, 33 Problem-Solving and Data Analysis and 28 Geometry and Trigonometry.
• Largest skills: linear functions (26), systems of equations (19), exponential functions (18), functions (14) and quadratic equations (14).
• Format: 164 multiple-choice questions and 36 typed-answer questions. 101 of the 200 have a video linked.

Use it in the last week, after you know the rules. It is practice on the skills most likely to return. It is not a copy of the December test. Most of what appears on a test date will not be in any prediction bank. The English bank built by the same model is the December 2026 English prediction bank. To see what students recalled from the last test date, read our November 2026 SAT Math recap.

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What to do next

Frequently Asked Questions

What is the December 2026 SAT Math prediction?

It is a ranking of Math skills built from 4,159 questions in 22 Digital SAT Math question banks on our site. Linear functions lead our fall 2026 banks at 14.9%, then linear equations at 8.3% and exponential functions at 6.6%. It predicts skills, not specific questions. It is not a leak or a guarantee, and most of what appears on a test date will not be in any prediction bank.

When is the December SAT in 2026?

The December SAT is on Saturday, December 5, 2026. The registration deadline is November 20, 2026, and the late registration deadline is November 24, 2026, per College Board's SAT dates and deadlines page.

How to study for SAT Math before the December SAT?

Study skills in the order they appear most in our fall 2026 banks: linear functions, linear equations, exponential functions, polynomials and systems of equations. Memorize the formulas the reference sheet does not give. In the last week, switch to timed 35-minute sets of 22 questions and redo every question you miss.

What are the hardest SAT Math question types?

This page sizes the hard questions and a separate guide on our site ranks the types. In our fall 2026 question banks we tagged 36.8% of Math questions Hard, 34.9% Intermediate and 28.3% Easy. Typed-answer questions were 22.8% of those banks. Those are our own tags, not College Board's.

What formulas are on the SAT Math reference sheet?

The reference sheet gives circle area and circumference, rectangle and triangle area, the Pythagorean theorem, the two special right triangles and five volume formulas. It does not give the slope formula, the quadratic formula, exponential growth, percent change or the circle equation. Memorize those.

What is the sum of solutions to a quadratic equation?

For ax^2 + bx + c = 0, the sum of the solutions is -b/a and the product of the solutions is c/a. Example: 2x^2 - 7x + 3 = 0 has solutions 3 and 1/2. Their sum is 7/2 and their product is 3/2.

What is in the December 2026 SAT Math prediction bank?

It holds 200 questions from the top of our model's December ranking: 75 Advanced Math, 64 Algebra, 33 Problem-Solving and Data Analysis and 28 Geometry and Trigonometry. It costs 99.99 dollars. In back-tests, 11.4% of a 200-question bank came back on an average 2026 test date, with a range from 2.0% to 25.0%. Most of what appears on a test date will not be in any prediction bank.

Related Concepts

SAT Digital SAT College Board Bluebook Desmos reference sheet Math section Algebra Advanced Math Problem-Solving and Data Analysis Geometry and Trigonometry December 5, 2026 The Test Advantage SAT Question Bank SkillDrill quadratic formula

Related Guides

Sources and Citation Targets

• College Board: SAT Dates and Deadlines
• College Board: December 5, 2026 SAT Test Date
• College Board: Math Specifications
• College Board: The Math Section Overview
• College Board: How the SAT Is Structured
• College Board: Bluebook Testing Tools
• College Board: Assessment Framework for the Digital SAT Suite (Appendix D reference sheet)