Differentiation
Differentiate 1/square root of x with respect to x
-1/2x to the power of -3/2
Simplify (x5)3
x15
Convert 24=16 to logarithm form
4=log216
Find how many even numbers can be formed using the digits 1,3,5,6,7 and 9 if no number can be repeated. The first number must be a 3 and the last number must be a 6.
4P2
G(x)=4/(w+1)
G(-6)=?
-4/5
Find the value of dy/dx of y= (x+5)/x at the point (5,2)
-1/5
Simplify (square root 8)2
8
Given that logpX=5 and logpY=2, find logpX2
10
John wants to put 5 books on the shelf out of the 8 books he has. Find the number of ways the books can be chosen if there are no restrictions.
8C5
f(x)=2x-3
g(x)=x/2
Find gf(x)
(2x-3)/2
Use product rule to differentiate x2(x-1)3 with respect to x
x(x-1)2(5x-2)
Solve the equation 23x+1=8
x=2/3
Given that logpX=5 and logpY=2, find logxyp
1/7
A code consists of 3 letters selected from W,D,S,C,V,X followed by 2 digits selected from 1,3,2,4,6
6P3x5P2=2400
f(x)=3x+2
g(x)=x2-1
fg(-3)=?
26
Find d2y/dx2 for y=(2x+5)/(3x-1)
y=102/(3x-1)3
Solve the simultaneous equation
125x/5y=25
23x x (1/8)1-y=32
x=7/6 y=3/2
Solve the simultaneous equation
xy=64
logxy=2
x=4 y=16
3 coats and 2 dresses are to be selected from 9 coats 7 dresses. Find the number of different selections that can be made.
9C3x7C2=1764
f(x)=x3+1
g(x)=2x-5
h(x)=f(x)-g(x)
Find h(-2)
-8
Find the coordinates of the stationary points on the curve y=2x3-15x2+24x+6
(1,17) maximum point
(4,-10) minimum point
Solve the equation 2y2-7y-4=0 then solve the equation 2(2x)2-7(2x)-4=0
2
Solve the simultaneous equation
2log3y=log5125+log3x
2y=4x
x=6.75 y=13.5
John wants to put 5 books on the shelf out of the 8 books he has. There are 5 comics, 2 textbooks and 1 storybook. Find the number of ways the 5 books can be chosen if there must be at least one type of book.
20 (1 storybook, 1 textbook, 3 comics) or 10 (1 storybook, 2 textbooks, 2 comics)
g(x)=(2x+3)/(x+1) for x>1
Find an expression for g-1(x)
g-1(x)=(x+3)/(x-2)