Week 3 Higher Summer Homework
1
Chelsea's height is 168 cm to the nearest cm.
b
(a) What is Chelsea's minimum possible height?
Make k the subject of the formula.
........................................................... cm(1)
(b) What is Chelsea's maximum possible height?
........................................................... cm(1)
(2)
..........................................................(3).
2
a
3
Simplify fully
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.
..........................................................(3)
Week 3 higher summer homework
(5)
4
Liam, Sarah and Emily shared some money in the ratio 2 : 3 : 7.
6
The lines y = x – 2 and x + y = 10 are drawn on the grid.
How many parts did they share the money in?
a
………………………….(1)
How many more parts did Emily get than Liam?
b
c
………………………….(1)
Emily got £80 more than Liam. Using your answer to (b), how much
money was one part worth?
…………………………(1)
How much money did Sarah get?
d
5
………………………….(1)
Write down the value of 10–1
............................ (1)
(b) Find the value of
in the form k
y>x–2
x + y < 10
............................(2)
(c) Write
On the grid, mark with a cross (×) each of the points with integer
coordinates that are in the region defined by
x>3
, where k is an integer.
............................(2)
(3)
Week 3 higher summer homework
7
B
The diagram shows the plan of a playground.
Calculate an estimate for the mean temperature.
........................................................... ° C(4)
c
Draw a frequency polygon for the information in the table.
Bill is going to cover the playground with tarmac. It costs £2.56 to
cover each square metre with tarmac. Work out the total cost of the
tarmac Bill needs.
..............................................................................................................(4)
8
The table gives information about the temperature, T °C, at noon in a
town for 50 days.
a
Write down the modal class interval.
Week 3 higher summer homework
......................................... (1)
(2)
(7)
9
10 Pavel has a combination lock. Pavel has to set each part of the lock to a digit
between 0 and 9 inclusive. One possible way to do this is shown in the
diagram.
A
How many different ways can Pavel set the lock?
ABCD is a rhombus.
M is the midpoint of BD.
E is the point on BD such that DE = CE.
Calculate the size of angle MCE.
……………………………….(2)
.
B
How many odd and how many even numbers are on each part of the lock?
………………………………. (1)
.
c
(3)
Pavel decides that the 1st and 3rd digits will be odd numbers and that the 2nd
and 4th digits will be even numbers greater than 0.
How many different ways are possible now?
……………………………….(1)
.(4)
Week 3 higher summer homework
Week 3 higher summer homework