EveryDay Science Math Expectations

The math requirements for acceptance at Rivier College are two years of algebra and a year of geometry. Some sections of this course require basic arithmetic and basic algebra skills as reviewed below.

1. You should be able to do normal arithmetic calculations, know the order of operations, understand scientific notation and be able to do the calculations in the microsoft calculator or a hand held calculator:

1. (10)(5)/(2) = 25


2. 10 + 5/2 = 12.5


3. (10 + 5)/2 = 7.5


4. (4)(3)/[(2)(2)] = 3


5. 2 x 10² = 2 x 100 = 200


6. 2 x 10^-2 = 2/100 = 0.02


7. (2 x 10²)(3 x 10^-2) = 6


8. (4 x 10²) + (2 x 10²) = 6 x 10²


9. (3 x 10²) + (4 x 10³) = 4.3 x 10³
       Note: The same as 300 + 4000 = 4300


10. Etc.

2. You should be able to solve for an unknown in an equation:

1. 6 = 2x;
   x = 6/2 = 3
2. x + 10 = 8;
   x = 8 - 10 = -2
3. 2(2 + x) = 6;
   2 + x = 6/2; x = 6/2 - 2 = 1
4. (4 + x)/2 = 4.5;
   4 + x = (2)(4.5); x = (2)(4.5) - 4 = 5
5. d = m/V;
   m = dV and V = m/d
6. 2x + (0.5)(6) = 5;
   2x = 5 - (0.5)(6); x = [5 - (0.5)(6)]/2 = 1
7. 32 = 2x²;
   x² = 32/2; x =(32/2)^½ = 4 (or -4)
      (A number raised to the ½ is the same as the square root of the number.)
8. 9 = 3x² + 6;
   3x² = 9 - 6; x² = (9 - 6)/3; x = [(9 - 6)/3]^½ = 1 (or -1)
9. 9x = 3x + 6;
   9x - 3x = 6; 3(3x - x) = 6; 2x = 6/3; x = 6/[(2)(3)] = 1

3. You should be able to use known values to calculate an unknown.

1. v_o = 2; a = 9.8; t = 5
   v = v_o + at = 2 + (9.8)(5) = 51
2. v_o = 2; a = 9.8; t = 5
   v² = v_o² + at² = (2)² + (9.8)(5)² = 249
   v = (249)^½ = 15.78 (or -15.78)
3. v_o = 2; a = 9.8; t = 5
   s = v_ot + ½at² = (2)(5) + ½(9.8)(5)² = 132.5
4. s = 2; a = 0; t = 5; s = v_ot + ½at²
   v_o = (s - 0)/t = 2/5 = 0.4
5. v = 15; v_o = 2; a = 9.8; v = v_o + at
   t = (v - v_o)/a = (15 - 2)/9.8 = 1.33

Here are a few practice problems:

1. x = 2 + 10/5
2. x = (2 + 10)/5
3. x = 2 + (10 - 5)/5
4. x = 2 + 10 - 5/5
5. x = (2)(5) + 10/5
6. x = 2/4 + 10/5
7. x = 2/(4 + 10)
8. 2x = 2 + 10
9. 3x = 2x + 5
10. 16 = 2x² + 5
11. x² = 2x² - 16
12. 4 - x = 2x + 10
13. x + 15 = 2/4
14. 6x = 2x + 10/5
15. v_o = 3; a = 6; t = 2; v = v_o + at;; v = ?
16. v_o = 5; a = 3; t = 8; v² = v_o² + at²; v = ?
17. v_o = 8; a = 2; t = 3; s = v_ot + ½at²; s = ?
18. s = 4; a = 0; t = 2; s = v_ot + ½at²; v_o = ?
19. v = 10; v_o = 3; a = 7; v = v_o + at; t = ?

Here are the answers:

1. x = 2 + 10/5; x = 4
2. x = (2 + 10)/5; x = 12/5 = 2.4
3. x = 2 + (10 - 5)/5; x = 3
4. x = 2 + 10 - 5/5; x = 11
5. x = (2)(5) + 10/5; x = 12
6. x = 2/4 + 10/5; x = 2.5
7. x = 2/(4 + 10); x = 2/14 = 0.143
8. 2x = 2 + 10; x = 6
9. 3x = 2x + 5; x = 5
10. 16 = 2x² + 5; x = [(16 - 5)/2]^½ = [11/2]^½ = 2.345 (or -2.345)
11. x² = 2x² - 16; 16 = 2x² - x²; x = 4 (or -4)
12. 4 - x = 2x + 10; 3x = -6; x = -2
13. x + 15 = 2/4; x = -14.5
14. 6x = 2x + 10/5; 4x = 2; x = 0.5
15. v = v_o + at = 3 + (6)(2) = 15
16. v² = v_o² + at² = (5)² + (3)(8)² = 217
    v = (217)^½ = 14.73 (or -14.73)
17. s = v_ot + ½at² = (8)(3) + ½(2)(3)² = 33
18. v_o = (s - 0)/t = 4/2 = 2
19. t = (v - v_o)/a = (10 - 3)/7 = 1

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David R. Burgess
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