Definition
Algebra
Geometry
Trigonometry
Probability
Statistics
200
The x - and y - axes divide the plane into four of these, which we usually refer to with Roman numerals.( 2 mins)
Answer: quadrant
200
My supersonic jet burns 4 gallons of jet fuel in 3 seconds. How many gallons of jet fuel do I need to fly for an hour? (2 mins)
Answer: 4800
(4 gallons/ 3 sec)* 3600 sec = 4800 gallons
200
Find the angle x given the angle measures shown in the figure. (2 mins)
Answer: x=114°
From △ABC, we have
35°+79°+∠ACB=180°,
so ∠ACB=66°. From line (BD) ⃡:
∠ACB+x=180°
so x=180°-66°=114°.
200
Based on the diagram, what is the sine of A?
(2 mins)
Answer: sine A = 5 / 13
200
If a die is rolled 6,000 times and the number '2' occurs 990 times, then what is the experimental probability that '2' shows up on the die? (2 mins)
Answer: 0.165
990 / 6000 = 0.165
200
The distances travelled by a group of people to their workplace in km are the following:
4, 2, 6, 3, 8, 6, 4, 7, 15, 8, 10, 5, 15, 1, 20, 3, 16
What is the range of the data?
(2 mins)
Answer: 19
400
The center of the plane, where the axes meet, is called the ________.( 3 mins)
Answer: origin
400
If a2 and b are directly proportional, and a=2 when b=9, then what is b when a=6?
( 3 mins)
Answer: b = 81
a2=kb
k=a2/b=22/9 = 4/9
so 62=(4/9)b
b= 81
400
In the figure, lines VY and WZ meet at X and ∠YXZ=55°. What is the measure of ∠WXY? ( 3 mins)
Answer: ∠WXY=125°
Since ∠WXY and ∠YXZ together make ∠WXZ, which is a straight angle, we know that
∠WXY+∠YXZ=180°.
Hence,
∠WXY=180°-∠YXZ=125°.
400
Based on the diagram, find the value of x. (3 mins)
Answer: x = 12 sin 33 degrees
sin 33 = x / 12
x = 12 sin 33 degrees
400
A card is drawn randomly from a deck of 52 playing cards. The pack consists of four suits and each suit has 13 cards. The suits are Spade ♠, Heart ♥, Diamond♦, and Club ♣. Find the probability that the card drawn is a picture card (king, queen, and jack). (3 mins)
Answer: 3/13
The picture cards consist of four kings, four queens, and four jacks.
∴P(a picture card) = 12/52 = 3/13
400
Ethan recorded the daily temperatures (in Celsius) over 10 days in May. The distribution of temperatures he recorded is 19,22, 24,24,24, 24, 25,25,25,28. What is the mean of the temperature in Ethan's data? ( 3 mins)
Answer: 24 Celsius
600
We denote the ______ of matrix A to be |A|, and if A has elements a,b,c,d, then this quantity is (a)(d) - (b)(c).
(5 mins)
Answer: determinant
600
Evaluate 4(x2-2y+7) - 2(2y2+4x+2) when x = -y. (3 mins)
Answer: 24
600
In the diagram, line m is parallel to line n, segment AB is perpendicular to line m, ∠ADC=∠BCE=3x,
∠CEB=50°, and ∠BCD=x. Find x. (3 mins)
Answer: x=40°
600
What is an equivalent trigonometric function to 1 / tangent x ?
(3 mins)
Answer: cotangent x
600
There are 40 students in a class. Six of them wear glasses, four of them wear contact lenses, and the rest can see without vision correction. A student is selected at random. Find the probability that the student selected does not have to correct his vision. (3 mins)
Answer: 0.75
30/40 = 3/4 = 0.75
600
Consider the data 20, 17, 50, 35, 13, 22, 40, 36, 44.
What is the upper quartile or Q3 of this data set?
(3 mins)
Answer: 42
800
It is a polygon in which all the sides are equal, and all the angles are equal. (4 mins)
Answer: regular polygon
800
Simplify (𝑖- 𝑖-1 )-1.
(4 mins)
Answer: −𝑖/2
800
The measures of the angles in the diagram below are as marked. Find ∠C. (4 mins)
Answer: x = 36 degrees
800
What is the cosine of the angle when its measure is θ = 60°? (4 mins)
Answer: 1/2
The cosine of 60° is the length of the shorter leg of the triangle.
In a 30°-60°-90° triangle, the shorter leg is half the hypotenuse.
cos 60° = length of shorter leg = 1 /2
800
In a batch of 20 vases, there are four defective ones. A quality control inspector checks the vases in the batch one by one without repetition. If the first vase checked is defective, find the probability that the second vase checked is also defective.
(4 mins)
Answer: 3/19
800
A farmer randomly measured the weight of some plums from his farm in grams. The data are as follows:
75, 71, 82, 80, 76, 74, 71, 63, 76, 75, 60, 73, 74, 76, 75
What is the interquartile range?
(4 mins)
Answer: 5 grams or 5
1000
This is any line segment, in general, from a vertex of a triangle to a point on the opposite side. (5 mins)
Answer: cevian
1000
Find all x such that
(5 mins)
Answer: x =4
1000
A regular pentagon and a regular hexagon share a common side AD, as shown. What is the degree measure of angle BAC? (5 mins)
Answer: 12 degrees
Each interior angle of the regular hexagon has measure 120 degrees, and each interior angle of the regular pentagon has measure 108 degrees. Therefore,
<CAB= <BAD - <CAD = 120 - 108= 12 degrees
1000
Find the value of tan (-5pi/6 ) given that in the unit circle, its coordinate is (-√(3 )/2 , -1 /2 )
(5 mins)
Answer: √(3 ) / 3 or square root (3) / 3
tan (-5pi /6 ) = opposite/ adjacent
= (- 1 /2 )/(- √(3 )/2 )
= 1 /√(3 )
= √(3 )/3
1000
During a fund-raising event in a school, 1,000 raffle tickets priced at $20 each were sold. The tickets are numbered from 000 to 999. There is one first prize of $3,000, two second prizes of $1,000 each, and three third prizes of $500 each. If a ticket is drawn at random, find the probability that the last digit is not a '9’. (5 mins)
Answer: 0.99
1 - 10/1000 = 99 / 100 = 0.99
1000
The ages (yrs.) of 8 children are 2, 5, 5, 6, 8, 10, 12, 16
If you solved the mean absolute deviation, what does it mean for this data set?
(5 mins)
Answer: 3.5 years or 3.5
mean absolute deviation = 3.5 yrs and it means that the ages of the children, on average, differ by 3.5 years from the mean.
1200
All the altitudes of a triangle intersect at what point of the triangle?
(5 mins)
Answer: orthocenter
1200
What values of x satisfy
( 5 mins)
Answer: 5/3
1200
A right triangle has an area of 210 and a hypotenuse of 29. Find the perimeter of the triangle. (5 mins)
Answer: 70
1200
Two rays with common endpoint O form a 30 degrees angle. Point A lies on one ray, point B on the other ray, and AB = 1. What is the maximum possible length of segment OB ?
(5 mins)
Answer: OB = 2
1200
Mr. Stewart’s math class has 16 boys, and 22 of his students bring their calculators to class. If 13 of the students with calculators are girls, then how many boys didn’t bring their calculators to class? (5 mins)
Answer: 7 boys do not have calculators
1200
Find the sample standard deviation in two decimal places of 3,4,6, and 10. ( 5 mins)
Answer: Standard Deviation = 3.10