This document contains 17 math problems involving solving systems of equations, simplifying expressions, evaluating functions, working with scientific notation, and other algebra topics. The problems range in complexity and cover multiple concepts.

1. Test 4 Sample Math 123a
Solve the following system
a. by substitution b. by elimination
x=6+y x –y =6
x + 2y = - 3 x + 2y = -3
Solve the following systems by any method
A. x + y = 6 B. y = 4 + x C. 3x – 2y = 3
x–y=2 x + 2y = 6 4x – 3y = -1
Simplify
1. 3x + 7(2x – 5) 2. 3(x + 7) – 2(3 – 4x)
3. 3x(4x2 – 2x + 1) – 4x2(5 – 3x) 4. 2x(xy – x) + x2(3 – 5y)
5. (3x + 7)(2x – 5) 6. (2x + 5)(x – 2) + (x – 1)(3x + 2 )
7. (3x – 5 ) 2 8. (4x – 5)(4x + 5)
9. (2x –3)(x + 1) – (4x – 3)(x – 1) 10. (2x + 3)(x – 3) – (2x – 3)2
11. a. Evaluate –2x2y – 3xy2 if y = –2. b. Evaluate –2x2y – 3xy2 at (3, –2).
12. Let x = price / lb of peanuts, y = price / lb for cashews. Find x and y given the following invoice.
Order 1. (in lb) Order 2 (in lb)
Cashews 2 3
Peanuts 3 1
Cost $16 $16
13. Peanuts costs $2/lb, cashews costs $8/lb. How many lbs of each are needed to get 50 lbs of
peanut–cashews–mixture that cost $3/lb? Write down what x and y represent and make a table.
14. We have $8,000 in two accounts, one at 8% and the other at 6%. Their combined interest is $600. How
much is in each account?
15. A. Calculate and leave the answer B. Calculate and leave the answer
as a reduced fraction 40 * 3 – 3 * 2 2 as a reduced fraction 40 * 3-1 – 3 * 2 -2
16. A. Write the number 2,340,000,000 in B. Convert 3.76 x 10 -5 into a decimal
the scientific notation
C. compute 2.3x1060 x 8.9 x10-38 and put the answer in the scientific notation
17. Simplify and leave the answer in positive exponent:
2 4 2 4
21 x y x y
A. 5 2
B. 5 2
14 x y x y