Oxford MAT Prep Multiple Choice Questions Dr J

Oxford MAT Prep: Multiple Choice Questions Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com Copyright Notice: This resource is free-to-use for all NOT FOR PROFIT contexts only. I do not give permission for them to be used in any context involving financial gain, notably by private tutors or Oxbridge preparation agencies. Last Updated: 28 th January 2016

Index Click to go to the corresponding section. Comparing Values Sequences Trapezium Rule Number Theory Area/Perimeter Remainder Theorem Logarithms Circles Graph Sketching Calculus Reasoning about Solutions Trigonometry

General Points 1. 2. 3. 4. 5. 6. 7. The Oxford MAT paper is the admissions test used for applicants applying to Oxford for Mathematics and/or Computer Science, or to Mathematics at Imperial. It consists of two sections. The first is multiple choice, consisting of 10 questions each worth 4% each (for a total of 40%). The second consists of 4 longer questions, each worth 15% (for a total of 60%). We deal with the first section here. The paper is non-calculator. You need roughly 50% to be invited for interviews. However, successful maths applicants have an average of around 75%. The questions only test knowledge from C 1 and C 2. You must ensure you know the content of these two modules inside out. You should also keep in mind that the MAT won’t test you on theory you wouldn’t have covered, so should think in the context of what you can be expected to do. The multiple choice questions become progressively easier (and quicker) the more you practise. So practise these papers regularly. Even redoing a paper you’ve done before has value. I’ve grouped some of the questions from these papers here by topic, to help you spot some of the common strategies you can use.

Comparing Values Preliminary Tips

Comparing values A B C D

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Comparing values A B C D

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Comparing values A B C D

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Comparing values A B C D

Sequences Preliminary Tips

Sequences A 2011 B C D

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Sequences A 2010 B C D

Key Points 1. If you have two interweaved sequences, find formulae for them separately. This means we just want the sum of the first n terms from each of the two. 2. Know your formulae for the sum/infinite sum of a geometric series like the back of your hand.

Sequences A 2009 B C D

Key Points 1. Sometimes it helps to think about the ‘running total’ as we progress along the sum. Our cumulative totals here are 1, -1, 2, -2, 3, -3, … 2. Alternatively, try to spot when you can pair off terms such that things either cancel or become the same. In this case, 1 -2 = -1, 3 -4=-1, and so on. Although this makes it harder to spot exactly when we hit 100 in this case. 3. Think carefully about what happens at the end. Looking at the running totals, if the 1 st is 1, the 3 rd is 2, the 5 th 3, then the (2 n-1)th gives us n. So when our running total was 100, 2 n-1 = 199.

Trapezium Rule Preliminary Tips Overestimates when line curves upwards. Underestimates when line curves downwards.

Trapezium Rule 2010 A B C D

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Trapezium Rule A 2009 B C D

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Trapezium Rule A 2008 B C D

Key Points 1. Thinking about the question visually helps. A function which curves upwards will give an overestimate, and a function which curves downwards gives an underestimate. 2. (d) is the only transform which changes the shape of the curve, giving us a reflection on the y-axis (in the line y=1). A curve for example curving up will now curve down, giving us an underestimate.

Number Theory Preliminary Tips

Number Theory A 2008 B C D

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Number Theory A 2008 B C D

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Number Theory A 2009 B C D

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Number Theory A 2007 B C D

Number Theory A 2010 B C D

Area/Perimeter Preliminary Tips 1 1 r The radius of the big circle is 1. What is the radius of the small circle? ?

Area/Perimeter A 2012 B C D

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Area/Perimeter A 2012 B C D

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Area/Perimeter A 2011 B C D

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Area/Perimeter A 2006 B C D

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Remainder Theorem Preliminary Tips

Remainder Theorem A 2008 B C D

Remainder Theorem A 2006 B C D

Remainder Theorem A 2009 B C D

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Logarithms Preliminary Tips

Logarithms A 2011 B C D

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Logarithms A 2007 B C D

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Circles Preliminary Tips The nearest point to this dot on the circumference of the circle can be found by drawing this straight line from the centre. Nearest points to each other.

Circles A 2012 B C D

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Circles A 2011 B C D

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Circles A 2009 B C D

Key Points (-3, -4) 1. As per usual, complete the square, and then a sketch may help. 2. By inspection, we can see the nearest point to the origin must be on the line that goes from the centre and through the origin. 3. Since the radius is 10 and the distance from the centre to the origin is 5 (by Pythagoras), then the answer must be 5.

Circles A 2007 B C D

Key Points 1. Again, draw a diagram! 2. Drawing a line between the centres of the circles often helps for questions like these. We can see visually that the nearest point must lie on this line.

Circles A 2006 B C D

Graph Sketching Preliminary Tips

Graph Sketching A 2011 B C D

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Graph Sketching A 2008 B C D

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Graph Sketching A 2007 B C D

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Graph Sketching A 2010 B C D

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Graph Sketching A 2012 B C D

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Calculus Preliminary Tips

Calculus A 2009 B C D

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Calculus A 2012 B C D

Key Points 1. You don’t need to actually do any integration here (and you won’t be able to unless you’ve done C 3!) 2. Looking at the multiple choice options, we only care if T is positive/negative/0. 3. Thus for each of the integrals, we only care whether the area under the graph is above the x-axis or below the x-axis. 4. By sketching the 3 graphs, we find the first area is positive, the second negative and the third positive. Thus T is negative.

Calculus A 2011 B C D

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Calculus A 2010 B C D

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Calculus A 2008 B C D

Calculus A 2007 B C D

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Calculus Important Note: This question is sufficiently old that it was before the ‘C’ modules existed at A Level (instead of C 1 -4 and FP 1 -3, there was P 1 -6). This kind of content would now appear in C 3, and thus a question like this would no longer appear in a MAT. A 2006 B C D

Reasoning about Solutions Preliminary Tips There’s three ways to consider the number of solutions: METHOD 1: Factorise (when possible!) METHOD 3: Consider the discriminant METHOD 2: Reason about the graph

Reasoning about Solutions Preliminary Tips More on METHOD 2: Reason about the graph

Reasoning about Solutions A 2009 B C D

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Reasoning about Solutions A 2009 B C D

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Reasoning about Solutions A 2008 B C D

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Reasoning about Solutions A 2007 B C D

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Reasoning about Solutions A 2006 B C D

Key Points Now it’s clear there’s no solutions.

Trigonometry Preliminary Tips

Trigonometry A 2007 B C D

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Trigonometry A 2008 B C D

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Trigonometry A 2009 B C D

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Trigonometry A 2011 B C D

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Trigonometry A 2010 B C D

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Trigonometry A 2008 B C D

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Trigonometry A 2011 B C D

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Trigonometry A 2011 B C D

Key Points • It’s helpful to draw out the two graphs on the same axis, and then shade the appropriate regions.

Trigonometry A 2011 B C D

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