Download 1. Five pipes labelled, “6 metres in length”, were delivered to a

1.
Five pipes labelled, “6 metres in length”, were delivered to a building site. The contractor
measured each pipe to check its length (in metres) and recorded the following;
5.96, 5.95, 6.02, 5.95, 5.99.
(a)
(b)
(i)
Find the mean of the contractor’s measurements.
(ii)
Calculate the percentage error between the mean and the stated, approximate
length of 6 metres.
Calculate
3.89 5  8.73 0.5 , giving your answer
(i)
correct to the nearest integer;
(ii)
in the form a ×10k, where 1  a  10, k 
.
Working:
Answers:
(a) (i)............................................
(ii)...........................................
(b) (i)............................................
(ii)...........................................
(Total 6 marks)
1
2.
(a)
Write down the following numbers in increasing order.
3.5, 1.6 ×10−19, 60730, 6.073×105, 0.006073×106, , 9.8×10−18.
(b)
Write down the median of the numbers in part (a).
(c)
State which of the numbers in part (a) is irrational.
Working:
Answers:
(a) ...................................................
...................................................
...................................................
...................................................
...................................................
...................................................
...................................................
(b) ...................................................
(c) ...................................................
(Total 6 marks)
2
3.
A store sells bread and milk. On Tuesday, 8 loaves of bread and 5 litres of milk were sold for
$21.40. On Thursday, 6 loaves of bread and 9 litres of milk were sold for $23.40.
If b = the price of a loaf of bread and m = the price of one litre of milk, Tuesday’s sales can be
written as 8b + 5m = 21.40.
(a)
Using simplest terms, write an equation in b and m for Thursday’s sales.
(b)
Find b and m.
(c)
Draw a sketch, in the space provided, to show how the prices can be found graphically.
5
4
m
3
2
1
0
0
1
2
3
4
b
Working:
Answers:
(a) .................................................
(b) .................................................
(Total 6 marks)
3
4.
The length of one side of a rectangle is 2 cm longer than its width.
(a)
If the smaller side is x cm, find the perimeter of the rectangle in terms of x.
The perimeter of a square is equal to the perimeter of the rectangle in part (a).
(b)
Determine the length of each side of the square in terms of x.
The sum of the areas of the rectangle and the square is 2x2 + 4x +1 (cm2).
(c)
(i)
Given that this sum is 49 cm2, find x.
(ii)
Find the area of the square.
Working:
Answers:
(a) .................................................
(b) .................................................
(c)
(i).........................................
(ii)........................................
(Total 6 marks)
4
5.
Jenny has a circular cylinder with a lid. The cylinder has height 39 cm and diameter 65 mm.
(a)
Calculate the volume of the cylinder in cm3. Give your answer correct to two decimal
places.
(3)
The cylinder is used for storing tennis balls.
Each ball has a radius of 3.25 cm.
(b)
Calculate how many balls Jenny can fit in the cylinder if it is filled to the top.
(1)
(c)
(i)
Jenny fills the cylinder with the number of balls found in part (b) and puts the lid
on. Calculate the volume of air inside the cylinder in the spaces between the tennis
balls.
(ii)
Convert your answer to (c) (i) into cubic metres.
(4)
(Total 8 marks)
6.
The natural numbers: 1, 2, 3, 4, 5… form an arithmetic sequence.
(a)
State the values of u1 and d for this sequence.
(2)
(b)
Use an appropriate formula to show that the sum of the natural numbers from 1 to n is
1
given by
n (n +1).
2
(2)
(c)
Calculate the sum of the natural numbers from 1 to 200.
(2)
(Total 6 marks)
5
7.
A geometric progression G1 has 1 as its first term and 3 as its common ratio.
(a)
The sum of the first n terms of G1 is 29 524. Find n.
(3)
A second geometric progression G2 has the form 1,
(b)
1 1 1
, ,
…
3 9 27
State the common ratio for G2.
(1)
(c)
Calculate the sum of the first 10 terms of G2.
(2)
(d)
Explain why the sum of the first 1000 terms of G2 will give the same answer as the sum
of the first 10 terms, when corrected to three significant figures.
(1)
(e)
Using your results from parts (a) to (c), or otherwise, calculate the sum of the first 10
1
1
1
terms of the sequence 2, 3 , 9 , 27
…
3
9
27
Give your answer correct to one decimal place.
(3)
(Total 10 marks)
6