Recoginising different forms of calculus notation.

(a) Read subscript notation to identify an element in a 3x3 matrix; (b) chose the correct subscripted name from a list for a given element in a 3x3 matrix.

Calculate the product of two 3D vectors in column notation.

Determine a finite sum and a limiting sum of a geometric series written using sigma notation. I'm not sure how to eliminate rounding errors...

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Match the greek letter to its pronunication.  15 common letters.

Convert numbers between 0 and 1 intro standard form/scientific notation.

Convert numbers greater than 1 into standard form/scientific notation.

Identify the truth value of an inequality (T/F) between two numbers

Evaluating a linear function for a given value of $x$.

Basic calculation from a sum given in Sigma notation.

Rewriting fractions of the form $\frac{\sqrt[m]{x^n}}{\sqrt[p]{x^q}}$ to $x^{\frac{n}{m}-\frac{q}{p}}$.

Rewriting expressions from $\sqrt[m]{x^n}$ to $x^\frac{n}{m}$.

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Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Convert numbers greater than 1 into standard form/scientific notation.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This question tests understanding of subscript notation for matrices

convert large numbers to scientific notation

Match prefixes with their abbreviations, from nano to giga. Match prefixes with equivalent scientific notation.

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By powers of ten I mean a 1 followed by some 0s. The scientific notation questions will take care of the power of ten notation.

This shows how to use a variable name annotation to put a hat on a variable name inside the \simplify command.

DCS 2023 Maths Entrance Test to be used September 2023

1.5 hours with 3 randomised questions from each of these groups:

• Notation and Algebra
• Calculus - Differentiation
• Calculus - Integration
• Trigonometry

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Write a large number and a small number in scientific notation. (Numbers contain 5 digits). Indices range from -7 to +7, excluding 0 and 1

Part of HELM Book 1.2