Essential Skills
What is the mean of the following set of numbers: 13, 15, 100, 54, 345, rounded to the nearest 1’s place?
105
54 – 6 ÷ 2 + 6 = ?
57
The sides of an equilateral triangle are 12, 4x+4, and 3y-3
Solve for x and y
x=2
y=5
You roll two 6-sided number cubes. What is the probability the first cube will show a 6 and the second cube will show a 2?
1/36
6r=7s+t
Give the equation that expresses s in terms of r and t
s=6r-t/7
What is the number 350,000,000 in scientific notation?
3.5 x 108
The lowest temperature on a winter morning was –8°F. Later that same day the temperature reached a high of 24°F. By how many degrees Fahrenheit did the temperature increase?
32
A square garden enclosed by a fence with perimeter 40 m is to be expanded so it includes 300 m2 more area but is still square. If the gardener can reuse the old fence pieces, what length of new fence must the gardener buy?
40m
Edward has a bag with three marbles in it. One is red, one blue, one orange. If he randomly selects two marbles without replacing them, what is the probability he selects first the orange then the blue?
1/6
The first term of a sequence is 9. Each term after the first is four times the preceding term. If w represents the nth term of the sequence, which equations gives w in terms of n?
w=9(4n-1)
Convert from decimal to scientific notation: 0.0000034
3.4 x 10-6
A biologist puts an initial population of 500 bacteria into a growth plate. The population is expected to double every 4 hours. Which of the following equations gives the expected number of bacteria, n, after x days? (24 hr=1 day)
n=500(2)6x
A rectangular garden has dimensions 30 feet by 20 feet. What is the area of the 2 foot wide walkway around the garden?
216 ft2
A candy shop sells Valentine's Day gift baskets that consist of chocolates, a basket, and a card. If there are five different types of chocolate, three types of baskets, and ten options for cards, how many different gift basket combinations are there?
150
What is the highest integral value of k for which the quadratic equation x2-6x+k=0 will have 2 real distinct roots?
a) 9 b)7 c) 8 d)1 e)2
c) 8
Given the equation 2xy + 4x² - y = 2x, if x = 2, what does y equal?
-4
Which of the following expressions is equivalent to
(x+7)(x2-3x+2)
x3+4x2-19x+14
In ∆ABC, m∠A = 23 and m∠B = 84. What is the longest side of ∆ABC?
AC
a number is chosen at random from 1-50. Find the probability that the number chosen is divisible by 2 as well as 5.
1/10
Which expression is equivalent to
8x(x-7)-3(x-7) / 2x-14
8x-3/2
Angela scores 17, 19, 13, 24, and 14 points in the first five games of a seven-game basketball season. If the scoring leader in Angela’s league averages 18 points per game, how many points must Angela score in the final two games combined to end the season with the highest scoring average in the league AND have a higher scoring average than any other player?
40
Which of the following best describes the range of y=-2x4+7
a. y ≤ -2 b. y ≥ 7
c. y ≤ 7 d. 0<y<7
b
In triangle ABC, C is a right angle. If Cos of A= 5/8, then what is Cos of B.
√39/8
the number of boys in a class is twice the number of girls. 20% of the girls are brunettes and of the rest, half are blondes: Mary, Clara, Gina, and Trisha. How many boys study in this class.
20
x2-2x-9=0
one solution to the given equation can be written as 1 + the square root of k, where k is constant. What is the value of k?
10