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Digital SAT Practice Test 7 — Module 1 Math: Full Walkthrough of All 22 Questions with Answers & Explanations

Every question on Digital SAT Practice Test #7, Math Module 1, transcribed verbatim, with the official College Board answer key, a step-by-step worked solution, a plain-English explanation for every item, theory refreshers on every tested skill, and a free PDF download. Built by SOMATH, the math school on the Upper West Side of Manhattan.

· By the SOMATH team · 226 W 79th St, UWS · (646) 668-6151

Looking for the answers, explanations, and full walkthrough of Digital SAT Practice Test 7 — Math Module 1? You are in the right place. This is a complete, question-by-question walkthrough of SAT Test #7, Math Module 1 — every one of the 22 questions transcribed verbatim, with the official College Board answer for each item and a worked solution showing exactly which SAT Math tool the question wants and how to apply it.

Use this post with the official PDF: first attempt each question on your own, then open the answer reveal only after you have committed to an answer. The module mixes equations, functions, data, and geometry, so it is also a useful checklist of the skills that need attention before the next test date.

Whether you are a student prepping for the next SAT, a parent looking for answer explanations, or a teacher building a review packet, this walkthrough is designed to be a clear, student-friendly study resource. It is written by the team that teaches Digital SAT prep at SOMATH, a math-focused school on the Upper West Side of New York City.

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Official College Board PDFOpen Digital SAT Practice Test 7 to view every graph, figure, and response grid.
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How to use this walkthrough: Attempt the question first. Then reveal the answer, compare your setup to the worked solution, and write down the skill tag if that step felt unfamiliar. Graphs and diagrams remain in the official PDF so you can practice reading the original test display.

Official answer key — SAT Practice Test 7, Math Module 1

Question #Correct Answer
1B
2D
3B
4A
5D
69
714; −5; −4
8A
9B
10D
11C
12D
13294
143
15A
16C
17B
18B
19D
205
2187
22B

Theory refresher: every skill tested in this module

Algebra

Translate words into equations, use slope-intercept form, and preserve equality by applying the same operation to both sides. For systems, substitution replaces one variable with an equivalent expression.

Advanced Math

Use the zero-product property on a factored polynomial, evaluate a function by substitution, and recognize that |u| = a usually gives two values. In exponential expressions, a base of 2 doubles whenever the exponent rises by 1.

Problem-Solving & Data Analysis

A line of best fit estimates a y-value for a given x-value; a bar height gives a frequency; and average rate of change is change in y / change in x. Always identify which quantities the graph’s axes measure.

Geometry & Trigonometry

Congruent triangles have matching corresponding angles. A circle (x-h)2 + (y-k)2 = r2 has center (h,k) and radius r; segments from its center to points on the circle are radii.

Questions 1–5: Problem-solving, data, geometry, and setup

Read a line of best fit, interpret a bar graph, subtract area, solve an absolute-value equation, and turn a purchase into an equation.

Question 1 · Problem-Solving & Data Analysis · Two-variable data/scatterplots

The scatterplot shows the temperature, in degrees Fahrenheit (°F), and the distance above sea level, in feet, measured at 6 locations on Mount Jefferson. A line of best fit is also shown.

At a distance of 4,000 feet above sea level, what is the temperature, in °F, predicted by the line of best fit?

See figure in the original College Board PDF above.

  • A) 47
  • B) 35
  • C) 25
  • D) 0

Answer: B) 35

Key idea. Read the y-value on the line of best fit at the stated x-value, not the height of a nearby plotted point.

At x = 4,000 feet, the line of best fit has y = 35. Predicted temperature = 35°F

Why this works. The question asks for the model’s prediction, so the line—not one of the six observed points—supplies the answer.

Question 2 · Geometry & Trigonometry · Area & volume

Rectangle P has an area of 72 square inches. If a rectangle with an area of 20 square inches is removed from rectangle P, what is the area, in square inches, of the resulting figure?

  • A) 92
  • B) 84
  • C) 80
  • D) 52

Answer: D) 52

Key idea. Removing a region subtracts its area from the original area.

original area − removed area = 72 − 20 = 52 square inches

Why this works. The remaining shape may not be a rectangle, but its area is still the original area less the part cut away.

Question 3 · Advanced Math · Radical/absolute value

|p| + 61 = 65

Which value is a solution to the given equation?

  • A) 65/61
  • B) 4
  • C) 126
  • D) 130

Answer: B) 4

Key idea. First isolate the absolute-value expression; then use the two possible values with that absolute value.

|p| + 61 = 65 |p| = 4 p = 4 or p = −4 Among the choices, 4 is listed.

Why this works. An absolute value of 4 has two solutions, but the question asks for a listed solution and choice B is the one shown.

Question 4 · Algebra · Linear equations/inequalities

Lorenzo purchased a box of cereal and some strawberries at the grocery store. Lorenzo paid $2 for the box of cereal and $1.90 per pound for the strawberries. If Lorenzo paid a total of $9.60 for the box of cereal and the strawberries, which of the following equations can be used to find p, the number of pounds of strawberries Lorenzo purchased? (Assume there is no sales tax.)

  • A) 1.90p + 2 = 9.60
  • B) 1.90p − 2 = 9.60
  • C) 1.90 + 2p = 9.60
  • D) 1.90 − 2p = 9.60

Answer: A) 1.90p + 2 = 9.60

Key idea. Write the variable cost and the fixed cost as addends that total the amount paid.

strawberries: 1.90p dollars cereal: 2 dollars total: 9.60 dollars 1.90p + 2 = 9.60

Why this works. The $1.90 rate is multiplied by the number of pounds, while the cereal contributes one fixed $2 charge.

Question 5 · Problem-Solving & Data Analysis · One-variable data/statistics

The bar graph summarizes the charge, in kilowatt-hours (kWh), a battery received each day for 15 days.

For how many of these 15 days did the battery receive a charge of 0 kWh?

See figure in the original College Board PDF above.

  • A) 0
  • B) 1
  • C) 4
  • D) 6

Answer: D) 6

Key idea. On a bar graph, the bar height gives the frequency of the category on the horizontal axis.

Locate the bar above 0 kWh. Its height is 6. The battery received 0 kWh on 6 days.

Why this works. The 0 labels the charge category; it is not the count. The corresponding bar height gives the number of days.

Questions 6–10: Algebra and functions

Identify slope, find zeros from factors, interpret an intercept, use congruence, and evaluate a function.

Question 6 · Algebra · Linear equations/inequalities

A line in the xy-plane has a slope of 9 and passes through the point (0, −5). The equation y = px + r defines the line, where p and r are constants. What is the value of p?

Student-produced response — enter the accepted answer format shown after revealing the solution.

Answer: 9 (enter 9)

Key idea. In slope-intercept form, the coefficient of x is the slope.

y = px + r slope = p Given slope = 9, p = 9

Why this works. The point determines the intercept r, but the prompt already states the slope, which immediately identifies p.

Question 7 · Advanced Math · Polynomial/rational

What is an x-coordinate of an x-intercept of the graph of y = 3(x − 14)(x + 5)(x + 4) in the xy-plane?

Student-produced response — enter the accepted answer format shown after revealing the solution.

Answer: 14; -5; -4 (enter one accepted value)

Key idea. At an x-intercept y equals 0, so a factored product is zero when any factor is zero.

0 = 3(x − 14)(x + 5)(x + 4) x − 14 = 0 → x = 14 x + 5 = 0 → x = −5 x + 4 = 0 → x = −4

Why this works. Each of the three zeros makes one factor equal to zero, making the entire product and therefore y equal to zero.

Question 8 · Problem-Solving & Data Analysis · Two-variable data/scatterplots

The graph shown gives the estimated value, in dollars, of a tablet as a function of the number of months since it was purchased. What is the best interpretation of the y-intercept of the graph in this context?

See figure in the original College Board PDF above.

  • A) The estimated value of the tablet was $225 when it was purchased.
  • B) The estimated value of the tablet 24 months after it was purchased was $225.
  • C) The estimated value of the tablet had decreased by $225 in the 24 months after it was purchased.
  • D) The estimated value of the tablet decreased by approximately 2.25% each year after it was purchased.

Answer: A) The estimated value of the tablet was $225 when it was purchased.

Key idea. A y-intercept describes the output when x is 0.

y-intercept: (0, 225) x = 0 months after purchase At purchase, the estimated value was $225.

Why this works. Because x measures months after purchase, zero months is the instant the tablet was purchased.

Question 9 · Geometry & Trigonometry · Lines/angles/triangles

Triangles EFG and JKL are congruent, where E, F, and G correspond to J, K, and L, respectively. The measure of angle E is 45° and the measure of angle F is 20°. What is the measure of angle J?

  • A) 20°
  • B) 45°
  • C) 135°
  • D) 160°

Answer: B) 45°

Key idea. Corresponding angles in congruent triangles have the same measure.

E ↔ J m∠E = 45° Therefore, m∠J = 45°

Why this works. The listed correspondence establishes which angle matches J; the 20° measure belongs to angle F and its partner K.

Question 10 · Advanced Math · Nonlinear functions

The function f is defined by f(x) = 1/2(x + 6). What is the value of f(4)?

  • A) 20
  • B) 12
  • C) 10
  • D) 5

Answer: D) 5

Key idea. Substitute 4 for x, then evaluate the product.

f(4) = (1/2)(4 + 6) = (1/2)(10) = 5

Why this works. The one-half multiplies the entire quantity x + 6; evaluating x + 6 first avoids treating the expression as x plus 6/2.

Questions 11–16: Systems, circles, and nonlinear equations

Locate a graphed system’s intersection, preserve equivalent equations, solve a system, read circle form, and work with absolute value.

Question 11 · Algebra · Systems of linear equations

The graph of a system of an absolute value function and a linear function is shown. What is the solution (x, y) to this system of two equations?

See figure in the original College Board PDF above.

  • A) (0, 8)
  • B) (7/2, 9/2)
  • C) (−7/2, 9/2)
  • D) (−3, 4)

Answer: C) (−7/2, 9/2)

Key idea. The solution of a graphed system is the coordinate pair at which the two graphs intersect.

From the graph, the intersection is: −4 < x < −3 4 < y < 5 Only (−7/2, 9/2) fits both ranges.

Why this works. The intersection lies left of −3 and above 4. The other answer choices describe a different notable point or have coordinates in the wrong region.

Question 12 · Algebra · Systems of linear equations

y = 6x + 3

One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which equation could be the second equation in this system?

  • A) y = 2(6x) + 3
  • B) y = 2(6x + 3)
  • C) 2y = 2(6x) + 3
  • D) 2y = 2(6x + 3)

Answer: D) 2y = 2(6x + 3)

Key idea. Infinitely many solutions require two equivalent equations, so multiply both sides of the original equation by the same nonzero number.

y = 6x + 3 multiply both sides by 2: 2y = 2(6x + 3)

Why this works. This second equation represents exactly the same line. A changed coefficient on only part of the equation would create a different line instead.

Question 13 · Algebra · Linear equations/inequalities

If 6/7p + 18 = 54, what is the value of 7p?

Student-produced response — enter the accepted answer format shown after revealing the solution.

Answer: 294 (enter 294)

Key idea. Isolate p first, then multiply the result by 7.

(6/7)p + 18 = 54 (6/7)p = 36 p = 42 7p = 7(42) = 294

Why this works. Multiplying by 7/6 reverses the coefficient 6/7; only after finding p should the requested expression 7p be evaluated.

Question 14 · Algebra · Systems of linear equations

y = 9x + 12
x + 7y = 20

The solution to the given system of equations is (x, y). What is the value of y?

Student-produced response — enter the accepted answer format shown after revealing the solution.

Answer: 3 (enter 3)

Key idea. Substitute the expression for y into the other equation, then back-substitute.

x + 7(9x + 12) = 20 64x + 84 = 20 64x = −64 x = −1 y = 9(−1) + 12 = 3

Why this works. One equation already isolates y, making substitution direct. The resulting ordered pair has y-coordinate 3.

Question 15 · Geometry & Trigonometry · Circles

A circle in the xy-plane has the equation (x − 13)2 + (y − k)2 = 64. Which of the following gives the center of the circle and its radius?

  • A) The center is at (13, k) and the radius is 8.
  • B) The center is at (k, 13) and the radius is 8.
  • C) The center is at (k, 13) and the radius is 64.
  • D) The center is at (13, k) and the radius is 64.

Answer: A) The center is at (13, k) and the radius is 8.

Key idea. Compare the equation with the standard circle form and take the positive square root of the right side for the radius.

(x − h)² + (y − k)² = r² h = 13 k = k r² = 64 → r = 8 center: (13, k)

Why this works. The signs inside the squared terms identify the center coordinates, while 64 is r²—not the radius itself.

Question 16 · Advanced Math · Radical/absolute value

The function f is defined by f(x) = |x − 4x|. What value of a satisfies f(5) − f(a) = −15?

  • A) −20
  • B) 5
  • C) 10
  • D) 45

Answer: C) 10

Key idea. Simplify the function, evaluate f(5), and solve the resulting absolute-value equation.

f(x) = |−3x| = 3|x| f(5) = 15 15 − 3|a| = −15 3|a| = 30 |a| = 10 a = −10 or 10

Why this works. Both −10 and 10 satisfy the equation, but only 10 appears among the answer choices.

Questions 17–22: Exponentials, rational expressions, rates, and circles

Evaluate exponential models, rearrange rational expressions, calculate a rate of change, model a word problem, and use a triangle’s perimeter.

Question 17 · Advanced Math · Exponential functions

For the exponential function f, the value of f(0) is c, where c is a constant. Of the following equations that define the function f, which equation shows the value of c as the coefficient or the base?

  • A) f(x) = 22(1.5)x+1
  • B) f(x) = 33(1.5)x
  • C) f(x) = 49.5(1.5)x−1
  • D) f(x) = 74.25(1.5)x−2

Answer: B) f(x) = 33(1.5)x

Key idea. Evaluate each expression at x = 0; the correct equation already has f(0) as its coefficient.

For choice B: f(0) = 33(1.5)⁰ = 33(1) = 33 The coefficient is c.

Why this works. In the other choices, the shifted exponent means their displayed coefficients represent the function at an x-value other than 0.

Question 18 · Advanced Math · Exponential functions

The function f(t) = 40,000(2)t/790 gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

  • A) 2
  • B) 790
  • C) 1,580
  • D) 40,000

Answer: B) 790

Key idea. For a base-2 exponential expression, the quantity doubles when its exponent increases by 1.

f(t) = 40,000 · 2t/790 To double, t/790 must increase by 1. That requires t to increase by 790. Doubling time = 790 minutes

Why this works. The 40,000 is the starting quantity; the denominator 790 in the exponent controls how long it takes the exponent to rise by one.

Question 19 · Advanced Math · Polynomial/rational

12/n = 2/t − 2/w

The given equation relates the variables n, t, and w, where n > 0, t > 0, and w > t. Which expression is equivalent to n?

  • A) 12tw
  • B) 6(t − w)
  • C) w − t/6tw
  • D) 6tw/w − t

Answer: D) 6tw/w − t

Key idea. Combine the fractions on the right, then solve for n by taking reciprocals after isolating it.

12/n = 2/t − 2/w 12/n = (2w − 2t)/(tw) 12/n = 2(w − t)/(tw) 12tw = 2n(w − t) 6tw = n(w − t) n = 6tw/(w − t)

Why this works. The positivity conditions make the denominators and w − t nonzero, so the algebraic rearrangement is valid.

Question 20 · Problem-Solving & Data Analysis · Two-variable data/scatterplots

During a study, the temperature, in degrees Celsius (°C), of the air in a chamber was recorded to the nearest integer at certain times. The scatterplot shows the recorded temperature y, in °C, of the air in the chamber x minutes after the start of the study.

What was the average rate of change, in °C per minute, of the recorded temperature of the air in the chamber from x = 5 to x = 7?

See figure in the original College Board PDF above.

Student-produced response — enter the accepted answer format shown after revealing the solution.

Answer: 5 (enter 5)

Key idea. Use the two plotted values and compute change in temperature divided by change in time.

At x = 5, y = 14. At x = 7, y = 24. average rate = (24 − 14)/(7 − 5) = 10/2 = 5 °C per minute

Why this works. Average rate of change compares endpoints only; the graph provides the two y-values needed for the slope calculation.

Question 21 · Algebra · Linear equations/inequalities

In August, a car dealer completed 15 more than 3 times the number of sales the car dealer completed in September. In August and September, the car dealer completed 363 sales. How many sales did the car dealer complete in September?

Student-produced response — enter the accepted answer format shown after revealing the solution.

Answer: 87 (enter 87)

Key idea. Represent September sales with one variable and translate the August statement before adding the two months.

Let x = September sales. August sales = 3x + 15. x + (3x + 15) = 363 4x = 348 x = 87

Why this works. The phrase “15 more than 3 times” means 3x + 15, not 3(x + 15).

Question 22 · Geometry & Trigonometry · Circles

Points Q and R lie on a circle with center P. The radius of this circle is 9 inches. Triangle PQR has a perimeter of 31 inches. What is the length, in inches, of QR?

  • A) 13/2
  • B) 13
  • C) 9/2
  • D) 9

Answer: B) 13

Key idea. Radii from the center to points on the circle give two known sides of the triangle.

PQ = 9 and PR = 9 perimeter = PQ + PR + QR 31 = 9 + 9 + QR QR = 13

Why this works. Q and R are on the circle, so PQ and PR are both radii. The third side is what remains after subtracting those two radii from the perimeter.

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Digital SAT Practice Test 7 Math Module 1 FAQ

What does this Practice Test 7 Math Module 1 walkthrough cover?

It covers all 22 questions in the module, including the multiple-choice questions and student-produced responses. Every item has the official answer, a worked solution, and a short explanation of the underlying Digital SAT Math skill.

Which questions in Practice Test 7 Math Module 1 are student-produced responses?

Questions 6, 7, 13, 14, 20, and 21 are student-produced responses. Question 7 accepts 14, −5, or −4; the other accepted answers are 9, 294, 3, 5, and 87.

How should I handle the graph and figure questions in this module?

Read the graph or figure directly in the College Board PDF, then translate the visual information into a mathematical statement. In this module, that is especially useful for the line of best fit, bar graph, tablet-value graph, system graph, and temperature scatterplot.

What is the key idea in Question 7?

At an x-intercept, y = 0. The factored equation 3(x − 14)(x + 5)(x + 4) is zero when x is 14, −5, or −4, and any one of those values can be entered.

What is the key idea in Question 22?

PQ and PR are both radii, so each is 9 inches. The perimeter equation 9 + 9 + QR = 31 gives QR = 13.

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