Test of Mathematics for University Admission specimen ...

TEST OF MATHEMATICS FOR UNIVERSITY ADMISSION

PAPER 1

SPECIMEN

Additional Materials: Answer sheet

Time: 75 minutes

INSTRUCTIONS TO CANDIDATES

Please read these instructions carefully, but do not open the question paper until you are told that you may do so.

A separate answer sheet is provided for this paper. Please check you have one. You also require a soft pencil and an eraser.

This paper is the first of two papers.

There are 20 questions on this paper. For each question, choose the one answer you consider correct and record your choice on the separate answer sheet. If you make a mistake, erase thoroughly and try again.

There are no penalties for incorrect responses, only points for correct answers, so you should attempt all 20 questions. Each question is worth one mark.

Any rough work should be done on this question paper. No extra paper is allowed.

Please complete the answer sheet with your candidate number, centre number, date of birth, and full name.

Calculators must NOT be used. There is no formulae booklet for this test.

Please wait to be told you may begin before turning this page

This question paper consists of 12 printed pages and 4 blank pages

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2 BLANK PAGE

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1. The sum of the two values of that satisfy the simultaneous equations 3 1 0 and 3 7 5 is

A

8.5

B

7.5

C

1.5

D 3.5

E 4.5

F

5

2. The number of solutions in the interval 0 sin 3 cos 3 is

4 of the equation

A 0 B 1 C 2 D 3 E 4 F 5 G 6

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4 3. The perpendicular bisector of the line segment joining the points 2, 6 and 5, 4 cuts

the -axis at the point with -coordinate

A B C D E

4. The complete set of values of for which

1

2 0 is

A

1, 1

2

B

1, 2

C

1

2

D

1, 2

E

1

1, 2

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5. Given that

5 log 1 for 1, find in terms of .

A

B

1 log

C

1 log

D

1 10

E

10 1

F

10

6. It is given that 2 is a factor of

4

The sum of the possible values of is

A

10

B

6

C 0

D 6

E 10

1 6.

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6 7. A bag contains red balls, yellow balls, and blue balls.

One ball is selected at random and not replaced. A second ball is then selected at random and not replaced. Each ball is equally likely to be chosen. The probability that the two balls are not the same colour is A B C D E F

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8. Given that

A log B C D E log F G H

7 2, where , , and are positive real numbers, then

9. The roots of the equation 2 11

0 differ by 2. The value of is

A B C D

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10. The curve cos is reflected in the line 1 and the resulting curve is then translated by units in the positive -direction. The equation of this new curve is

A B C D .

2 cos 2 cos 2 cos 2 cos

11. The sum of the roots of the equation 2 8 2 15 0 is

A 3 B 8 C 2 log 2 D log E

? UCLES 2017

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