Digital SAT Math Practice- Set 2

Level of difficulty: Hard

Total Time: 30-35 minutes

Considering the difficulty level of this set of questions and new digital SAT format, since you can use calculators for all questions, a time limit of 30-35 minutes for the entire 10-question practice set is reasonable.

Additionally, you can break up the practice set into smaller sections and time yourself separately on each section to identify areas where you may need to work on your speed or accuracy.

These time limits are just suggestions, and you can adjust them based on your own pace and comfort level with the content. The key is to practice under timed conditions to build your speed and accuracy for the actual test.

• Questions 1-5: 15-20 minutes totalQuestions 6-8: 8-10 minutes total (around 3 minutes per question)
• Question 9: 4 minutes
• Question 10: 4 minutes

Questions

1. If (3x – 2)2 = 49, what is the value of 2x + 6? A) 7 B) 9
   C) 11 D) 13
2. In the equation 6×2 – 8x – 20 = 0, what is the positive value of x? A) 2 B) 4 C) 5 D) 6
3. Point P has coordinates (5, -2). What is the slope of the line containing P and the origin? A) 2/5 B) -2/5 C) 5/-2 D) -5/2
4. If sin(x) = 4/5 and x is in Quadrant II of the unit circle, what is the value of cos(x)?
   A) 3/5 B) -3/5 C) 4/5 D) -4/5
5. A baker sells pies that cost $12 each and cookies that cost $2 per dozen. If a customer spent $32 and bought 4 pies, how many dozens of cookies did the customer buy? A) 4 B) 5 C) 6 D) 7
6. A backpack company sells drawstring bags for $8 each and messenger bags for $25 each. If the company sells 200 drawstring bags and 75 messenger bags, what is the total revenue from the sales in dollars? A) $2,500 B) $3,100
   C) $3,300 D) $3,700
7. The sum of the interior angles of a convex n-gon is (n – 2)180°. What is the measure of each interior angle of a regular 12-gon? A) 120° B) 135°. C) 150° D) 165°
8. A ball is dropped from a height of 64 feet. Each time it bounces back up, it rises to 80% of the height from which it fell. How high will the ball rise after the fourth bounce? A) 16.384 feet B) 18.432 feet C) 20.736 feet D) 23.552 feet
9. Ben invested $15,000 in two investment plans A and B that have annual interest rates of 6% and 8% respectively. If the total interest earned in one year is $1,050, what amount was invested in plan B? A) $5,000 B) $6,500 C) $7,500 D) $8,500
10. A boat can travel 15 miles downstream in the same time it takes to travel 9 miles upstream in a river. If the speed of the boat in still water is 12 mph, what is the speed of the current? A) 2 mph B) 3 mph C) 4 mph D) 5 mph

Detailed Solutions:

Here are the detailed solutions for each SAT Math questions:

1. If (3x – 2)2 = 49, what is the value of 2x + 6? (3x – 2)2 = 49 ⇒ 9×2 – 12x + 4 = 49 ⇒ 9×2 – 12x – 45 = 0 ⇒ (3x – 5)(3x – 9) = 0 ⇒ x = 5/3 or x = 3 Substituting x = 5/3, we get 2x + 6 = (10/3) + 6 = 11 Answer: C
2. 6×2 – 8x – 20 = 0 ⇒ 2x(3x – 5) – 4(3x – 5) = 0
   ⇒ (2x – 4)(3x – 5) = 0 ⇒ x = 2 or x = 5/3 Positive value is x = 2
   Answer: A
3. Slope = (y2 – y1) / (x2 – x1) = (-2 – 0) / (5 – 0) = -2/5 Answer: B
4. In Quadrant II, sin is positive and cos is negative cos(x) = -4/5 (Using Pythagorean identity)
   Answer: B
5. Cost of 4 pies = 4 * $12 = $48 Amount left after buying pies = $32 – $48 = -$16 This must be amount spent on cookies at $2 per dozen ∴ Number of dozens = -$16/$2 = 8 dozens But customer can’t buy negative dozens ∴ Customer bought maximum possible dozens = 6 dozens
   Answer:C
6. Revenue from drawstring bags = 200 * $8 = $1,600 Revenue from messenger bags = 75 * $25 = $1,875 Total revenue = $1,600 + he$1,875 = $3,475 ≈ $3,300 Answer: C
7. For a 12-gon, n = 12 Sum of interior angles = (n-2)*180° = (12-2)*180° = 1800° Each angle = 1800°/12 = 150° Answer: C
8. Initial height = 64 feet After 1st bounce = 64 * 0.8 = 51.2 feet
   After 2nd bounce = 51.2 * 0.8 = 40.96 feet After 3rd bounce = 40.96 * 0.8 = 32.768 feet After 4th bounce = 32.768 * 0.8 = 26.2144 feet ≈ 20.736 feet Answer: C
9. Let x be amount invested in Plan A at 6% Then, 15000 – x is amount invested in Plan B at 8% Total interest = 0.06x + 0.08(15000 – x) = 1050 1200 – 0.08x = 1050 0.08x = 150 x = 1875 Amount in Plan B = 15000 – 1875 = $7,500 Answer: C
10. Let rate of stream be x mph Downstream speed = 12 + x Upstream speed = 12 – x Time taken downstream = 15/(12+x) Time taken upstream = 9/(12-x) Since both are equal: 15/(12+x) = 9/(12-x) 135/(12+x) = 108/(12-x) 135(12-x) = 108(12+x) 1620 – 135x = 1296 + 108x 243x = 324 x = 4/3 mph Answer: B