Rational vs. Irrational
Which number is the square root of 53 closest to?
A) 4
B) 6
C) 8
D) 7
Answer:
D) 7
square root of 53 is 7.2 and is in between the square root of 49 and 64, which are 7 and 8.
Simplify the expression with exponents.
y^ -4 * y ^ -5
Answer: y^ -9 or 1/y^9
Remember when multiplying you add the exponents!
Write the following number in scientific notation:
4,500
Answer: 4.5 x 10^3
Step by Step:
1) Make the smallest whole number possible by the moving the decimal point 3 places to the left.
2) Rewrite in scientific notation
Remember when moving the decimal to the left the exponent will be positive!
Solve and tell whether the equation has 1 solution, no solution, or infinitely many solutions.
-3x + 8 - 5x = 21 - 8x
Answer: No Solution
Step by Step:
-3x + 8 - 5x = 21 - 8x
Combine like terms
-3x-5x + 8 = 21 - 8x
-8x + 8 = 21 - 8x
Solve for x
8x+ -8x + 8 = 21 - 8x+8x
8 = 21
Find the slope of the line through two given points.
(7,7) and (9,9)
Answer: slope = 1
Use formula: y2-y1 / x2-x1
9-7 / 9-7 = 2/2=1
Which of the following is a rational number?
A) square root of 6
B) 2 pi
C) square root of 196
D) square root of 8
Answer: C) square root of 196
square root of 196 is 14
Simplify the expression with exponents.
(n^ -2)^ -2
Answer: n^4
Write the number in scientific notation:
0.0578
Answer: 5.78 x 10^-2
Step by Step:
1) Move the decimal over to the right 2 places to make the smallest whole number possible.
2) Rewrite in scientific notation.
Remember when moving the decimal place to the right the exponent will be negative!
Solve and tell whether the equation has 1 solution, no solution, or infinitely many solutions.
-2y - 7 + 5y = 13 - 2y
Answer: One solution; y = 4
Go over on the white board step by step!
Find the slope of the line through two given points.
(-8, 17) and (-5, 19)
Use formula: y2-y1 / x2-x1
19-17 / -5- -8= 2/3
Put the following fractions in order from LEAST to GREATEST:
5/7, 2/3, 3/4, 8/11
Answer:
2/3, 5/7, 8/11, 3/4
Simplify the expression with exponents.
w^5 / w^ -7
Answer: w^12
Step by Step:
1)Change the division problem into a multiplication problem by multiplying by w^-7.
2) Now the problem should look like this: w^5-(-7). Combine the exponents by adding them together. The two negative will make a positive, so it will be w^5+7, which is w^12.
Write the number in standard form:
7.65 x 10^3
Answer: 7,650.
Remember when the exponent is positive you are moving the decimal place to the right.
Solve and tell whether the equation has 1 solution, no solution, or infinitely many solutions.
6 + 3m - 4 = -5 + 3m + 7
Answer: Infinite Solutions 0=0
Show step by step on white board
Yamini starts a savings account with $12. She will put in an equal amount each week. After 6 weeks, she will have $54.
Answer: y = 7x + 12.
Order the following decimals from GREATEST to LEAST:
2.022, 202.2, 2.202, 20.22, 2.222
Answer:
202.2, 20.22, 2.222, 2.202, 2.022
Simplify the expression with exponents.
4^0 * 4^ -3
Answer: 1/64
Step by Step:
1) 4^0=1
2) 1*4^-3= 4^-3
3) Flip the base and exponent to get rid of the negative exponent and simplify.
1/ 4^3
1/64
Write the number in standard form:
4.6 x 10^-5
Answer: 0.000046
Remember when the exponent is negative you will move the decimal place to the left, which makes the number smaller.
Solve system of equations using substitution.
y=4x
2y+ 2.5x = 105
Answer: x=10, y=40
Use the top equation and plug 4x in in y's place in the 2nd equation find x, than plug x's value back into the top equation to find y. Show on white board!
Give the rate of change and the initial value from each description.
Jordan has some music books. He will buy 9 new music books each year. He will have 52 music books in 5 years.
Rate of change =
Initial Value=
Answer: Rate of change= 9
Initial Value = 7
Explain on white board
Draw a number and plot and label the following points:
P= -2 3/4
Q= - 2 1/4
R= - 1 3/4
S= -1 1/4
Answer: Check the number line
Simplify the expression with exponents.
(3^ -2)^-2
Answer: 81
Step by Step:
1) Multiply the exponents together: -2*-2, now it will be 3^4.2) Simplify 3^4 = 3*3*3*3= 81
Write the number in scientific notation:
0.1456
Write the number in standard form:
8.0 x 10^7
Answer:
0.1456 = 1.456 x 10^-1
8.0 x 10^7 = 80,000,000
Solve system of equations by any method.
3x - 4y = 7
3x - 4y = 9
Answer: No Solution; 7=9
Pick one equation solve for y. Plug that answer in for y on the 2nd equation and solve. Show on white board!
Give the rate of change and the initial value from each description.
Kahn starts a savings account with $14. He will put in an equal amount each week. After 7 weeks, he will have $56.
Rate of change =
Initial Value =
Answer: Rate of change= 6
Initial Value= 14