A block of given mass is sliding down the plane, with given acceleration or a given coeff-of-friction. Find the normal reaction force, the parallel force and the missing value of a and mu.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

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

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Calculating the definite integral $\int_{n_1}^{n_2}ax^b dx$.

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given a proportion of students who DO speak a language other than English at home, and are asked to find the percentage who do NOT. The fraction denominator is either 20 or 25, and the numerator is randomised.

An order of operation question using +,-,* with signed integers, with up to 4 variables.

The questions are the exercises from Q3 of HELM Book 1.1.5

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

Compute the modulus of (a) a positive rational, (b) a negative rational, (c) 0

Simplify three expressions: (a^b)^c, a^b * a^c, a^b/a^c where a, b and c are randomised. a is a letter, and b and c are rational numbers.

Part of HELM Book 1.2

Use a calculator to evaluate a number to the power of a fractional index. Both the number (a positive integer) and the index (a rational) are randomised.

Part of HELM Book 1.2

Part of HELM Book 1.1

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.

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.

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

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

Rate of change problem involving velocity & acceleration

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

A quick practice set of problems for education students to take in preparation for their numeracy test.

Evaluating arithmetic operations, and the order of operations.