1
The volume of a sphere is 70 cm3 correct to the nearest cm3.
Calculate the upper bound for the surface area of the sphere.
Give your answer correct to 1 decimal place. You must show all
your working.
A and B are points on the circumference of a circle, centre O.
AT is a tangent to the circle. Angle TAB = 58°.
Angle BTA = 41°.
Calculate the size of angle
OBT. You must give
reasons at each stage of
your working.
...........................................................cm2(4)
(5)
2
Here is a shaded parallelogram inside a rectangle.
The area of the parallelogram
is (10x + 50) cm2. Work out the
length of the base of the
parallelogram.
The table gives some information about the average price of a litre of
petrol in England.
Work out the percentage increase in the average price of a litre of petrol
in England between January 2007 and January 2012. Give your answer
correct to 3 significant figures.
____________________(5)
Week 6 Higher Summer Homework
........................................................... %(3)
b
The average price of a litre of petrol in England increased by
20% from January 2010 to January 2012.
The expression x2 – 8x + 21 can be written in the form (x – a)2 + b for all
values of x. Find the value of a and the value of b.
Work out the average price of a litre of petrol in England in
January 2010. Give your answer in pence, correct to 1 decimal
place.
a=......................
b=......................
(3)
The equation of a curve is y = f(x) where f(x) = x2 – 8x + 21
The diagram shows part of a sketch of the graph of y = f(x).
........................................................... pence(3)
(6)
5
Express as a power of 5:
a 53 × 54
____________________
b
511
52
____________________
c
(52 )6
____________________
d
The minimum point of the curve is M.
5
(53 )
54
b
__________________(4)
Write down the coordinates of M.
.................................................................................................(1)
(4)
Week 6 Higher Summer Homework
7
The diagram shows a concrete pipe with outer diameter 12 cm
and
inner diameter 10.5 cm.
(a)8a Expand and simplify x(x + 1)(x − 1)
………………………………………….. (2)
Calculate the volume of concrete
used to make a 2-metre length
of this pipe.
In a list of three consecutive positive integers at least one of the numbers
is even and one of the numbers is a multiple of 3. n is a positive integer
greater than 1.
3
b Prove that n – n is a multiple of 6 for all possible values of n.
____________________(4)
(2)
61
2 – 1 is a prime number.
c
Explain why 261 + 1 is a multiple of 3.
(2)
(6)
Week 6 Higher Summer Homework
9
The diagram shows the cross-section of the water in a drainage
channel.
A
The water flows along the drainage channel at a rate of 486 000 litres per
minute. The depth of the water is constant.
Work out the speed of the water. Give your answer in metres per second.
The cross-section is in the shape of a trapezium with one line of
symmetry.
The base of the drainage channel is horizontal. The two equal
sides of the trapezium are each inclined at 45° to the horizontal.
The length of the base of the trapezium is 3 metres. The depth
of the water is d metres.
(4)
(9)
10
A school has a biathlon competition. Each athlete has to throw a javelin and
run 200 metres.
a The points scored for throwing a javelin are worked out using the formula
The area of the cross-section is A m2.
a
P1 = 16(D – 3.8)
Write a formula for A in terms of d. Give your answer in its
simplest form.
Where P1 is the number of points scored when the javelin is thrown a
distance D metres.
(3)
b
The depth of the water in the drainage channel is 1.5 metres.
Find the area of the cross-section of the water.
(2)
Week 6 Higher Summer Homework
i Lottie throws the javelin a distance of 42 metres. How many points does
Lottie score?
Ii
Ingrid scores 584 points for throwing the javelin. Work out the
distance that the javelin was thrown by Ingrid.
(4)
Iii
The points scored for running 200 metres are worked out using
the formula
P2 = 5(42.5 – T)2
where P2 is the number of points scored when the time taken to
run 200 metres is T seconds.
Bi
ii
Suha scores 1280 points in the 200 metres work out the time, in
seconds, it took Suha to run 200 metres.
The formula for the number of points scored in the 200 metres
should not be used for T > n. State the value of n.. Give a
reason for your answer.
(4)
(8 )
Week 6 Higher Summer Homework