date: time: total marks available: total marks achieved: · 6/6/2015 · q7. make t the subject of...

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Question 1-11 Non Calc Questions 12-21 Calculator

Questions Q1.

(a) Factorise fully 6ab + 10ac

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(2)

(b) Expand and simplify (x − 5)(x + 7)

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(2)

(c) Simplify

Give your answer in its simplest form.

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(2)

(d) Factorise y2 − 16

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(1)

(e) Simplify (h2)−3

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(1)

(Total for Question is 8 marks)

Q2.

The point A has coordinates (3, 8). The point B has coordinates (7, 5). M is the midpoint of the line segment AB. Find the coordinates of M.

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Q3.

Simplify fully

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Q4.

* The diagram shows a pentagon.

All measurements are in centimetres.

Show that the area of this pentagon can be written as 5x2 + x – 6


5.

Solve the simultaneous equations

5x + 2y = 11 4x – 3y = 18

x = . . . . . . . . . . . . . . . . . . . . . .

y = . . . . . . . . . . . . . . . . . . . . . .


Q6.

On the grid, draw the graph of y = 2x – 3 for values of x from –2 to 2


Q7.

Make t the subject of the formula

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Q8.

*This formula is used to work out the body mass index, B, for a person of mass M kg and height H metres.

A person with a body mass index between 25 and 30 is overweight.

Arthur has a mass of 96 kg. He has a height of 2 metres.

Is Arthur overweight? You must show all your working.


Q9.

You can use the graph opposite to find out how much Lethna has to pay for the units of electricity she has used.

Lethna pays at one rate for the first 100 units of electricity she uses. She pays at a different rate for all the other units of electricity she uses.

Lethna uses a total of 900 units of electricity.

Work out how much she must pay.

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Q10.

ABC is a triangle.

Angle ABC = angle BCA.

The length of side AB is (3x − 5) cm.

The length of side AC is (19 − x) cm.

The length of side BC is 2x cm.

Work out the perimeter of the triangle.

Give your answer as a number of centimetres.

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Q11.

(a) Expand and simplify (p + 9)(p – 4)

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(b) Solve = 4w + 2

w = . . . . . . . . . . . . . . . . . . . . . .

(3)

(c) Factorise x2 – 49

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(d) Simplify (9x8y3)½

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Q12.

k = 3e + 5

(a) Work out the value of k when e = –2

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(b) Solve 4y + 3 = 2y + 14

y =. . . . . . . . . . . . . . . . . . . . . (2)

(c) Solve 3(x – 5) = 21

x =. . . . . . . . . . . . . . . . . . . . . (2)

–3 < n < 4 n is an integer.

(d) Write down all the possible values of n.

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Q13.

The straight line P has been drawn on a grid.

Find the gradient of the line P.

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Q14.

T is inversely proportional to d2

T = 160 when d = 8

Find the value of T when d = 0.5

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Q15.

Here are the first five terms of an arithmetic sequence.

4 9 14 19 24

(a) Find, in terms of n, an expression for the nth term of this sequence.

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Here are the first five terms of a different sequence.

2 2 0 −4 −10

An expression for the nth term of this sequence is 3n − n2

(b) Write down, in terms of n, an expression for the nth term of a sequence whose first five terms are

4 4 0 −8 −20

........................................................... (1)


Q16.

The points A, B and C lie on a straight line.

The coordinates of A are (9, 0). The coordinates of B are (7, 4). The coordinates of C are (1, q).

Work out the value of q.

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Q17.

Stephanie is x years old. Tobi is twice as old as Stephanie. Ulrika is 3 years younger than Tobi.

The sum of all their ages is 52 years.

(a) Show that 5x − 3 = 52

(3)

(b) Work out the value of x.

x =.......................... (2)


Q18.

* Vicky makes 8 purses and 9 key rings to sell for charity.

The price of a purse will be twice as much as the price of a key ring.

Vicky wants to get a total of exactly £40 when she sells all the purses and all the key rings.

Work out the price Vicky needs to charge for each purse and for each key ring.

(Total for Question is 4 marks) Q19.

Julie is x years old. Kevin is x + 3 years old. Omar is 2x years old.

Write an expression, in terms of x, for the mean of their ages.

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Q20.

(a) Factorise x2 + 7x

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(b) Factorise y2 – 10y + 16

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*(c) (i) Factorise 2t2 + 5t + 2

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(ii) t is a positive whole number. The expression 2t2 + 5t + 2 can never have a value that is a prime number. Explain why.

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(3)


Mark Scheme Q1.

Q2.

Q3.

Q4.

Question Working Answer Mark Notes

*

(2x − 2)(2x +1) + ½ (2x − 2)((3x + 5) − (2x +1)) 4x2 – 2x – 2 + x2 + 4x – x - 4 = 5x2 + x – 6 Or (2x − 2)(3x + 5) − ½ (2x − 2)((3x + 5) − (2x +1)) = 6x2 – 6x + 10x - 10 - x2 - 4x + x + 4 = 5x2 + x – 6

Show 4 M1 for correct expression for a single rectangle area (2x − 2)(2x +1) or (2x − 2)(3x + 5) M1 for correct expression for triangle area ½ (2x − 2)((3x + 5) − (2x +1)) M1 for all 4 terms correct with or without signs or 3 out of no more than four terms correct with signs in expansion of any two linear expressions. C1 for 5x2 + x − 6 and all steps clearly shown in a logical progression QWC: All steps need to be clearly laid out showing a logical progression

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Q6.

Q7.

Q9.

Q10.

Q11.

Q12.

Q13.

Q14.

Q15.

Q17.

Q18.

Q19.

Q20.

date: time: total marks available: total marks achieved: · 6/6/2015 · q7. make t the subject of...

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