Digital SAT — Math, Module 1 (Practice Test A)

Format: 22 questions · 35 minutes · calculator permitted throughout Coverage: Algebra · Advanced Math · Problem-Solving & Data Analysis · Geometry & Trigonometry How to use: Work under timed conditions. Most questions are multiple-choice; the final few are student-produced response (grid-in) — write your own answer. Full worked solutions and a scoring note follow the paper.

Digital SAT note: The real test is section-adaptive — your performance on Module 1 determines whether Module 2 is the harder or easier form. This module is the routing module: it ramps from accessible to moderately hard. Module 2 (separate paper) is the harder adaptive form.

Questions

1. If $3x + 7 = 22$, what is the value of $x$? A) 3 B) 5 C) 7 D) 15

2. A line in the xy-plane passes through the points $(0, 4)$ and $(2, 10)$. What is its slope? A) 2 B) 3 C) 4 D) 6

3. A phone plan charges a fixed $$20$ per month plus $$0.05$ per text. Which equation gives the monthly cost $C$ for $t$ texts? A) $C = 0.05t$ B) $C = 20t + 0.05$ C) $C = 20 + 0.05t$ D) $C = 25t$

4. If $\dfrac{x}{4} = \dfrac{9}{12}$, what is $x$? A) 2 B) 3 C) 4 D) 6

5. The function $f$ is defined by $f(x) = 2x^2 - 3$. What is $f(4)$? A) 13 B) 19 C) 29 D) 35

6. A shirt originally priced at $$40$ is discounted by 25%. What is the sale price? A) $10 B) $15 C) $30 D) $35

7. If $5(x - 2) = 3x + 4$, what is $x$? A) 3 B) 5 C) 7 D) 9

8. The ratio of cats to dogs at a shelter is $3:5$. If there are 24 cats, how many dogs are there? A) 30 B) 36 C) 40 D) 45

9. A scatterplot shows a strong positive linear association between hours studied and test score. The line of best fit is $\hat{y} = 8x + 50$. By how many points does the model predict a score increases for each additional hour studied? A) 8 B) 50 C) 58 D) 4

10. Which expression is equivalent to $(x + 3)(x - 5)$? A) $x^2 - 2x - 15$ B) $x^2 + 2x - 15$ C) $x^2 - 8x - 15$ D) $x^2 - 15$

11. A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? A) 10 B) 12 C) 14 D) $\sqrt{28}$

12. If $2^x = 32$, what is the value of $x$? A) 4 B) 5 C) 6 D) 16

13. A survey of 200 students found that 140 prefer online classes. Based on this sample, how many of a school's 1,500 students would be expected to prefer online classes? A) 700 B) 840 C) 1,050 D) 1,200

14. The equation $y = x^2 - 6x + 5$ is graphed in the xy-plane. What is the x-coordinate of the vertex? A) $-3$ B) 3 C) 5 D) 6

15. If $f(x) = \dfrac{12}{x}$ and $f(a) = 4$, what is $a$? A) 2 B) 3 C) 4 D) 48

16. A circle in the xy-plane has equation $(x-2)^2 + (y+1)^2 = 49$. What is the radius? A) 7 B) 49 C) $\sqrt{7}$ D) 14

17. The mean of five numbers is 12. Four of the numbers are 8, 10, 14, and 16. What is the fifth number? A) 10 B) 12 C) 14 D) 18

18. A quantity grows according to $P = 500(1.04)^t$, where $t$ is in years. What does the 1.04 represent? A) a 4% decrease per year B) a 4% increase per year C) a 40% increase per year D) the starting amount

19. If $3x - 2y = 12$ and $x + 2y = 8$, what is the value of $x$? A) 3 B) 4 C) 5 D) 6

20. A cylinder has radius 3 and height 10. What is its volume? (Use $V = \pi r^2 h$.) A) $30\pi$ B) $60\pi$ C) $90\pi$ D) $300\pi$

Questions 21–22 are student-produced responses (grid-in). Write your answer.

21. If $\dfrac{x+1}{3} = \dfrac{x-1}{2}$, what is the value of $x$?

22. A line passes through $(1, 2)$ and is parallel to the line $y = 4x - 7$. What is the y-coordinate of the point on this line where $x = 3$?

Answer key

Worked solutions

1. (B) $3x = 22 - 7 = 15 \Rightarrow x = 5$.

2. (B) Slope $= \dfrac{10 - 4}{2 - 0} = \dfrac{6}{2} = 3$.

3. (C) Fixed cost $20 plus $0.05 per text $t$: $C = 20 + 0.05t$.

4. (B) $\dfrac{9}{12} = \dfrac{3}{4}$, so $\dfrac{x}{4} = \dfrac{3}{4} \Rightarrow x = 3$.

5. (C) $f(4) = 2(16) - 3 = 32 - 3 = 29$.

6. (C) $25%$ of $40 is $10; sale price $= 40 - 10 = $30$.

7. (C) $5x - 10 = 3x + 4 \Rightarrow 2x = 14 \Rightarrow x = 7$.

8. (C) $3:5$ with 24 cats means each part $= 8$; dogs $= 5 \times 8 = 40$.

9. (A) In $\hat{y} = 8x + 50$, the slope 8 is the predicted increase per additional hour. (Distractor 50 is the intercept; 58 adds them; 4 is unrelated.)

10. (A) $(x+3)(x-5) = x^2 - 5x + 3x - 15 = x^2 - 2x - 15$.

11. (A) $\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$ (a 6-8-10 triangle).

12. (B) $2^5 = 32$, so $x = 5$.

13. (C) Proportion preferring online $= \dfrac{140}{200} = 0.70$; $0.70 \times 1500 = 1050$.

14. (B) Vertex x $= -\dfrac{b}{2a} = -\dfrac{-6}{2(1)} = 3$.

15. (B) $\dfrac{12}{a} = 4 \Rightarrow a = 3$.

16. (A) In $(x-h)^2 + (y-k)^2 = r^2$, $r^2 = 49 \Rightarrow r = 7$.

17. (B) Sum of five $= 5 \times 12 = 60$. Known four sum to $8+10+14+16 = 48$. Fifth $= 60 - 48 = 12$.

18. (B) In $P = 500(1.04)^t$, the base 1.04 means multiply by 1.04 each year — a 4% increase.

19. (C) Add the equations: $(3x - 2y) + (x + 2y) = 12 + 8 \Rightarrow 4x = 20 \Rightarrow x = 5$.

20. (C) $V = \pi (3)^2 (10) = \pi \cdot 9 \cdot 10 = 90\pi$.

21. (5) Cross-multiply: $2(x+1) = 3(x-1) \Rightarrow 2x + 2 = 3x - 3 \Rightarrow x = 5$.

22. (10) Parallel lines share slope 4: $y - 2 = 4(x - 1) \Rightarrow y = 4x - 2$. At $x = 3$: $y = 12 - 2 = 10$.

Scoring note (routing logic)

Count your correct answers out of 22.

• 0–9 correct: Module 2 would be the easier adaptive form. Focus revision on Heart of Algebra basics (linear equations, slope) — see the Algebra and Problem-Solving & Data Analysis revision guides.
• 10–15 correct: Solid middle. Drill the moderate items (quadratics, systems, ratios) to unlock the harder Module 2.
• 16–22 correct: You'd route to the harder Module 2 — attempt Math Module 2 (harder form) next, and concentrate on Advanced Math and Geometry/Trig.

Pedagogy: Every distractor above targets a specific misconception (e.g. Q9 confuses slope with intercept; Q10 mishandles the middle term; Q18 confuses growth factor with percentage). Reviewing why a wrong choice is tempting is as valuable as confirming the right one.