Assessment Exercise GCSE Maths RevisingUnits and Sample Assessment Material
This assessment exercise provides you with the opportunity to demonstrate your skills of creativity, innovation and subject knowledge in the revision of assessment materials.
1Spirals are seen a lot in nature.
Here are two mathematical spirals.
A B
(a)Write down two facts about the symmetry of spirals.
______[1]
(b)What is the difference in the way spiral A and spiral B are built up?
______[1]
[1]
The Spiral of Theodorus is a spiral which is constructed from a sequence of right-angled triangles. Each triangle in the sequence has height 1 and a base constructed from the hypotenuse of the previous triangle. The sequence starts with the unit-length isosceles triangle. It was first constructed by the Ancient Greek mathematician Theodorus of Cyrene.
The spokes of thespiral are labelled S1, S2, S3 etc.
Answer these questions about the spiral of Theodorus.
(c)Do the angles between each spoke, increase, decease or stay the same?
Support your answer with some calculations.
______[2]
(d)Show mathematically which spoke is closest to making a straight line with with spoke S1.
______[3]
2A pile-driver is used to drive a post into the ground.
At the first blow it drives the post 80 cm into the ground.
With each subsequent blow it drives the post half the distance in of the blow before.
How far in will the post go?
______cm [3]
3One penny saved for 1000 years at 4% compound interest gives a £1 000 000 000 total accrued.
Show whether or not this could in theory be true.
______because______
______[2]
4A 4-digit number can be represented as abcd which is equivalent to 1000a + 100b + 10c + d.
Use this idea and some algebra to prove that 4-digit numbers which read the same when reversed e.g. 5115 or 9339 are always multiples of 11.
[4]
1 / (a) / No reflection symmetry or equivalentNo rotation symmetry or equivalent / 1
1
(b) / A goes anti-clockwise and
B goes clockwise / 1 / Or equivalent statement
(c) / Angle between spokes deceases, supported by “numbers” / 3 / 2: 1 for each correct angle seen; maximum of 2
1: Statement to the effect that angles between spokes decrease round the spiral.
(d) / S6
support by evidence of trials / 3 / 2: 1 for each correct angle to S1, seen; maximum of 2
1: Statement to the effect that S6 almost makes a straight line with S1 / Dependent on gaining at least 1 mark previously
2 / 160 cm / 3 / 2: 159.9 ……
1: At least 1 correct total depth
3 / True because total is about £1015 / 2 / 1: (figures 104)1000 seen in working
4 / 4 / 1: abba seen or implied
1: a + 10b + 100b + 1000c
1: = b(110) + a(1001)
1: both are multiples of 11
1