HELM Book 1.1.5 exercises

This exercise will help you rearrange some complex equations.

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Multiplication of $2 \times 2$ matrices.

Addition, subtraction and multiplication by a scalar for 2 x 2 matrices.

Divisor is single digit. There is a remainder which we express as a decimal by continuing the long division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

A question to practice equation line and finding gradients

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

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Multiplication and adding matrices.

A question to practice functions, graphs and domains

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Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Definite Intgerals

Definite Integrals

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Recovering original function given some information such as derivative and value at some point.

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