GRADE 12
MATHEMATICS PAPER 3
DATE:
28 July 2008 / TIME: 2 HOURS
TOPIC:
MID YEAR EXAM / TOTAL MARK: 100
EXAMINER:
Mrs. P Copeland / MODERATOR:
Mrs. M Klein

Name:______Teacher: ______

Learning Outcomes / Assessment Standards / Question / Mark
3 / Space, Shape & Measurement / Quadrilaterals
10.3.2 Definitions of polygons
11.3.2 Similar Triangles
Midpoint Theorem
Ratio
Pythagoras Theorem by similar triangles / 3
4
9
10
8 / A:5
A: 9
B:14
B:15
B:10
4 / Data Handling
& Probability / Probability
10 4.2 Disjoint ( mutually exclusive) events, addition rule
Complementary events
11.4.2 Dependent and independent events
Venn diagrams and probability
Tree Diagrams and probability
Bias and Error
11.4.3 Misuses of statisitics and charts
Analysis of data
11.4.4 Differentiate between symmetric and skewed data / 7b
1
2
7a,c
6
5a,c
5b / B:2
A: 18
A: 8
B:11
A:5
A: 5
A:2
Total / 100

SECTION A: KNOWLEDGE & ROUTINE PROCEDURES50 Marks

QUESTION 118 Marks

At a school for boys there are 120 learners in grade 12. The following information was gathered about school sport.

  • 61 boys play rugby (R)
/
  • 11 swim and play rugby

  • 48 play golf (G)
/
  • 13 play golf and swim

  • 29 swim (S) for the school
/
  • 107 play rugby or golf or swim

  • 8 boys participate in all three

a) / Draw a Venn diagram for this survey. / (8)
b) / How many learners do not participate in any sport? ______/ (1)
c) / How many learners play rugby and golf? ______/ (2)
d) / Determine the probability that is a learner is selected at random that he:-
i) / only play rugby ______/ (2)
ii) / does not play golf ______/ (2)
iii) / participates in two sports ______/ (3)

QUESTION 28 Marks

A sample of 60 people is asked which of 3 sports they watch on TV. The sports are Ruby (R), Soccer (S) and Cricket (C) .

The results are shown in the Venn diagram below.

A person is selected at random from the group. Giving all your answers in simplest fraction form, find the probability that a randomly selected person

a) / watches none of the sports / (1)
b) / watches soccer / (1)
c) / watches rugby AND soccer / (1)
d) / watches cricket OR soccer / (1)
e) / watches rugby but does not watch cricket / (2)
f) / watches neither rugby NOR cricket / (2)

QUESTION 3 5Marks

ABCD is a rhombus. AC = 10 cm and BD = 22 cm with AD =

Calculate , correct to the nearest whole number.

QUESTION 49 Marks

In the figure, RV // STU and QW // RT.

PV = 16 mm and UV = 8 mm.

a) / Write down the following as a ratio without reasons.
i. / / (1)
ii. / / (1)
iii. / / (1)
iv. / / (2)
b) / Name a triangle that is similar to ∆PWV ______/ (2)
c) / Name a triangle that is similar to ∆QRW ______/ (2)

QUESTION 57 Marks

Study the following growths showing the number of South African males who die at a certain age.

a. Describe the difference in distribution of the age at death for males in 1990 and 1999.

(3)

b. Would you say that the graph for 1999 is symmetrical or skewed. Give a

social / political or economic reason for your answer.

(2)

c. How does it affect a country if there is a high death rate amongst the young,

economically active people between 15 and 49 years of age?

(2)

QUESTION 65 Marks

a. Study the following two graphs and explain why the second one is misleading. (3)

b. A school announces in its media release:(2)

“The Grade 12 pass rate has improved by a 100% from last year.”

Why is this statement misleading?

SECTION B: COMPLEX PROCEDURES & PROBLEM SOLVING50 Marks

QUESTION 713 Marks

In a soccer match between Manchester United and Everton, there was no score at full time. The winning team will be decided by a penalty shootout. Each team has three shots at the goal.

The striker for Manchester United has a record of scoring off 73% of the penalty shots he attempts.

a) / Draw a tree diagram to represent the possible outcomes of the penalty shootout. / (6)
b) / Are the events goal on attempt 1 and goal on attempt 2 independent or dependent events? Why? / (2)
c) / What is the probability that Manchester United will score”
i) / all three goals / (1)
ii) / no goals / (1)
iii) / on the first goal and not score on the others / (1)
v) / one goal / (2)

QUESTION 810 Marks

a) / Prove ∆ABD /// ∆ADC / (3)
b) / Hence deduce an expression for AD² / (3)
c) / Assuming that DC² = CB.CA, prove the theorem of Pythagoras for Use your expression in b) to help you. / (4)

QUESTION 914 Marks

FGHI is a rectangle with FG = 6 units and FI = 8 units. J and K are the midpoints of GH and HI respectively. FJ and FK meet diagonal GI at L and M respectively. JNKP is a straight line.

a) / Prove JK//GI / (3)
b) / Why is FH = 10 units? / (2)
c) / Show that ON = 2 units / (3)
d) / Determine the length of IP / (4)
e) / Explain why L is the centroid( the point of intersection of the medians of a triangle) of ∆FGH. A median is the line drawn from the vertex to the midpoint of the opposite side. / (2)

QUESTION 1015 Marks

The image below is an aerial photograph of circles made in fields by flattened crops.

  1. Find the equation of the circle with centre B.(3)
  1. Find the co-ordinates of D(3)
  1. If the radius of the larger circle is 25 units and the radius of the smaller

circle is 5 units:

i)Find the value of (2)

ii)Hence, find the length of QR(2)

iii)Find the length of ER and hence write down the equation of

The circle with centre E(5)

QUESTION 118 Marks

The digits 1,2,3,4 and 5 are used to form natural numbers. The number may consist of 1 digit, 2 digits, 3, 4 or 5 digits. The digits may not be repeated.

a) / How many natural numbers may be formed? / (6)
b) / What is the probability that a 3 digit number can be formed whose last two digits are even. / (2)