Crazy Ideas and Scientific Theories
Mathematical Review

The math requirements for acceptance at Rivier College are two years of algebra and a year of geometry. Although this course doesn't have any investigation that specifically requires algebra, there may be some sections of this course where the basic arithmetic and algebra skills as reviewed below could be useful.

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:

(10)(5)/(2) = 25
10 + 5/2 = 12.5
(10 + 5)/2 = 7.5
(4)(3)/[(2)(2)] = 3
2 x 10² = 2 x 100 = 200
2 x 10^-2 = 2/100 = 0.02
(2 x 10²)(3 x 10^-2) = 6
(4 x 10²) + (2 x 10²) = 6 x 10²
(3 x 10²) + (4 x 10³) = 4.3 x 10³
    Note: The same as 300 + 4000 = 4300
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