10 c1 specimen paper

8/3/2019 10 C1 Specimen Paper

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Paper Reference (complete below)CentreNo.

Candidate

No.

Paper Reference(s)

6663

Edexcel GCECore Mathematics C1

Advanced Subsidiary

Specimen Paper

Time: 1 hour 30 minutes

Examiners use only

Team Leaders use only

QuestionNumber

LeaveBlank

1

2

3

4

5

6

Materials required for examination Items included with question papers 7

Mathematical Formulae Nil8

9

Calculators may NOT be used in this examination.10

Instructions to Candidates

Tour candidate details are printed next to the bar code above. Check that these are correct

and sign your name in the signature box above.

If your candidate details are incorrect, or missing, then complete ALL the boxes above.

You must write your answer for each question in the space following the question.

If you need more space to complete your answer to any question, use additional answer

sheets.

Information for CandidatesA booklet mathematical Formulae and Statistical Tables is provided.

Full marks may be obtained for answers to ALL questions.

This paper has 10 questions.

Advice to Candidates

You must ensure that your answers to parts of questions are clearly labelled.

You must show sufficient working to make your methods clear to the examiner. Answers

without working may gain no credit.

Total

Turn over

Surname Initial(s)

Signature


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blank1. Calculate =

+20

1

)25(r

r .

(3)

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2. Find

(5x + 3x) dx.

(4)

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blank3. (a) Express 80 in the form a 5, where a is an integer.

(1)

(b) Express (4 5)2 in the form b + c 5, where b and c are integers.

(3)

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Leaveblank4. The pointsA andB have coordinates (3, 4) and (7, 6) respectively. The straight line l

passes throughA and is perpendicular toAB.

Find an equation forl, giving your answer in the form ax + by + c = 0, where a, b and

c are integers.

(5)

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blank5. Figure 1

y(1, 2)

(0, 1)

O (3, 0) x

Figure 1 shows a sketch of the curve with equationy = f(x).

The curve crosses the coordinate axes at the points (0, 1) and (3, 0). The maximum

point on the curve is (1, 2).

On separate diagrams in the space opposite, sketch the curve with equation

(a) y = f(x + 1),

(3)

1 (b) y = f(2x).

(3)

On each diagram, show clearly the coordinates of the maximum point, and of each point

at which the curve crosses the coordinate axes.

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6. (a) Solve the simultaneous equations

y + 2x = 5,

2x23xy = 16.(6)

(b) Hence, or otherwise, find the set of values ofx for which

2x23x16 > 5 2x. (3)

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Leaveblank7. Ahmed plans to save 250 in the year 2001, 300 in 2002, 350 in 2003, and so on until

the year 2020. His planned savings form an arithmetic sequence with common

difference 50.

(a) Find the amount he plans to save in the year 2011.

(2)

2 (b) Calculate his total planned savings over the 20 year period from 2001 to 2020.

(3)

Ben also plans to save money over the same 20 year period. He saves A in the year2001 and his planned yearly savings form an arithmetic sequence with common

difference 60.

Given that Bens total planned savings over the 20 year period are equal to Ahmeds

total planned savings over the same period,

(c) calculate the value ofA.

(4)

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Leaveblank8. Given that

x2 + 10x + 36 (x + a)2 + b,

where a and b are constants,

(a) find the value ofa and the value ofb.

(3)(b) Hence show that the equationx2 + 10x + 36 = 0 has no real roots.

(2)

The equationx2 + 10x + k= 0 has equal roots.

3 (c) Find the value ofk.

(2)

4 (d) For this value ofk, sketch the graph ofy =x2 + 10x + k, showing the coordinates of

any points at which the graph meets the coordinate axes.

(4)

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Leaveblank9. The curve Chas equationy = f(x) and the pointP(3, 5) lies on C.

Given that

f (x) = 3x28x + 6,

(a) find f(x).

(4)

5 (b) Verify that the point (2, 0) lies on C.

(2)

The point Q also lies on C, and the tangent to Cat Q is parallel to the tangent to CatP.

(c) Find thex-coordinate ofQ.

(5)

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Leaveblank10. The curve Chas equation

y =x35x +x

2, x 0.

The pointsA andBboth lie on Cand have coordinates (1, 2) and (1, 2) respectively.

(a) Show that the gradient ofCatA is equal to the gradient ofCatB.

(5)

(b) Show that an equation for the normal to CatA is

4y =x 9.

(4)

The normal to CatA meets they-axis at the pointP. The normal to CatB meets the

y-axis at the point Q.

(c) Find the length ofPQ.

(4)

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Paper Reference (complete below)CentreNo.

Candidate

No.

Paper Reference(s)

6664

Edexcel GCECore Mathematics C2

Advanced Subsidiary

Specimen Paper

Time: 1 hour 30 minutes

Examiners use only

Team Leaders use only

QuestionNumber

LeaveBlank

1

2

3

4

5

6

Materials required for examination Items included with question papers 7

Mathematical Formulae Nil8

9

Candidates may use any calculator EXCEPT those with the facility for

symbolic algebra, differentiation and/or integration. Thus candidates may NOT

use calculators such as the Texas Instruments TI 89, TI 92, Casio CFX 9970G,

Hewlett Packard HP 48G..

Instructions to Candidates

Tour candidate details are printed next to the bar code above. Check that these are correct

and sign your name in the signature box above.

If your candidate details are incorrect, or missing, then complete ALL the boxes above.

When a calculator is used, the answer should be given to an appropriate degree of accuracy.

You must write your answer for each question in the space following the question.

If you need more space to complete your answer to any question, use additional answer

sheets.

Information for Candidates

A booklet mathematical Formulae and Statistical Tables is provided.

Full marks may be obtained for answers to ALL questions.

This paper has 9 questions.

Advice to Candidates

You must ensure that your answers to parts of questions are clearly labelled.

You must show sufficient working to make your methods clear to the examiner. Answers

without working may gain no credit.

Total

Turn over

17

Surname Initial(s)

Signature


18/57

Leave

blank1. Find the first 3 terms, in ascending powers ofx, of the binomial expansion of (2+ 3x)6.

(4)

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blank2. The circle Chas centre (3, 4) and passes through the point (8, 8).

Find an equation forC.

(4)

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blank3. The trapezium rule, with the table below, was used to estimate the area between the

curvey = (x3+ 1), the linesx = 1,x = 3 and thex-axis.

x 1 1.5 2 2.5 3

y 1.414 2.092 3.0000

(a) Calculate, to 3 decimal places, the values ofy forx = 2.5 andx = 3.

(2)

1 (b) Use the values from the table and your answers to part (a) to find an estimate, to

2 decimal places, for this area.

(4)

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blank4. Solve, for 0 x < 360, the equation

3 sin2x = 1 + cosx,

giving your answers to the nearest degree.

(7)

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blank5. Figure 1

The shaded area in Fig. 1 shows a badge ABC, whereAB andACare straight lines, with

AB =AC= 8 mm. The curveBCis an arc of a circle, centre O, where OB = OC= 8 mm

and O is in the same plane asABC. The angleBACis 0.9 radians.

(a) Find the perimeter of the badge.

(2)

(b) Find the area of the badge.

(5)

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22

8 mm

8 mm

8 mm

8 mm

O A

B

C


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blank6. At the beginning of the year 2000 a company bought a new machine for 15 000. Each

year the value of the machine decreases by 20% of its value at the start of the year.

(a) Show that at the start of the year 2002, the value of the machine was 9600.

(2)

When the value of the machine falls below 500, the company will replace it.

(b) Find the year in which the machine will be replaced.

(4)

To plan for a replacement machine, the company pays 1000 at the start of each year

into a savings account. The account pays interest at a fixed rate of 5% per annum. The

first payment was made when the machine was first bought and the last payment will be

made at the start of the year in which the machine is replaced.

(c) Using your answer to part (b), find how much the savings account will be worthimmediately after the payment at the start of the year in which the machine is

replaced.

(4)

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blank2 7. (a) Use the factor theorem to show that (x + 1) is a factor of

3

x3x210x8.4 (2)

(b) Find all the solutions of the equationx

3

x2

10x8 = 0. (4)

(c) Prove that the value ofx that satisfies

2 log2x + log2 (x1) = 1 + log2 (5x + 4) (I)

is a solution of the equation

x3x210x8 = 0.(4)

(d) State, with a reason, the value ofx that satisfies equation (I).

(2)

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10 c1 specimen paper

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