Digital SAT — Math, Module 1 (Practice Test B)
Format: 22 questions · 35 minutes · calculator permitted throughout Coverage: Algebra · Advanced Math · Problem-Solving & Data Analysis · Geometry & Trigonometry Routing module — ramps from accessible to moderately hard. Full worked solutions and scoring guidance follow. (Answer key balanced across A–D.)
Questions
1. If $5x - 3 = 12$, what is $x$? A) 3 B) 5 C) 9 D) 15
2. A line passes through $(0, 2)$ and $(3, 11)$. What is its slope? A) 2 B) 3 C) 9 D) 11
3. A gym charges a $30 joining fee plus $15 per month. Which equation gives the total cost $C$ after $m$ months? A) $C = 15m$ B) $C = 30m + 15$ C) $C = 30 + 15m$ D) $C = 45m$
4. If $\dfrac{x}{6} = \dfrac{10}{15}$, what is $x$? A) 3 B) 4 C) 6 D) 9
5. If $f(x) = 3x^2 - 2$, what is $f(3)$? A) 7 B) 25 C) 16 D) 27
6. A jacket priced at $80 is discounted 20%. What is the sale price? A) $16 B) $60 C) $64 D) $76
7. Solve $4(x + 1) = 2x + 14$. A) 3 B) 4 C) 5 D) 6
8. The ratio of pens to pencils is $2:5$. If there are 20 pens, how many pencils are there? A) 8 B) 50 C) 40 D) 25
9. A line of best fit is $\hat{y} = 5x + 20$. By how much does the model predict $y$ increases per unit increase in $x$? A) 5 B) 20 C) 25 D) 4
10. Which is equivalent to $(x - 4)(x + 2)$? A) $x^2 - 2x - 8$ B) $x^2 + 2x - 8$ C) $x^2 - 6x - 8$ D) $x^2 - 8$
11. A right triangle has legs 9 and 12. What is the hypotenuse? A) 15 B) 21 C) 18 D) $\sqrt{63}$
12. If $3^x = 81$, what is $x$? A) 3 B) 4 C) 5 D) 27
13. In a survey, 60 of 150 students bike to school. How many of 1,000 students would be expected to bike? A) 250 B) 300 C) 400 D) 600
14. The equation $y = x^2 - 8x + 12$ has its vertex at $x =$ A) 2 B) 6 C) 4 D) 8
15. If $g(x) = \dfrac{24}{x}$ and $g(a) = 6$, what is $a$? A) 2 B) 4 C) 6 D) 18
16. A circle has equation $(x+3)^2 + (y-2)^2 = 36$. What is the radius? A) 6 B) 36 C) 9 D) $\sqrt{6}$
17. The mean of six numbers is 9. Five of them are 6, 8, 10, 11, and 13. What is the sixth? A) 4 B) 6 C) 8 D) 9
18. A quantity grows by $P = 800(1.05)^t$. What does 1.05 represent? A) a 5% decrease B) a 5% increase per period C) a 50% increase D) the starting amount
19. If $2x + y = 13$ and $x - y = 2$, what is $x$? A) 3 B) 4 C) 5 D) 6
20. A cylinder has radius 4 and height 5. What is its volume? ($V = \pi r^2 h$) A) $20\pi$ B) $40\pi$ C) $80\pi$ D) $100\pi$
Questions 21–22 are student-produced responses.
21. If $\dfrac{x-2}{4} = \dfrac{x+4}{6}$, what is $x$?
22. A line is perpendicular to $y = 2x + 1$ and passes through $(0, 5)$. What is its $y$-value at $x = 4$?
Answer key
| Q | Ans | Q | Ans | Q | Ans | Q | Ans |
|---|---|---|---|---|---|---|---|
| 1 | A | 7 | C | 13 | C | 19 | C |
| 2 | B | 8 | B | 14 | C | 20 | C |
| 3 | C | 9 | A | 15 | B | 21 | 14 |
| 4 | B | 10 | A | 16 | A | 22 | 3 |
| 5 | B | 11 | A | 17 | B | ||
| 6 | C | 12 | B | 18 | B |
Key distribution (MC): A×5, B×8, C×7.
Worked solutions
1. (A) $5x = 15 \Rightarrow x = 3$. 2. (B) $(11-2)/(3-0) = 9/3 = 3$. 3. (C) Fixed $30 + 15$ per month → $C = 30 + 15m$. 4. (B) $10/15 = 2/3$; $x/6 = 2/3 \Rightarrow x = 4$. 5. (B) $3(9) - 2 = 25$. 6. (C) $20%$ of 80 = 16; $80 - 16 = 64$. 7. (C) $4x + 4 = 2x + 14 \Rightarrow 2x = 10 \Rightarrow x = 5$. 8. (B) $2:5$ with 20 pens → each part 10; pencils $= 5 \times 10 = 50$. 9. (A) Slope 5 is the predicted increase per unit $x$. 10. (A) $x^2 + 2x - 4x - 8 = x^2 - 2x - 8$. 11. (A) $\sqrt{81 + 144} = \sqrt{225} = 15$. 12. (B) $3^4 = 81$. 13. (C) $60/150 = 0.4$; $0.4 \times 1000 = 400$. 14. (C) $-b/2a = 8/2 = 4$. 15. (B) $24/a = 6 \Rightarrow a = 4$. 16. (A) $r^2 = 36 \Rightarrow r = 6$. 17. (B) Sum $= 6 \times 9 = 54$; known five sum to 48; sixth $= 6$. 18. (B) Base 1.05 → 5% increase per period. 19. (C) Add equations: $3x = 15 \Rightarrow x = 5$. 20. (C) $\pi (16)(5) = 80\pi$. 21. (14) Cross-multiply: $6(x-2) = 4(x+4) \Rightarrow 6x - 12 = 4x + 16 \Rightarrow 2x = 28 \Rightarrow x = 14$. 22. (3) Perpendicular slope $= -\tfrac12$; line $y = -\tfrac12 x + 5$; at $x=4$, $y = -2 + 5 = 3$.
Scoring & routing note
Count correct out of 22.
- 0–9: Module 2 would be the easier form — drill linear equations, slope, and ratios.
- 10–15: Solid — target quadratics, systems, and exponential models.
- 16–22: You'd route to the harder Module 2 — focus on Advanced Math and Geometry/Trig.
Pedagogy: distractors target specific errors — Q9 confuses slope with intercept, Q10 mishandles the middle term, Q18 confuses growth factor with percentage. Review why each wrong answer tempts.