Download Classified Past papers Chapter one Arithmetic 1. Marcus sees a

Classified Past papers
Chapter one
Arithmetic
1. Marcus sees a motorbike advertised for ₤ 750. This is the price after reduction of
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Classified Past papers
Chapter one
15%. Work out the original price of the motorbike.
(1998)
.
₤………………..
(3 marks)
-------------------------------------------------------------------------------------------------2. Calculate, giving your answer in standard form correct to 3 significant figures.
1.52 105  4.6 104
4.56 102
(1998)
…………………
(4 marks)
----------------------------------------------------------------------------------------------3. Astrid bought a motor car for ₤ 10 000 on the first of January 1996. It lost 15%
of its value during 1996 and then 10% every year from the first of January 1997.
Work out the value of the car on the first of January 1999.
₤………………
4.
Calculate the value of
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(5 marks)
(June 1998)
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Classified Past papers
21.7  32.1
16.20  2.19
Chapter one
Give your answer correct to 3 significant figures.
………………..
(3 marks)
-------------------------------------------------------------------------------------------------5. The star Sirius is 81 900 000 000 000 km from the Earth.
(June 1998)
(a) Write 81 900 000 000 000 in standard form.
……………….
Light travels 3  10
5
(2 marks)
km in 1 second.
(b) Calculate the number of seconds that the light takes to travel from Sirius to
the Earth.
Give your answer in standard form correct to 2 significant figures.
………………… (3 marks)
(c) Convert your answer to part (b) to days.
Give your answer as an ordinary number.
………………..
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(2 marks)
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Classified Past papers
Chapter one
6. A Shop has a sale of jackets and shirts. In a sale there are a total of 120 jackets
and shirts.
(Nov. 1998)
The jackets and shirts are in the ratio 5 : 3.
(a) Work out the number of jackets.
…………. (3 marks)
(b) Calculate the percentage that is shirts.
…………% (2 marks)
-------------------------------------------------------------------------------------------------THE SENATE
5
Petrol 9 litres per 100
7.
1 km =
mile. 1 gallon = 4.54 litre. (Nov. 1998)
km
8
(a) Change 9 litres per 100 km into miles per gallon.
…………………. (4 marks)
Correct to the nearest whole number, the petrol consumption of the Brighton is
30 miles per gallon.
(b) (i) Write down the maximum the petrol consumption could be.
…………… miles per gallon
(ii) Write down the minimum the petrol consumption could be.
……………. miles per gallon
(2 marks)
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Classified Past papers
Chapter one
F
8.
ab
a b
(June 1999)
Imam uses this formula to calculate the value of F. Imam estimates the value
of F without using the calculator.
a = 49.8 and b = 30.6
(a) (i) Write down approximate values for a and for b that Imam could use to
estimate the value of F.
approximate value for a …………………….
approximate value for b ……………………
(ii) Work out the estimate for the value of F that these approximate give.
………………………………
(iii) Use your calculator to work out an accurate value For F.
Use the a = 49.8 and b = 30.6.
Write down all the figures on your calculator display.
………………………..
(4 marks)
Imam Works out the value of F With two new values for a and b.
(b) Calculate the value of F when
a = 9.6  10
12
and
b = 4.710 11.;
Give your answer in standard form, correct to two significant figures.
……………………….
(3 marks)
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Classified Past papers
9.
Chapter one
Joe put ₤ 5000 in a building society saving account. Compound interest at 4.8 %
was added at the end of each year.
(a) Calculate the total amount of money in Joe’s saving account at the end of 3 years.
(Nov. 1999)
₤……………..
(4 marks)
Sarah also put a sum of money in a building society saving account. Compound
interest at 5% was added at the end of each year.
(b) Work out the single number by which Sarah has to multiply hr sum of money to
find the total amount she will have after 3 years.
…………………. (2 marks)
-----------------------------------------------------------------------------------------------10. Use your calculator to work out the value of
(June 2000)
12.32  7.9
1.8  0.17
Give your answer correct to 1 decimal place.
…………………. (3 marks)
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Chapter one
11. y is directly proportional to x. y = 8 when x = 5.
(Nov. 1999)
(a) Calculate the value of y when x = 7.
………………. (2 marks)
w is inversely proportional to u 2
(b) Draw a sketch of the graph of w against u.
Use the axes given below
w
O
u
(2 marks)
w = 12 when u = 5.
(c) Calculate the value of u when w = 27
……………………… (3 marks)
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Classified Past papers
Chapter one
12. The price of anew television is ₤423. This price includes value added tax (VAT)
at 17.5%. (a) Work out the cost of the television before VAT was added.
(June 2000)
………………………. (3 marks)
By the end of each year the value of television has fallen by 12% of its value at
the start of that year.
The value of the television was ₤423 at the start of the first year.
(b) Work out the value of the television at the end of the third year.
Give your answer to the nearest penny.
………………………… (4 marks)
-------------------------------------------------------------------------------------------------13. In a sale all prices are reduced by 30%. The sale of a Jacket is ₤28.
(Nov. 2000)
Work out the price of the Jacket before sale.
…………………. (3 marks)
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Chapter one
14. y is inversely proportional to the square of x.
(Nov. 2000)
y = 3 when x = 4.
(a) Write y in terms of x
y = …………………….. (3 marks)
(b) Calculate the value of y when x = 5.
y = …………………….. (2 marks)
-------------------------------------------------------------------------------------------------15. ₤5 000 is invested for 3 years at 4% per annum compound interest. (June 2001)
Work out the total interest earned over the three years.
₤………………… (3 marks)
------------------------------------------------------------------------------------------------
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16. Calculate the value of
Chapter one
5.98  108  4.32  109
6.14  102
Give your answer in standard form correct to 3 significant figures.
………………………..(3 marks)
------------------------------------------------------------------------------------------------17. x = 3, correct to 1 significant figure.
(June 2001)
y = 0.06, correct to 1 significant figure.
Calculate the greatest possible value of
y
x 7
x
…………………….. (2 marks)
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Chapter one
18. y is directly proportional to x2. When x = 2, y = 36.
(June 2002)
(a) Express y in terms of x.
y = ………………… (3 marks)
z is inversely proportional to x.
When x = 3, z = 2.
(b) Show that z = c y n, where c and n are numbers and c > 0.
(You must find the values of c and n)
…………………………… (4 marks)
------------------------------------------------------------------------------------------------19. The distance of the earth from the sun at a particular moment is 93.5 million miles
(a) Write 93.5 million in standard form.
(Mock 1998)
………………………( 2 marks)
The distance of the earth from the moon at a particular moment is 2.5 × 105 miles.
(b) Write 2.5 × 105 as an ordinary number.
………………………( 1 mark)
(c) How many times further is the earth from the sun than it is from the moon?
Give your answer in standard form.
……………………….(2 marks)
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Chapter one
20. Natalie measured the distance between two points on a map.
(Mock 1998)
The distance she measured was 5 cm correct to the nearest centimetre.
(a) Write down the
(i) least upper bound at the measurement.
……………………. cm
(ii) greatest lower bound of the measurement.
…………………….. cm
(2 marks)
The scale of the map is 1 to 20 000
(b) Work out the actual distance in real life between the upper and lower bounds.
Give your answer in kilometres.
…………………………...km (2 marks)
-------------------------------------------------------------------------------------------------21. The temperature from a factory furnace varies inversely as the square of the
distance from the furnace.
(Mock 1998)
The temperature 2 metres from the furnace is 50o C.
Calculate the temperature 3.5 metres from the furnace. Give your answer to 2
decimal places.
…………………………..oC (5 marks)
------------------------------------------------------------------------------------------------22. Change 0.4 5 into a fraction in its lowest term.
(Mock 1998)
……………………….(3 marks)
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Classified Past papers
Chapter one
23. £500 is invested for 2 years at 6% per annum compound interest.
(June 1998)
(a) Work out the total interest earned over the two years.
£………………….(3 marks)
£250 is invested for 3 years at 7% per annum compound interest.
(b) By what single number must £250 be multiplied to obtain the total amount at the
end of the 3 years?
…………………….(1 marks)
-------------------------------------------------------------------------------------------------24. The numbers a and b are irrational and not equal.
(June 1998)
a + b is rational
(a) Write down possible values of a and b.
a = ……………………..
b = ……………………. (2 marks)
Two other numbers c and d are also irrational and not equal.
cd is rational.
(b) Write down possible values of c and d.
c = ………………………
d = ……………………..(2 marks)
-------------------------------------------------------------------------------------------------25. Use your calculator to work out the exact value of
(Nov. 1998)
14.82  (17.4  9.25)
(54.3  23.7)  3.8
………………………………… (3 marks)
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Classified Past papers
Chapter one
26. Here are the first five terms of a sequence.
5
8
11
14
(Nov. 1998)
17
Find, in terms of n, an expression for the nth term of the sequence.
……………………………..(2 marks)
-------------------------------------------------------------------------------------------------27. Sally estimates the value of
42.8  63.7
to be 8.
285
(Nov. 1998)
(a) Write down three numbers Sally could use to get her estimate.
........  ........
.........
(b) Without finding the exact value of
(2 marks)
42.8  63.7
, explain why it must be more
285
than 8.
…………………………………………………………………………………………………………………………………………….
………………………………………………………………………………………………………………………………………………
(2 marks)
-------------------------------------------------------------------------------------------------28. A shop is having a sale. each day, price are reduced by 20% of the price on the
previous day.
(Nov. 1998)
Before the start of the sale, the price of a television is £540.
On the first day of the sale, the price is reduced by 20%.
(a) Work out the price of the television on
(i) the first day of the sale.
£…………………………..
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Chapter one
(ii) the third day of the sale.
£……………………….
(5 marks)
on the first day of the sale, the price of a cooker is £300.
(b) Work out the price of the cooker before the start of the sale.
£................................(2 marks)
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29. (a) Write down all the factors of 15.
(June 2004)
...................... (2 marks)
(b) Write down all the multiples of 4 which are between 15 and 25.
................... (2 marks)
(c) Write down all the prime numbers which are between 15 and 25.
................... (2 marks)
(d) Write down the first square number which is greater than 25.
.................... (1 marks)
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Chapter one
30. The engine of a new aircraft had a major inspection after 1.2× 104 hours flying time.
The aircraft flies at an average speed of 900 km/h.
(June 2001)
(a) Calculate the distance travelled by the new aircraft before its engine had a
major inspection. Give your answer in standard form.
……………………km (3 marks)
In 2000 the aircraft carried a total of 1.2 × 105 passengers.
In 2001 The aircraft carried a total of 9 × 104 passengers.
(b) Calculate the difference in the number of passengers the aircraft carried in
2000 and in 2001. Give your answer as an ordinary number.
…………………..(2 marks)
-------------------------------------------------------------------------------------------------31. (a) (i)Write down the number 5.01 × 10 4 as an ordinary number.
(June 2001)
…………………………….
(ii) Write the number 0.0009 in standard form.
…………………..(2 marks)
(b) multiply 4 ×104 by 6 × 105.
Give your answer in standard form.
……………………….(2 marks)
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Chapter one
p = 8 × 103
32.
(June 2000)
q = 2 × 104
(a) Find the value of p × q.
Give your answer in standard form.
………………….(2 marks)
(b) Find the value of p + q.
Give your answer as an ordinary number.
………………….(2 marks)
-------------------------------------------------------------------------------------------------33. (a) Work out an estimate for
3.08  693.89
0.47
(June 2000)
………………………..(3 marks)
The length of a rod is 98 cm correct to the nearest centimetre.
(b) (i) Write down the maximum value that 98 cm could be.
…………………….cm
(ii) Write down the minimum value that 98 cm could be.
………………..cm (2 marks)
--------------------------------------------------------------------------------------------------
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Classified Past papers
Chapter one
34. Here are the first four terms of an arithmetic sequence.
3
7
11
(June 2002)
15
Find an expression, in terms of n, for the nth term of the sequence.
…………………….(2 marks)
-------------------------------------------------------------------------------------------------35. (a) Write 84 000 000 in standard form.
(Nov. 2000)
………………………..(2 marks)
(b)Work out
84000000
4  1012
Give your answer in standard form.
…………………….(3 marks)
-------------------------------------------------------------------------------------------------36. Wallace bought a computer for £3000.
(June 2002)
Each year the computer depreciated by 20%.
Work out its value two year after he bought it.
…………………………….(3 marks)
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