Percents and Algebra
Geometry and Radicals
Exponents and Scientific Notation
Statistics and Probability
Ratios and Proportions
Extra Hard
(Each 500 points)
(Each 500 points)
100
A shirt that originally costs $80 goes on sale for a price of $45. What is the percent discount?
Percent change = ((new-old)/old) x 100
Percent change = (45-80)/80*100
Percent change = (35/80)*100
ANS: 43.75%
100
Simplify:
sqrt88
Prime factorization of 88 = 2 x 2 x 2 x 11
= 22 x 2 x 11
=sqrt(2^2)*sqrt2*sqrt11
OR
sqrt88=sqrt4*sqrt22
sqrt88=2sqrt22
100
Express the following number in scientific notation: 0.0000234
2.34 x 10-5
100
A quarter has two sides: Heads and Tails. If you flip a quarter two times, what is the probability of getting Heads twice?
P(heads first time) x P(heads second time)
(1/2)(1/2) = 1/4
ANS: 1/4
100
3 workers can paint 5 houses in a week. How many houses can 12 workers paint in a week?
3 workers: 5 houses: 1 week
12 workers: x houses: 1 week
5 x 4 = 20 houses
ANS: 20
100
You are building a rectangular fence and have 80 feet of fencing. You are going to use all 80 feet of fencing. What is the maximum possible area for the fence?
Max area of a rectangle is the shape of a square
80 feet is the perimeter each side will be 20 feet
Max area will be 202 = 400 feet2
200
Find the GCF and LCM of the following numbers: 24, 30, and 48.
24 = 2 x 2 x 2 x 3
30 = 2 x 3 x 5
48 = 2 x 2 x 2 x 2 x 3
GCF = 2 x 3 = 6
LCM = 2 x 2 x 2 x 2 x 3 x 5 = 240
ANS: GCF = 6, LCM = 240
200
The diameter of a circle is 8 inches. What is the area of the circle in square inches? Leave your answer in terms of pi.
A =
pir^2=pi(4)^2=16pi
200
Simplify the expression: (3.15 x 10-3) x (2.4 x 105)
3.15 x 2.4 = 7.56
10-3 x 105 = 102
ANS: 7.56 x 102
200
You flip a coin 5 times and it lands on Heads 5 times. What is the probability that the next flip (the 6th flip) will land on Heads as well?
ANS: 1/2
200
There are two triangles that are similar:
Triangle ABC is similar to triangle XYZ. The length of AB = 5, and length of the BC is 6. If the length of XY is 8, what is the length of YZ?
(AB)/(BC)=(XY)/(YZ)
5/6=8/(YZ)
5(YZ)=8(6)
5YZ = 48
YZ=
48/5
200
A squirrel can run at a speed of 120 feet per min. How fast is that in miles per day? Answer must be a simplified fraction
1 mile = 5280 feet
(120 feet)/(1 min)*(60 min)/(1 hour)*(24hours)/(1day)*(1 mi)/(5280)
ANS:
360/11 or 32 8/11
300
What is the GCF of 24x7y4 and 9x5y7 ?
GCF = 3x^5y^4
300
A triangle has three interior angles. The largest angle is 3 times the smallest angle. The 2nd largest angle is double the smallest angle. What is the measure of the largest angle?
Let x = the smallest angle
2nd largest angle = 2x
Largest angle = 3x
Total degrees in a triangle = 180 = x + 2x + 3x
180 = 6x
x = 30
Largest angle = 3x = 3(30) = 90
ANS: 90
300
Simplify:
(8x^3y^8)/((2xy^2)^3
Your answer must not have negative exponents
(8x^3y^8)/((2xy^2)^3
(8x^3y^8)/(8x^3y^6)
y^2
300
A student is about to take a final chemistry test. She currently has a class average of 80 across her first 4 tests. The final is going to be worth 2 test grades. If she wants to get an average of 85 in the class, what must she get on the final exam?
Average = (sum of all test scores / # of tests)
Sum of all test scores = average x # of tests
Current sum after 4 tests = 4 x 80 = 320 points
Desired sum = 6 x 85 = 510 points
510 - 320 = 190 points
190/2 = 95 on the final
ANS: 95
300
The equation,
y=4/5x
describes a proportional relationship and forms a straight line on the graph. A point with a y-coordinate of 5 lies on the line. What is the corresponding x-coordinate?
y=(4/5)(x)
5=(4/5)(x)
x = 5(5/4)
x = (25/4)
300
FOIL and Simplify :
(x+2)(x-3)(x-2)
(x+2)(x-3)(x-2)
(x^2-3x+2x-6)(x-2)
(x^2-x-6)(x-2)
(x^3-2x^2-x^2+2x-6x+12)
x^3-3x^2-4x+12
400
38% of a number is equal to 24. What is the number rounded to the hundredths place?
0.38x=24
x=24/0.38
x=63.157
x=63.16
400
Find the area of this trapezoid:
Area =
(1/2)(base 1 + base 2)(height)
(1/2)(12+50)(28)
868
400
Simplify the product of (3x3y-2)2 with (2x2y5)
(3x3y-2)2 (2x2y5)
(9x6y-4)(2x2y5)
9*2 = 18
x6*x2=x8
y-4*y5=y
ANS: 18x8y1
400
You roll 2 standard 6 - sided dice. What is the probability that the sum of the two dice will be equal to 6?
Total combinations = 6 x 6 = 36
Total ways to getting 6: (1,5) (5,1) (2,4)(4,2)(3,3)
ANS: 5/36
400
In a jar, the ratio of quarters to dimes to nickels is 6:8:5 respectively. If the total value of the coins in the jar is $7.65, how many quarters, dimes and nickels are there?
6(0.25) + 8(0.1) + 5(0.05) = $2.55
$7.65/$2.55 = 3
3 x (6:8:5) = 18:24:15
quarters = 18
dimes = 24
nickels = 15
400
There are 6 different cookies in a tray. You get to choose 3 of them. How many different combinations of cookies can you take?
Let cookies be A,B,C,D,E,F
Combinations: ABC, ABD, ABE, ABF
ACD, ACE, ACF
ADE, ADF
AEF
BCD, BCE, BCF, etc.
Faster method: Find how much combinations can be made with the same three cookies.
ABC = ACB = BAC = BCA = CAB = CBA
Combos = ((6)(5)(4))/6=20
ANS: 20
500
Simplify:
5(1+0.3)^2-5
5(1.3)^2-5
5(1.69)-5
8.45-5
3.45
500
The measure of 1 interior angle of a regular polygon is 162 degrees. How many sides does the polygon have?
((n-2)*180)/n=162
(n-2)*180=162n
180n-360=162n
-360=-18n
n=20
500
Solve for x if: 327 = 93x
327 = 93x
9 = 32
93x = (32)3x
(32)3x = 36x
327 = 36x
27 = 6x
x = 27/6 = 9/2
ANS: 9/2
500
What is the mean, median and mode for the following data set?
25, 22, 17, 10, 11, 12, 15, 16, 25
Data set:
10, 11, 12, 15, 16, 17, 22, 25, 25
Mean = (sum of all values / # of values)
Mean = (10+11+12+15+16+17+22+25+25) / 9
Mean = 17
Median = value in the middle when arranged in order
Median = 16
Mode = 25
500
There are two similar rectangles where each corresponding side of the large rectangle is triple that of the smaller rectangle. What would be the ratio of the area of the smaller rectangle to that of the larger rectangle?
Area of smaller rectangle = length x width
Area of larger rectangle = 3length x 3 width = 9 lw
The ratio of the small to large rectangle = 1:9
ANS: 1:9
500
The equation for the volume of a sphere is
4/3pir^3
How many times does the volume increase if a sphere's radius is quadrupled?
V=4/3pir^3
4/3pi(4r)^3
Only difference is r^3 vs (4r)^3
(4r)^3=64r^3
Volume will be 64 times larger