Algebra
Solve for all real values of x:
x + 4/x = 5
x=1, 4
Without a calculator, evaluate:
sin60cos30
3/4
The graph of
y= 6/x
passes through the point (a,3).
Find the value of a.
a=2
An investment earns 8% compound interest per annum.
By what single percentage has the investment increased after 2 years?
16.64%
What is the sum of the interior angles of a regular octagon?
1080
Solve:
2x+1 = 16x-2
x=3
Evaluate:
(sin45+cos45)/tan45
sqrt 2
Find the coordinates of the turning point of
y=x2 +6x +13.
Vertex = (-3,4)
A jacket is discounted by 20%, then the sale price is increased by 20%.
Overall, has the price increased, decreased or stayed the same? By what percentage?
Decreased by 4%
In △ ABC, the internal bisector of angle A meets the circumcircle of △ ABC at point D. If AB = 6 and AC = 8, find the exact ratio of the lengths of the segments BD to CD.
1:1
If a + b = 9, and ab = 14,
Find a2 + b2
53
The area of the sector of a circle with a radius of 6 cm is 50 cm². Find the length of the arc of the sector.
50/3 cm
The line y=2x+k is tangent to the parabola
y=x2−4x+7.
Find the value of k.
k=-2
A bank offers 4.8% p.a. compounded monthly.
Approximately how many years will it take for an investment to double in value?
(Give your answer to the nearest year.)
14 years
Triangle ABC is similar to Triangle XYZ. If the sides of Triangle ABC are half the length of the sides of Triangle XYZ, what is the ratio of the area of Triangle ABC to the area of Triangle XYZ?
1:4
Find every real solution of:
x4-10x2+9=0
x=1, -1, 3, -3
The line y=mx+1 intersects y=x2−4x+5 at exactly one point.
Find all possible values of m.
m = 0, -8
Matthew bought a laptop priced at $2800. He paid a 10% deposit and made monthly repayments of $95.20 for 3 years.
What annual flat rate of interest was Matthew charged?
12% p.a.
A farmer wants to create a right-angled triangular enclosure against a long, straight stone wall. The stone wall will act as the hypotenuse of the triangle, meaning the farmer only needs to buy fencing for the other two perpendicular sides. If the farmer has exactly 28m of fencing available and must use all of it, what is the maximum possible area of the enclosure?
98m2
Find all real values of x such that:
x2 + 1/x2 =2
x = +1, -1
Find the equation of the circle passing through the points
(5,2), (−1,2), (2,5).
(x−2)2+(y−2)2 = 9
A student loan of $50,000 continuously accrues interest at an instantaneous rate of 5% per annum. If repayments are made continuously at a constant annual rate of $4,000, what is the number of years it will take to entirely extinguish the debt to the nearest year?
20 years
A solid is formed by hollowing out a conical cavity from a right circular cylinder. The cylinder has a base radius of 6 cm and a height of 10 cm. The conical cavity shares the exact same base radius and has a height of 8 cm. What is the total exact volume of the remaining solid?
264π cm3