**Scientific Notation**

1. Write the following numbers in scientific notation.

(a) 80,516

(b) 0.0751

(c) 3,520,000

(d) 0.000 000 081

2. Evaluate (without a calculator):

3. Evaluate, in scientific notation (try to do the exponents without a calculator):

4. Evaluate (without a calculator):

**Linear Equations – one variable**

5. Solve for x:

**Simultaneous Equations**

6. Solve for both unknowns:

Hint for (c): Resist the temptation to multiply both
equations by xy to clear the denominators.

Just let u = 1/x and v = 1/y and solve first for u and v, then find x and y.

**Polynomials**

7. Multiply

(3x^{2} + 4x – 5) by (2x –1)

**Quadratic Equations**

8. Solve these quadratic equations by completing the square:

(a) x^{2} – 4x – 12 = 0

(b) 9x^{2} – 6x – 1= 0

(c) x + 2x^{2} = 5/8

(d)(x + 2)(2x – 1) + 3(x +1) = 4

9. Solve these quadratic equations by the general quadratic formula:

(a) 2x^{2} = 9x – 8

(b) Solve for t:

(c) 5x (x + 2) = 2(1 – x)

(d)0.2x^{2} –1.5x = 3

(e) Solve for x: x^{2} – 2sx =1 – 2s^{2}

**Combining Fractions**

10. Evaluate the following combinations of fractions,
bringing the result to a single denominator

in each case and canceling where possible:

**Laws of Exponents**

11. Evaluate (without a calculator):

12. Solve for x (without a calculator):

**Fractional Exponents**

13. Simplify and evaluate (without a calculator):

**Exponentials as Functions**

14. Combine and simplify (without a calculator):

**Logarithms
**

15. Find (without a calculator):

**Using Logarithms
**

16. Given find (without a calculator):

17. Use your calculator to evaluate the antilogs (base 10) of the following logarithms:

(a) 5

(b) 3.30103

(c) –0.69897

(d) the sum of (b) and (c)

(e) the difference of (b) and (c)

**Right Triangles**

SOHCAHTOA

cosecant = 1/sine; secant = 1/cosine; cotangent =
1/tangent

(adjacent)^{2} + (opposite)^{2} = (hypotenuse)^{2}

18. Cover up the formulas above. Then, for the triangle
shown here, find

(without a calculator):

(a) sin θ

(b) cos θ

(c) tan θ

(d) csc θ

(e) sec θ

(f) cot θ

19. For this triangle, find (without a calculator):

(a) sin (90° – θ)

(b) sin θ + cos (90° – θ)

(c) tan θ + cot (90° – θ)

(d) sec θ + csc (90° – θ)

20. Sorry folks. No picture this time. You draw the
triangle. If A is an acute angle and sin A =

7/25, find all the other trigonometric functions of the angle A:

21. For the triangle labeled here, find:

(a) a, if c = 5 and θ = 20°

(b) b, if a = 8 and ø = 40°

(c) c, if b = 6 and θ = 53°

22. For the previous triangle, find all angles and lengths of the sides if:

(a) b = 6, θ = 30°

(b) a = 13, b = 13

(c) c = 10, ø = 30°

(d) c = 12, θ = 45°

(e) c = 1, b =

(f) c = 4, b = 4

**Geometry**

**
**

23. Find three similar triangles in the figure shown, and
show that s^{2} = rt

**Graphing (Analytic Geometry)**

**Straight Lines
**(y = mx + b, where m = slope and b = y-intercept)

24. Draw a set of xy axes, marked off in equal intervals
between –5 and +5 for both x and y, and

sketch straight lines with the following values of m and b:

(a) m = +2, b = –4

(b) m = –1, b = +4

(c) m = +1/2, b = +1

(d) m = –1, b = –1/3

25. Draw another set of xy axes, marked off as in exercise
24, and draw the following lines, all

passing through the point (2, 1):

(a) m = 0 (c) m = ∞

(b) m = +3/2 (d) m = –2/3

26. Draw another set of xy axes, marked off as before, and
draw lines described by the following

equations:

(a) x + y = 2 (c) x + 2y + 4 = 0

(b) 2x – y + 3 = 0 (d) x – 4 = 0

**Parabolas
**(x = ay

(y = ax

27. Take some squared paper and sketch the following parabolas:

(a) y = –x^{2}

(b) x = 2(y -1)^{2}

(c) y = (x + 2)^{2}