Math 1 Final Review 1

Linear Equations

100

Solve for x.

x - 7 = 15

x = 22

200

Solve for a.

2a + 9 = 3

a = -3

300

Solve for t.

t - 2 = -t + 3

t = 5/2

400

Solve for p.

7p + 8 = 22 - 4p

p = 14/11

500

Solve for y.

2/5 x - 9/10y + 1 = 4/3 x + 1/3 - y

y = -2/3 x - 20/3

Inequalities

100

Solve for x.

2x < 4

x < 2

200

Solve for s.

13s - 4 > 22

s > 2

300

Solve for k.

4k - (3 + 3k) > 2

k > 5

400

Solve for n.

4n + 3 < 6n + 8 - 2n

no solution

500

Solve for c.

-1 < 45c + 2 < 92

-3/45 < c < 2

Linear Systems

100

Solve the system.

y = 7

x = 1

(1,7)

200

Solve the system.

y = x

y = 3

(3,3)

300

Solve.

y = x +1

y = -x +3

(1,2)

400

Solve.

3x - 2y = 7

y = 4x + 3/2

(-2 , -13/2)

500

Explain why this system has no solution.

5y + 2x = 17

-1/5 x = 1/2 y - 1

They have the same slope, m=-2/5, but different intercepts (b₁=17, b₂=2)

Sequences

100

Find an expression for the n^th term of the sequence.

1, 3, 5, 7, ...

2n - 1

200

Find an expression for the n^th term.

3, 6, 12, 24, ...

3(2)ⁿ

300

Write a recursive rule for the sequence.

100, -50, 25, -12.5, ...

a₁=100; a_n+1=(-1/2)a_n

400

Find the seventh term.

a₁=1

a₂=7 

a_n=(a_n-1 - a_n-2)/2

a₇ = 9/8

500

Write a rule for the sequence.

1, 3, 6, 10, 15, ...

a_n = n(n+1)/2

OR

a₁ = 1;  a_n = n + a_n-1

Absolute Value

100

Solve for P.

|P| = 6.725

P = 6.725 or -6.725

200

Solve for w.

|3w - 12| = 21

w = -3 or 11

300

Solve for t.

|4t - 6| = |3t +9|

t = 15 or -3/7

400

Explain why the following equation has only one solution.

|7x - 14| = 0

-0 = 0

500

Describe the solution to the inequality in terms of distances.

|x - a| < b

All solutions are no further than a units from b.