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Differentiate $\displaystyle ax^b, ax^b+cx^{1/d}, \frac{a}{x^{1/c}}+\frac{b}{x^{-1/d}}+c$ with respect to $x$.

Find the gradient of  $ \displaystyle ax^b+\frac{c}{x^{d}}+f$ at $x=a$

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

Elementary examples of multiplication and powers of complex numbers. Four parts.

This question aims to test understanding and ability to use the laws of indices.

Factorising 5 to 7 digit numbers into a product of prime powers.

Uses the marking algorithms from question 1 of this CBA

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

Information on inputting powers

Questions testing understanding of the index laws.

Questions testing understanding of the index laws.

Questions testing understanding of the index laws.

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Find the squares, and cubes, of some numbers.

Finally, find a square number between two given limits.

Fill in a table of powers of 10.

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Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q}\;dx$.

indefinite integration

Find $\displaystyle \int ax ^ m+ bx^{c/n}\;dx$.

rebel

rebelmaths

Given value of x^(1/n), x^(-1/n) find x.

Given a number evaluate simple power, negative power, to one half.

Distinguishing -(72) and (-7)2.

Information on inputting powers.

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Information on inputting powers