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# A*/A Level Math Questions Essay

1724 words - 7 pages

Edexcel GCSE
Mathematics (Linear)
A* Paper (not for the faint hearted)
Higher Tier
Time: 2 hours

Materials required for examination Items included with question papers
Ruler graduated in centimetres and Nil
millimetres, protractor, compasses,
pen, HB pencil, eraser.
Tracing paper may be used.

Instructions to Candidates_____________________________________________________
Check that you have the correct brain power required to attempt this question paper.

.....................................

(ii)
[pic]

ABC is a right-angled triangle. k is a positive integer.

Find the value of k.

k = .....................................
(5)
(Total 7 marks)
GCSE A* Questions

Skill: Solve direct and inverse variation problems

Question 2

The force, F, between two magnets is inversely proportional to the square of the distance, x, between them.

When x = 3, F = 4.

(a) Find an expression for F in terms of x.

F = ...............................
(3)

(b) Calculate F when x = 2.

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

(c) Calculate x when F = 64.

.................................
(2)

(Total 6 marks)
GCSE A* Questions

Skill: Calculate the limits of compound measures

Question 3

He then used the formula g = [pic] to calculate an estimate for g.

T = 1.3 correct to 1 decimal place. L = 4.50 correct to 2 decimal places. x = 30 correct to the nearest integer.

(a) Calculate the lower bound and the upper bound for the value of g. Give your answers correct to 3 decimal places.

Lower bound .........................................

Upper bound ..........................................
(4)
(b) Use your answers to part (a) to write down the value of g to a suitable degree of accuracy. Explain your reasoning.

...................................................................................................

...................................................................................................

(1)
(Total 5 marks)
GCSE A* Questions

Skill: Solve a pair of simultaneous equations where one is linear and the other is non-linear

Question 4

Solve the simultaneous equations

x2 + y2 = 29

y – x = 3

………………………………………………………
(Total 7 marks)

GCSE A* Questions

Skill: Rearrange more complicated formulae where the subject may appear twice or as a power

Question 5

[pic]

Rearrange the formula to make a the subject.

a =.....................................
(Total 4 marks)

GCSE A* Questions

Skill: Simplify algebraic fractions by factorisation and cancellation

Question 6

Simplify [pic]

.....................................

(Total 3 marks)
GCSE A* Questions

Skill: Solve a quadratic equation obtained from manipulating algebraic fractions where the variable appears in the denominator

Question 7

Solve the equation

[pic]

…………………………

(Total 7 marks)
GCSE A* Questions

Skill: Solve equations using the intersection of two graphs

Question 8

The diagram shows a circle of radius 5 cm, centre the...

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