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) 9 B) 2 C) 3 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 = 30m + 15 B) C = 15m C) C = 30 + 15m D) C = 45m
4. If x/6 = 10/15, what is x?
A) 4 B) 9 C) 6 D) 3
5. If f(x) = 3x² − 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) $64 C) $60 D) $76
7. Solve 4(x + 1) = 2x + 14.
A) 6 B) 4 C) 5 D) 3
8. The ratio of pens to pencils is 2:5. If there are 20 pens, how many pencils are there?
A) 25 B) 8 C) 50 D) 40
9. A line of best fit is ŷ = 5x + 20. By how much does the model predict y increases per unit increase in x?
A) 4 B) 25 C) 20 D) 5
10. Which is equivalent to (x − 4)(x + 2)?
A) x² − 6x − 8 B) x² − 8 C) x² + 2x − 8 D) x² − 2x − 8
11. A right triangle has legs 9 and 12. What is the hypotenuse?
A) 21 B) √63 C) 15 D) 18
12. If 3ˣ = 81, what is x?
A) 4 B) 27 C) 3 D) 5
13. In a survey, 60 of 150 students bike to school. How many of 1,000 students would be expected to bike?
A) 300 B) 250 C) 600 D) 400
14. The equation y = x² − 8x + 12 has its vertex at x =
A) 8 B) 4 C) 2 D) 6
15. If g(x) = 24/x and g(a) = 6, what is a?
A) 4 B) 18 C) 6 D) 2
16. A circle has equation (x+3)² + (y − 2)² = 36. What is the radius?
A) √6 B) 9 C) 36 D) 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) 9 C) 8 D) 6
18. A quantity grows by P = 800(1.05)ᵗ. What does 1.05 represent?
A) a 50% increase B) a 5% increase per period C) the starting amount D) a 5% decrease
19. If 2x + y = 13 and x − y = 2, what is x?
A) 5 B) 4 C) 6 D) 3
20. A cylinder has radius 4 and height 5. What is its volume? (V = πr²h)
A) 20π B) 80π C) 40π D) 100π
Questions 21–22 are student-produced responses.
21. If (x − 2)/4 = (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 | D | 19 | A |
| 2 | C | 8 | C | 14 | B | 20 | B |
| 3 | C | 9 | D | 15 | A | 21 | 14 |
| 4 | A | 10 | D | 16 | D | 22 | 3 |
| 5 | B | 11 | C | 17 | D | ||
| 6 | B | 12 | A | 18 | B |
Key distribution (MC): A×5, B×5, C×5, D×5.
Worked solutions
1. (A) 5x = 15 ⇒ x = 3.
2. (C) (11 − 2)/(3 − 0) = 9/3 = 3.
3. (C) Fixed 30 + 15 per month → C = 30 + 15m.
4. (A) 10/15 = 2/3; x/6 = 2/3 ⇒ x = 4.
5. (B) 3(9) − 2 = 25.
6. (B) 20% of 80 = 16; 80 − 16 = 64.
7. (C) 4x + 4 = 2x + 14 ⇒ 2x = 10 ⇒ x = 5.
8. (C) 2:5 with 20 pens → each part 10; pencils = 5 × 10 = 50.
9. (D) Slope 5 is the predicted increase per unit x.
10. (D) x² + 2x − 4x − 8 = x² − 2x − 8.
11. (C) √(81 + 144) = √225 = 15.
12. (A) 3⁴ = 81.
13. (D) 60/150 = 0.4; 0.4 × 1000 = 400.
14. (B) −b/(2a) = −(−8)/(2 × 1) = 4.
15. (A) 24/a = 6 ⇒ a = 4.
16. (D) r² = 36 ⇒ r = 6.
17. (D) Sum = 6 × 9 = 54; known five sum to 48; sixth = 6.
18. (B) Base 1.05 → 5% increase per period.
19. (A) Add equations: 3x = 15 ⇒ x = 5.
20. (B) π(4)²(5) = π × 16 × 5 = 80π.
21. (14) Cross-multiply: 6(x − 2) = 4(x+4) ⇒ 6x − 12 = 4x + 16 ⇒ 2x = 28 ⇒ x = 14.
22. (3) Perpendicular slope = −1/2; line y = −(1/2)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.