Show:
Simple and Compound Interest
Probability and Combinatorics
Triangles and Coordinate Geometry
Shapes and Other Shapes
Intro to Differential Calculus
100
Unoka borrows 200 cowrie shells from his friend Okoye at a rate of 5% simple interest per week. If he ended up owing 350 cowries, how many weeks did he wait to pay back the loan?
8 Weeks
100
Eight runners are racing in the 200-meter dash. In how many different sequences could the runners finish the race?
8! = nPr(8,8) = 40,320
100
If Okonkwo casts a 5.5-foot shadow, and at the same time a tree casts a 28-foot shadow, how tall is the tree?
15.272 ft
100
A cone with a radius of 8 is similar to a cone with a radius of 2 and a height of 3. Determine the volume of the larger cone and the ratio of the volumes.
Volume of larger cone = 256 pi Ratio of volumes = 64
100
What is the limit as x approaches c of y if y = x^2+3x+6 and c = 4?
34
200
What is the formula for simple interest?
Interest = P ⋅ r⋅ t
200
How many different arrangements are possible using the letters in the word “IHATEMATH”?
45,360
200
What is the equation of the line passing through points (2,-5) and (3,7)?
y +5 = 12(x-2)
200
Two secants intersect outside of a circle. The angle between them is 20 degrees, and one of the intercepted arcs has a measure of 86 degrees. What is the measure of the other intercepted arc?
46 degrees
200
What is the limit as x approaches infinity of the function y = (3x-4)/(2x+1)?
3/2 or 1.5
300
What is the formula for compound interest?
A=P(1+(r/n))^nt
300
Define a permutation and give its formula
Definition : A permutation of objects is a selection of objects from a group where no object is allowed to be selected more than once and the order of selection matters. Formula: P = n!/(n-k)!
300
Determine the set of all points in three dimensions whose distance from the origin is 5. Write an equation to describe this shape.
x^2 + y^2 + z^2 = 25
300
Two chords intersect within a circle and divide each other into parts. The two parts of one chord are 2 and 6-x respectively, while the two parts of the other chord are 12-x and 18. What is x?
x = 12.75
300
Differentiate the function why = x^4 + (3/4)x^3 + 2x + 2
y' = 3x^3 + (3/2)x^2 +2
400
If $200 is invested at 2.5% APR compounded quarterly (four times per year), how much is the investment worth at the end of seven years?
$238.12
400
Give the definition of a combination and its formula
Definition : A combination of objects is a selection of objects from a group where no object is allowed to be selected more than once and the order of selection doesn’t matter Formula : nCr = n!/r!(n-r!)
400
What is the midpoint of the line segment from (2, 11, 16, 3) to (16, –4, 8, 10)?
(9, 3.5, 12, 6.5)
400
Two tangent lines intersect at a point 13 cm away from the center of a circle. The distance between the point of intersection and the point of tangency is 12 cm. What is the radius of the circle?
r = 5 cm
400
When is a graph continuous? Is the graph of why = tan(x) continuous?
A graph is continuous if, at each x-value where the graph exists, the limit of the graph agrees with the value of the graph for each x-value No, why = tan(x) is not continuous
500
What APR is necessary for an investment to double in 10 years if compounded monthly?
6.512%
500
I ran out of time while taking the music test and plan to guess on the last 6 questions. Each question has 4 possible choices, one of which is correct. Let X= equal the number of answers I correctly guesses in the last 6 questions. What is the P(X<2)?
53.39%
500
What is the length of the diagonal of a fantasy coffin shaped like a raisin box of dimensions 4 m, 5 m , and 25 cm?
640.80 cm, or 6.480 m
500
Find the area of a regular dodecagon (12-sided figure) with a side length of 5cm. Hint: divide it into triangles
The regular dodecagon can be split into twelve congruent isosceles triangles with vertices meeting at the center of the dodecagon. The interior angles of a dodecagon sum to 1800°, so each angle is 150°. Since this is a regular dodecagon, the isosceles triangles will have base angles of 75°, and 2·tan 75° as the height of the triangle. Therefore, the area of the dodecagon is 12 ⋅ 0.5 ⋅ 4 ⋅ 2⋅ tan75 , or 179.14cm^2
500
The graph of y = (1/3)x^3 + 4x^2 +7x + 10 has two horizontal tangents. Find the equations of these horizontal tangent lines.
y =(128/3) y = (20/3)