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Name _____________________________________
Final Review
Final Review #5
Date ____________
Math 8H
1) Solve each system of equations algebraically.
a)
y = 5x + 8
y = -10x + 3
b)
10x + 8y = 2
8x + 6y = 1
c)
3x – 6y = 30
y = -6x + 34
2) Solve each word problem algebraically by setting up a system of equations. Show all work!
a) If five times the smaller of two numbers is subtracted from twice the larger, the result is 16. If the
larger is increased by 3 times the smaller, the result is 63. Find the numbers.
b) The owner of a men’s clothing store bought 6 shirts and 8 hats for $70. A week later, at the same
prices, he bought 9 shirts and 6 hats for $66. Find the price of a shirt and the price of a hat.
3) Solve the following system of equations graphically.
4x + 3y = 6
5=x-y
4) Graph the following system of inequalities. Identify a point in the solution set.
x + 2y ≤ 8
9x – 3y < -6
5) Determine if (2, 1) is a solution to the system of inequalities given.
a)
y – 3x < 7
b)
2x + y ≥ -6
y > 2x + 5
3x + 4y < 12
6) The world population is about 7 billion. There are 4.6 x 10 7 ants for every human on the planet. About how
many ants are there in the world? Express your answer in scientific notation.
7) The distance to the Moon from Earth is 5.05 × 10 8 miles. The distance to the planet Pluto is 5.05 × 10 16 miles.
How many times the distance to the Moon is it to Pluto? Express your answer in scientific notation.
8) Let f(x) = x4 – 3x. What is f(-2)?
9) Simplify:
a)
2 52
10) What are the coordinates of (-9, 3) after a:
b)
a) rx-axis
5 x 27
b) T-5,
1
c) ry-axis