AS Core 1 Mathematics paper May 2016 - non-calculator PDF

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Past paper from May 2016 ...

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PMT

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AS MATHEMATICS Unit Pure Core 1 Non-Calculator Wednesday 18 May 2016

Morning

Time allowed: 1 hour 30 minutes

Materials For this paper you must have: l the blue AQA booklet of formulae and statistical tables. You must not use a calculator.

Instructions l l l l l l l l l

Use black ink or black ball-point pen. Pencil should only be used for drawing. Fill in the boxes at the top of this page. Answer all questions. Write the question part reference (eg (a), (b)(i) etc) in the left-hand margin. You must answer each question in the space provided for that question. If you require extra space, use an AQA supplementary answer book; do not use the space provided for a different question. Do not write outside the box around each page. Show all necessary working; otherwise marks for method may be lost. Do all rough work in this book. Cross through any work that you do not want to be marked. The use of calculators is not permitted.

Information l l

The marks for questions are shown in brackets. The maximum mark for this paper is 75.

Advice l l

Unless stated otherwise, you may quote formulae, without proof, from the booklet. You do not necessarily need to use all the space provided.

(JUN16MPC101)

PB/Jun16/E2

MPC1

PMT Do not write outside the box

2

Answer all questions. Answer each question in the space provided for that question.

The line AB has equation 5x þ 3y þ 3 ¼ 0 .

1

The line AB is parallel to the line with equation y ¼ mx þ 7 .

(a)

Find the value of m. [2 marks] (b)

The line AB intersects the line with equation 3x  2y þ 17 ¼ 0 at the point B. Find the coordinates of B. [3 marks] The point with coordinates ð2k þ 3, 4  3kÞ lies on the line AB.

(c)

Find the value of k. [2 marks] QUESTION PART REFERENCE

Answer space for question 1

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(02)

PB/Jun16/MPC1

PMT Do not write outside the box

3 QUESTION PART REFERENCE

Answer space for question 1

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(03)

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PB/Jun16/MPC1

PMT Do not write outside the box

4

 pffiffiffi 2

Simplify 3 5

2 (a)

(b)

QUESTION PART REFERENCE

.

 pffiffiffi 2 pffiffiffi pffiffiffi 3 5 þ 5 Express pffiffiffi in the form m þ n 5 , where m and n are integers. 7þ3 5

[1 mark]

[4 marks]

Answer space for question 2

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(04)

PB/Jun16/MPC1

PMT Do not write outside the box

5 QUESTION PART REFERENCE

Answer space for question 2

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(05)

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6 3 (a) (i)

2

Express x 2  7x þ 2 in the form ðx  pÞ þ q , where p and q are rational numbers. [2 marks]

(ii) Hence write down the minimum value of x 2  7x þ 2 . (b)

QUESTION PART REFERENCE

[1 mark]

Describe the geometrical transformation which maps the graph of y ¼ x 2  7x þ 2 2 onto the graph of y ¼ ðx  4Þ . [3 marks]

Answer space for question 3

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(06)

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PMT Do not write outside the box

7 QUESTION PART REFERENCE

Answer space for question 3

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(07)

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8 The polynomial pðxÞ is given by pðxÞ ¼ x 3  5x 2  8x þ 48 .

4 (a) (i)

Use the Factor Theorem to show that x þ 3 is a factor of pðxÞ.

[2 marks]

(ii) Express pðxÞ as a product of three linear factors. [3 marks] (b) (i)

Use the Remainder Theorem to find the remainder when pðxÞ is divided by x  2 . [2 marks]

(ii) Express pðxÞ in the form ðx  2Þðx 2 þ bx þ cÞ þ r , where b, c and r are integers. [3 marks] QUESTION PART REFERENCE

Answer space for question 4

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(08)

PB/Jun16/MPC1

PMT Do not write outside the box

9 QUESTION PART REFERENCE

Answer space for question 4

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(09)

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10 A circle with centre Cð5, 3Þ passes through the point Að2, 1Þ.

5 (a)

Find the equation of the circle in the form

ðx  aÞ2 þ ðy ...