MATH161, Algebra/Trigonometry Check
This test is for your own checking. If you find this kind of problems hard, you are likely to
have problems with MATH 161.
1. Expand and simplify. (2x + 5)2 =
For problems 2-5, simplify the following expressions, if possible (combine like terms, no
negative exponents, evaluate numerical coefficients, etc).
2.
3.
4.
en+1
(n+1)!
en
n!
√
x2 + 4
(n+1)xn+1
2n+1
nxn
2n
√
(x2 )2 y 4/3 z
5.
x(y 3 )2 z 2
6. Solve x2 + 5x + 6 = 0.
7. Solve for x, i.e. find the values of x described by the following expression: |x − 1| < 3/2
8. If |2x + 1| = 3, then x =
1
9. sin
3π
=
2
10. cos
5π
=
4
11. Given that sin θ = 1/2, find cos θ.
1
12. Solve for x, 0 ≤ x < 2π: cos(2x) = .
2
√
√
13. If tan θ = − 3 and sin θ = 3/2, then cos θ =
14. If x = 2 sin θ, then √
1
=
4 − x2
15. If x = 3 tan θ, then (9 + x2 )3/2 =
16. cos 0 =
17. Write x2 + 50x + 32 in the form (x + a)2 + b with a and b real numbers
2