Digital SAT Math · 14 strategies
DSAT Math Strategy Hub
Fourteen strategies for the question types that appear on almost every Digital SAT. Each one shows how to spot the question, the method that solves it fastest, a worked example and the trap that costs most students the point.
By Engin Savaş · MATHIGH · mathematics educator with 20+ years of AP and IB teaching
Algebra · about 35% of the test
Algebra strategies
1
Linear equations
Simplify first, then read the structure
Spot it
Parentheses, fractions or a parameter such as k or a, often with “no solution” or “infinitely many solutions”.
Method
- Distribute and clear fractions, multiplying every term.
- Collect the x-terms on one side and the constants on the other.
- Compare both sides: same x-coefficient, different constants means no solution; both the same means infinitely many.
Worked example
For what value of k does 3(x − 2) + kx = 5x + 4 have no solution?
left side: (3 + k)x − 6
no solution ⇒ 3 + k = 5 and −6 ≠ 4
k = 2
!
Distributing a negative: −2(x − 4) is −2x + 8, not −2x − 8.
2
Systems of linear equations
Choose the path, then answer what is asked
Spot it
Two unknowns and two relationships, often two plans, prices or people being compared.
Three paths
- Elimination when both equations are in ax + by = c form.
- Substitution when one variable is already isolated.
- Desmos when the equations are messy: graph both and read the intersection.
Worked example
If 3x + 2y = 11 and x + 2y = 5, what is the value of 2x?
subtract the equations: (3x + 2y) − (x + 2y) = 11 − 5
2x = 6, with no need to find x or y
!
The question often asks for x + y, 2x or a total cost, not x itself. Read the last line before you start.
3
Linear models in context
Translate the story into slope and intercept
Spot it
Words such as per, each, every, initial, fixed fee or starting value.
Translation rules
“starts at”, “fixed fee”, “initial”
intercept b
“per”, “each”, “every”
slope m
“what does 40 represent?”
name the units
Worked example
A plumber’s charge is C = 40h + 65, where h is the number of hours. What does 65 represent?
65 is the value of C when h = 0
a fixed fee of $65 charged before any hours of work
!
Do not confuse the initial value with a later value mentioned in the text, such as “after 3 hours the cost is $185”.
Advanced Math · about 35% of the test
Advanced Math strategies
4
Quadratics
Pick the form that shows the answer
Which form shows what
vertex form a(x − h)² + k
max or min, vertex (h, k)
factored form a(x − p)(x − q)
zeros p and q
standard form ax² + bx + c
y-intercept c, axis x = −b/2a
discriminant b² − 4ac
number of real solutions
Worked example
For what value of c does x² + 6x + c = 0 have exactly one real solution?
one solution ⇒ b² − 4ac = 0
36 − 4c = 0
c = 9
!
Solving the whole quadratic when the question only needs the vertex, the sum of the roots or the y-intercept.
5
Exponential functions
Look for a constant ratio
Spot it
Growth or decay by a percentage, doubling time, half-life, or a table where each value is multiplied by the same number.
Key ideas
- Constant difference means linear; constant ratio means exponential.
- In f(t) = a · bᵗ, a is the initial value and b is the growth factor.
- b = 1 + r for growth and b = 1 − r for decay, with r as a decimal.
Worked example
The value of a car is modelled by V(t) = 18,000(0.85)ᵗ, where t is in years. What does 0.85 tell you?
b = 0.85 = 1 − 0.15
the value decreases by 15% each year
!
Reading 0.85 as an 85% decrease. The factor shows what remains, not what is lost.
Problem-Solving and Data · about 15% of the test
Problem-Solving and Data strategies
6
Percent change
Turn every percentage into a multiplier
Method
increase by r%
× (1 + r/100)
decrease by r%
× (1 − r/100)
r% of a value
× r/100
successive changes
multiply the factors
Worked example
A price rises by 20% and then falls by 20%. What is the overall change?
1.20 × 0.80 = 0.96
a 4% decrease, not “no change”
!
“Increased by 20% twice” is × 1.2 × 1.2 = × 1.44, a 44% increase, not 40%.
7
Weighted mean
Work with totals, not averages
Method
- Total for each group = mean × number of items.
- Add the totals.
- Divide by the total number of items.
Worked example
Class A has 20 students with a mean score of 80. Class B has 30 students with a mean of 70. What is the mean of all 50 students?
totals: 20 × 80 = 1600, 30 × 70 = 2100
(1600 + 2100) ÷ 50
74, not the simple average 75
!
Averaging the two means. That only works when the groups are the same size.
8
Two-way tables and probability
Find the right denominator first
Spot it
A table with row and column totals, and wording such as “given that”, “of those who” or “if a student is selected from”.
Method
- Underline the group you are choosing from.
- Use that row or column total as the denominator.
- Find the cell that also meets the second condition.
Worked example
Of the 40 students who take Spanish, 15 are seniors. A Spanish student is chosen at random. What is the probability that the student is a senior?
group chosen from: Spanish students (40)
15/40 = 0.375
!
Dividing by the grand total of the table when the question restricts the group.
Geometry and Trigonometry · about 15% of the test
Geometry and Trigonometry strategies
9
Similar figures
Find the scale factor first
Method
- Confirm similarity: equal angles, often from parallel lines or a shared angle.
- Match corresponding sides and find the scale factor k.
- Lengths scale by k, areas by k², volumes by k³.
Worked example
Two similar triangles have corresponding sides in the ratio 2:3. The smaller triangle has area 20. What is the area of the larger triangle?
area factor = (3/2)² = 9/4
20 × 9/4 = 45
!
Scaling an area by k instead of k². It gives 30 here, which is usually one of the answer choices.
10
Right-triangle trigonometry
Use SOH CAH TOA and the complement rule
Key ideas
- sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
- sin x° = cos(90° − x°): this complement rule appears on almost every test.
- Look for special triangles: 3-4-5, 5-12-13, 30-60-90 and 45-45-90.
Worked example
In a right triangle, sin x° = 0.6. What is the value of cos(90° − x°)?
cos(90° − x°) = sin x°
0.6
!
Reaching for a calculator when the question only needs the complement rule or a special triangle.
11
Circle equations
Complete the square to find the centre and radius
Method
- Group the x-terms and the y-terms.
- Complete the square for each, adding the same amounts to the other side.
- Read (x − h)² + (y − k)² = r²: the centre is (h, k) and the radius is r.
Worked example
Find the centre and radius of x² + y² − 6x + 4y − 12 = 0.
(x² − 6x + 9) + (y² + 4y + 4) = 12 + 9 + 4
(x − 3)² + (y + 2)² = 25
centre (3, −2), radius 5
!
Sign errors: (y + 2)² means k = −2. Also, the radius is √25 = 5, not 25.
Every question
Strategies for the whole test
12
Accuracy
The re-read filter
Why it matters
Many lost points come from correct work that answers the wrong quantity. Wrong answer choices are often built from exactly these slips.
Rule
- Before solving, underline what is asked: x, 2x, x + 3, a total, a difference, a percentage.
- After solving, read the last line again and check that your answer matches it, including units.
13
Pacing
The 2-minute escape rule
Why it matters
Each module gives you 35 minutes for 22 questions, about 95 seconds each. One stubborn question can cost you two easier ones later in the module.
Rule
- If you have no clear path after 2 minutes, choose your best answer.
- Use Mark for Review in Bluebook and move on.
- Return with the time you have left. There is no penalty for wrong answers, so never leave a blank.
14
Calculator
Use Desmos where it really saves time
Use Desmos for
- Intersections of two equations or models
- Vertices and zeros of quadratics
- Checking whether two expressions are equivalent
- Regression from a table of data
Solve by hand
- One- or two-step linear equations
- Basic percentages and unit conversions
- Questions answered by structure, such as “no solution” conditions
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