代考Mathematics-代写数学考试-考试助攻

Mathematics

2018-19

Test Session

代考Mathematics Find the equation of the line which passes through the point(-6,11) and is perpendicular to the line with equation 3𝑥 ＋ 2𝑦 ＋ 1＝0.

INSTRUCTIONS TO STUDENTS

SECTION A Answer ALL questions. This section carries 40 marks.

SECTION B Answer 4 questions ONLY. This section carries 60 marks.

The marks for each question are indicated in square brackets [ ].

Answers must not be written during the first 10 minutes.
A formula booklet and graph paper will be provided.
An approved calculator may be used in the test.
Show ALL workings in your answer booklet.
Test materials must not be removed from the room.

Section A 代考Mathematics

Answer ALL questions. This section carries 40 marks.

Question A1

Find the equation of the line which passes through the point(-6,11) and is perpendicular to the line with equation 3𝑥 ＋ 2𝑦 ＋ 1＝ 0.

Give your answer in the form 𝑎𝑥 ＋ 𝑏𝑦 ＋ 𝑐 ＝0 where 𝑎, 𝑏 and 𝑐 are integers.[ 4 ]

Question A2

A student plays two games of tennis. The probability that she wins the first game is If she wins the first game, the probability she wins the second is If she does not win the first game, the probability she wins the second is

a) Draw and label a tree diagram. [ 2 ]

b) Find the probability the student wins both games. [ 2 ]

Question A3

When 2x³＋5x²-7𝑥＋k is divided by x＋2, the remainder is 4𝑘.

Use the Remainder Theorem to find the value of 𝑘. Show all working.[ 3 ]

Question A4

In the expansion of(p+6x)⁶the coefficient of the term in x⁴ is 12 times larger than the coefficient of the term in x³. Find the value of 𝑝. [ 4 ]

Question A5

Solve the equation log4𝑥-log3(x-5)＝ 2.Each stage of your working must be clearly shown.[ 4 ]

Question A6

Solve 2 cos(𝜃＋75°) 1 for 0°≤θ≤ 360°[ 5 ]

Question A7 代考Mathematics

An equation is defined as 𝑦＝e^x2-ln 𝑥.

Find and hence find its value when 𝑥=0.6

Give your answer to 2 significant figures. All working must be shown.

In this question, 1 mark will be given for the correct use of significant figures. [ 4 ]

Question A8

A curve has equation 𝑦= 𝑥³-4𝑥² + 7𝑥-1.

Find the equation of the tangent at the point (2, 5).

Give your answer in the form 𝑦= 𝑚𝑥+c.

All working must be shown.[ 4 ]

Question A9

Find

[ 4 ]

Question A10

Evaluate

Give your answer in exact form.

All working must be shown. Just quoting the answer, even the correct one, will score no marks if this working is not seen.[ 4 ]

Section B 代考Mathematics

Answer 4 questions ONLY. This section carries 60 marks.

Question B1

a)Line 𝑙₁has equation 𝑦=11-3𝑥.

Line 𝑙₂ has equation 𝑦=2𝑥-9.

Find the coordinates of the point where line 𝑙₁ intersects with line 𝑙₂ .[ 3 ]

b) Find the range of values which satisfy 6𝑥²-13𝑥- 63 ≤ 0.[ 4 ]

c)The function 𝑓(𝑥)is defined as 𝑓(𝑥)=𝑥²+6𝑥 + 4.

i.Write 𝑓(𝑥) in the form (𝑥+a)²+b where 𝑎 and 𝑏 are integers.[ 2 ]

ii.Hence solve the equation 𝑓(𝑥= 0, giving your answers in surd form.[ 1 ]

iii. Sketch the graph of 𝑦=𝑓(𝑥) (this must not be done on graph paper). On your sketch, show clearly the coordinates where the curve crosses the 𝑥-axis and 𝑦- axis. Show also the coordinates of any stationary value.[ 3 ]

d) Divide 𝑥³-5𝑥²-6𝑥 + 30 by (𝑥²-6) .[ 2 ]

Question B2

a)The probability a student is late for college on any given day is 11𝑝- 7.

The probability that he is not late is 9𝑝-5.

i.Find the value of 𝑝.[ 2 ]

ii.Find the probability that, over two consecutive days, he is late exactly once.[ 3 ]

Figure 1 shows two acute-angled triangles ABC and ACD. AD=12 cm,AC=10 cm, DC=√84 cm and AB=𝑘√5 cm. Angle DAC=𝜃° and angle CAB=30°.

i.Find the value of cos 𝜃, giving your answer in the form where 𝑚 and 𝑛 are integers.[ 3 ]

ii.Without working out the size of 𝜃 and showing all working, show that sin .[ 2 ]

iii. Find the size of angle ADC.[ 2 ]

The area of triangle ABC is half of the area of triangle ACD. 代考Mathematics

iv.Find the value of 𝑘.[ 3 ]

Question B3

a)In an arithmetic series, the first term is -75 and the 14th term is half of the common difference.

i.Find the common difference.[ 2 ]

ii.Find the sum of the first 30 terms.[ 3 ]

b)In a geometric series, the 3rd term is 80 and the 6^thterm is 156.

i.Find the common ratio.[ 3 ]

ii.Find the first term.[ 2 ]

iii. How many terms are needed for the sum of the series to exceed 30000?[ 4 ]

iv.Is it possible to find the sum to infinity? Give a reason.[ 1 ]

Question B4 代考Mathematics

a)A survey is carried out on the population growth in a village. The number of people,began is given by 𝑁, who live in the village 𝑡 years after the survey

i.State the number of people at the start of the survey.[ 1 ]

ii.How many people are there after 2 years?[ 2 ]

iii. Find an expression for .[ 1 ]

iv.What does the value of tell us?[ 1 ]

v.Find the value of 𝑡 when=90.[ 3 ]

b) Solve

[ 4 ]

c) Simplify

Your answer must contain no logarithms.

Each stage of your working must be clearly shown.[ 3 ]

Question B5

Figure 2 shows a solid cuboid which is tall. The total surface area is 6804 cm2 . 3.5𝑥 cm wide, 4𝑥 cm long and ℎ cm Find an expression for ℎ in terms of 𝑥.[ 2 ]

b) Show that the volume of the cuboid, 𝑉, is given by

[ 3 ]