AP Physics - Problem Drill 02: Basic Math for Physics No. 1 of 10 1. Solve the following equation for time (with the correct number of significant figures): (A) 6.79 s (B) 6.785 s (C) 0.147 s (D) 0.1474 s (E) 6.7853 s A. Correct! Solve for a variable on the bottom by first moving it to the top. The answer should have the least number of significant figures in the problem (3 in this case). B. Incorrect! The answer should have the least number of significant figures in the problem. Solve for a variable on the bottom by first moving it to the top. The answer should have the least number of significant figures in the problem. The answer should have the least number of significant figures in the problem. time = 6.7853 s 2.25 has 3 significant figures; 15.627 has 5 significant figures. The answer should have 3 significant figures. The correct answer is (A).
No. 2 of 10 2. If a problem contained these two measurements, 1.546 m and 1.34 m, what is the correct answer to 1.546 m + 1.34 m? (A) 2.886 m (B) 3 m (C) 2.9 m (D) 2.89 m (E) 2.88 m Too many decimal places. B. Incorrect! Too few decimal places. Too few decimal places. D. Correct! 1.34 m has 2 decimal places, so add the numbers first and then round to 2 decimal places. E. Incorrect Always round to the correct number of decimal places last. 1.34 m has 2 decimal places, so add the numbers first and then round to 2 decimal places. 1.546 m + 1.34 m = 2.886 m Round the answer to 2 decimal places. 2.89 m The correct answer is (D).
No. 3 of 10 3. If a problem contained these two measurements 4.65 N and 3.021N, what 4.65N would be the correct answer for the calculation: (A) 1.53 (B) 1.54 (C) 1.539 (D) 1.5392 (E) 1.53922 Check for errors in rounding. 3.021N B. Correct! The least number of significant figures in the given measurements is 3, so use 3 sig figs in the answer. Too many significant figures. Too many significant figures. Too many significant figures. The least number of significant figures in the given measurements in 3 sig. fig., so use 3 sig. fig. in the answer. The correct answer is (B).
No. 4 of 10 4. Write out the following: 1.756 10-6 (A) 1756000 (B) 0.0000001756 (C) 0.000001756 (D) 1756 (E) 1.756 A negative exponent indicates a tiny number. B. Incorrect! Move the decimal place the number of times indicated by the exponent rather than giving that many zeros. C. Correct! Move the decimal six times to the left to create a tiny number. An exponent of -6 implies a small number (much smaller than 1). This answer leaves the 10-6 out. Move the decimal place 6 times (given by the exponent) The exponent is negative so move the decimal to the left to make the number a small number (<1). 0.000001756 The correct answer is (C).
No. 5 of 10 5. Calculate 3.2 x 10 5 + 2.0 x 10 4 (A) 5.2 x 10 9 (B) 5.2 x 10 20 (C) 5.2 x 10 5 (D) 3.4 x 10 5 (E) 3.22 x 10 5 Science notation rule 1 does not apply if there are different powers of 10. B. Incorrect! Science notation rule 1 does not apply if there are different powers of 10. Science notation rule 1 does not apply if there are different powers of 10. D. Correct! Science notation rule 1 does not apply if there are different powers of 10, so you need to write out these numbers before adding them. You can then write the answer using scientific notation. Check you wrote out both numbers correctly. Science notation rule 1 does not apply if there are different powers of 10, so you need to write out these numbers before adding them. You can then write the answer using scientific notation. 3.2 x 10 5 = 320000 2.0 x 10 4 = 20000 Add = 340000 Use scientific notation = 3.4 x 10 5 The correct answer is (D).
No. 6 of 10 6. Which of these equations is correct? (A) sin = opposite/adjacent (B) cos = opposite/hypotenuse (C) tan = opposite/hypotenuse (D) sin = adjacent/hypotenuse (E) tan = opposite/adjacent A. Incorrect The equation for sin contains the hypotenuse. B. Incorrect The equation for cos contains the adjacent. C. Incorrect The equation for tan does not contain the hypotenuse. D. Incorrect The equation for Sin contains the opposite. E. Correct Tan = opposite/adjacent To remember the trigonometric functions for sin, cos, and tan use SOH CAH TOA The correct answer is (E).
No. 7 of 10 7. Solve for the missing angle as shown. (A) 0.0073 (B) 0.43 (C) 24.6 (D) 65.4 (E) 22.6 Use arc sin to solve for angle, not sin. B. Incorrect Your calculator is in radians. Switch it degrees. C. Correct! Use arc sin to solve for angle. You used cos (which uses adjacent and hypotenuse). You used tan (which uses opposite and adjacent). Use arc trig functions to solve for an angle. You know the hypotenuse and the side opposite of the missing angle. Opposite and hypotenuse are sin. sin 1 opposite hypotenuse 3.7m sin 1 8.9m The correct answer is (C).
No. 8 of 10 8. Solve the following ( x is time in seconds): 2x 2 + 4x 3 = 0 (A) 0.33 s (B) 0.58 s (C) 2.6 s (D) 2.58 s (E) 0.58 s and -2.58 s You forgot to square the b in the quadratic formula (inside the square root). B. Correct! Use the quadratic formula to solve for x and discount the negative answer. The time can t be a negative number. You used the quadratic formula correctly, but a negative result is not possible for time. You used the quadratic formula correctly and got both answers, but a negative result is not possible for time. The problem can be solved by using the quadratic equation. When ax 2 +bx + c = 0 then 2x 2 + 4x 3 = 0 so a = 2, b = 4, c = -3 x = 0.58 and x = -2.58 time cannot be negative so the correct answer is 0.58 s The correct answer is (B).
No. 9 of 10 9. Use your calculator to solve: ( 2.5 x 10 3 ) x ( 1.7 x 10-4 ) ( 7.5 x 10 8 ) x ( 2.2 x 10 5 ) (A) 1.2 10 16 (B) 1.2 10 12 (C) 2.6 10-15 (D) 1.2 10-4 (E) 2.58 10-15 Use the EE or EXP button in place of x10. B. Incorrect! Use the EE or EXP button in place of x10. C. Correct! Use the EE or EXP button in place of x10 and use the divide key when dividing by more than one number. Use the divide key when dividing by more than one number. You use the correct method but this answer has too many sig. figs. ( 2.5 x 10 3 ) x ( 1.7 x 10-4 ) ( 7.5 x 10 8 ) x ( 2.2 x 10 5 ) Enter into your calculator: 2.5E3 1.7E-4 7.5E8 2.2E5 The correct answer is (C).
No. 10 of 10 10. Which of these is the correct method of entering into the calculator the equation? 35.1-6.7 x 2 2.1 x 10 3 + 1.3 x 10 2 (A) 35.1 6.7 x 2 2.1 x 10 3 + 1.3 x 10 2 (B) 35.1 6.7 x 2 (2.1E3 + 1.3E2) (C) (35.1 6.7) x 2 2.1 x 10 3 + 1.3 x 10 2 (D) (35.1 6.7) x 2 2.1E3 + 1.3E2 (E) 35.1 6.7 x 2 (2.1 x 10 3 + 1.3 x 10 2 ) Use the format 2.1E3 not 2.1 x 10 3 B. Correct! Use the EE or EXP key and put the addition in parenthesis to ensure it happens before the division. The parenthesis around the subtraction will mean that this happens before the multiplication. Use the format 2.1E3 not 2.1 x 10 3 The parenthesis around the subtraction will mean that this happens before the multiplication. Use the format 2.1E3 not 2.1 x 10 3 Use the EE or EXP key and put the addition in parenthesis to ensure it happens before the division. The correct answer is (B).