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GRADE 10

MATHEMATICS ASSESSMENT EXEMPLARS

Grade 10 - 2 - Exemplar Assessments 2012

Dear Teacher

1. This resource is a compilation of 14 tests that cover all the grade 10 topics.

2. Each test is out of 50 marks and is 1 hour long.

3. These tests are exemplars which may be used as they are or adapted to suit your context.

4. They may also be used to compile your midyear or end-of-year examination.

5. When you do that you must ensure that you adhere to the topics weighting as specified in the

CAPS documents

Summary of Schools Based Assessment Tasks for Grades 10

Term 1 Term 2 Term 3 Term 4 PROMOTION MARK

Assessment

tasks

Test

Proj

ect/

Inve

stig

atio

n

Assig

nmen

t/Te

st

Exam

inat

ion

Test

Test

Test

Year

-mar

k

End-

of-y

ear

exam

inat

ion

TOTA

L

Total marks 50 50 50 100 50 50 50 200 300

Convert to a mark out of:

10 20 10 30 10 10 10 100 200 300


Test 1: Algebra 1Time: 1 hour Marks: 50

Question 1

1.1 Consider: A=

If , which value(s) of x will make A:

1.1.1 Rational (1)

1.1.2 Irrational (1)

1.1.3 Undefined (1)

1.1.4 Non-real (1)

[4] Question 2

2.1 Calculate the following products:2.1.1 (4)2.1.2 (4)2.1.3 (4)

2.2 Factorise fully:2.2.1 (4)2.2.2 (4)2.2.3 (4)

[24]Question 3

3.1 What must be added to to make it equal to (3)

3.2 With what expression must be divided to get a quotient of (3)

3.3 Evaluate if x =7,85 without using a calculator. Show all your work. (4)

3.4 With what expression must be multiplied to get a product of (3)[13]

Question 4

Simplify the following algebraic fractions

4.1 (4)

4.2 (5)


[9]


Test 2: Algebra 2Time: 1 hour Marks: 50

Question 1

1.1 Show that can be simplified to (6)

1.2 Solve for :1.2.1 (3)1.2.2 x(2x+3) = 2 (4)

1.3 Represent graphically: (5)

1.4 Solve the following system of equations:3x –2y + 8 = 0 and 4y–6 = 2x (6)

[18]Question 2One side of a rectangular field is metres long. Given that the area is

square metres, calculate the perimeter in terms of x and y[8]

Question 3

3.1 Simplify the following expressions(Give your answer with positive exponents)

3.1.1 (3)

3.1.3 (4)

3.1.4 (4)

3.2 Solve for if

3.2.1 (3)

3.2.2 (3)3.2.3 (4)

[24]


3.1.2 (3)

Test 3: Number PatternsTime: 1 hour Marks: 50

Question 1

1.1 Write down the next three terms and the general (or nth term) of each pattern:

1.1.1 2; 4; 6; 8; … 1.1.2 1; 7; 13; 19; …

1.1.3 1; 4; 9; 16; … 1.1.4 25; 21; 17; 13; …

1.1.5 1.1.6

1.1.7 1.1.8

(24)

Question 22.1 Consider the following pattern.

Arrangement 1 Arrangement 2 Arrangement 3{{{ {{{{ {{{{{

{{{{ {{{{{{{{{{

2.1.1 How many flowers will be used in the 4 arrangement? (1)2.1.2 How many flowers will be used in the n arrangement (2)2.1.3 Which arrangement will have 99 flowers (3)

2.2 The height of water in a tank is recorded whilst the tank is being filled. The results have been recorded at five minute intervals:

First reading After 5 minutes

After 10 minutes

After 15 minutes

After 20 minutes

Level in 3 11 19 27 35

2.2.1 What will be the height of the water after 25 minutes? (1)2.2.2 What will be the height after an hour? (2)2.2.3 At what rate is the level rising? Give your answer in minute. (2)2.2.4 What will be the water level after minutes? (3)2.2.5 After how many minutes will the water level be 403 ? (3)


2.3 Consider the following sequence of Es:

2.3.1 How many blocks will be needed to build the 10th E? (3)2.3.2 How many blocks will be needed for the nth E? (3)2.3.3 116 blocks are needed for the kth E. Calculate the value of k. (3)2.3.4 Can the total number of blocks ever be a multiple of 10? Explain. (3)

[26]Test 4 FinanceTime: 1 hours Marks: 50

Question 11.1 Simphiwe plans to travel to New Zealand. Her flight is paid for. However,

she will need spending money of about NZ$ 300. If the exchange rate is currently 5,1265 Rand to the NZ$ how much will she need in South African Rand ? (2)

1.2 Simphiwe has just received a gift of R 500 from her grandmother and she promises another R 500 in a year’s time. She decides to invest this money in an account which pays 8,5% p.a. compounded annually. How much additional money will she have to save to add to her investment after two years if she withdraws all the money for her trip. (8)

[10]Question 2

2.1 Determine through calculation which of the following investments will be more profitable:(a) R7 000 at 10% p.a compound interest for 5 years. (4)(b) R7 000 at 12% p.a simple interest for 5 years. (3)

2.2 Inflation is set at 5,5% for the next three years. A small scooter currently costs R7999,00. I want to buy this scooter on my birthday in 3 year’s time.

2.2.1 What will it cost in three year’s time? (3)2.2.2 The dealer offers me a hire purchase on the scooter on the following

terms: 15% deposit and the balance payable over 36 months. The current interest rate on a hire purchase deal is 23% per annum. Calculate my monthly payments. (6)

2.2.3 What is the total amount that I pay to the the dealer (2)2.2.4 Every year on my birthday I receive R3000 from my grandfather.

If I save this money in an account that pays 11% per annum compound interest, will I be able to pay in cash for the scooter after 3 years? Show all calculations to justify your answer (8)


Question 3

3.1 Below is a table with the buying and selling prices of different currencies: (13 /09/ 06)

3.1.1You have

R5000 to spend in Switzerland. How much Francs can

you buy? (2)3.1.2 What will it cost you in Rands to purchase 5000 Yen? (2)3.1.3 If you exchange 1000 NZD how much Rands will you get? (2)

3.1.4 You want to import a personal computer from Japan at a total cost of 96180 Yen. The equivalent computer cost R8 500 in South Africa. Will you import or buy locally? Show all calculations to justify your answer. (3)

3.2 Draw two graphs on the same set of axes to illustrate the difference between compound interest and simple interest graphically. (5)

[14]

Test 5: FUNCTIONS 1Time: 1 hours Marks: 50

Question 1

If and and , answer the following questions;

1.1 Determine the values of the following;1.1.1 1.1.21.1.3 if 1.1.41.1.5 1.1.6 if 1.1.7 1.1.8 (16)

1.2 Name the type of function that is defined in each case. (3)

1.3 Draw a sketch graph of each of the functions showing all critical points, asymptotes, axes of symmetry and intercepts with the axes. You can use the values in question 1.1 to assist you if necessary. Each function must be sketched on a separate set of axes. (6)

1.4 Determine the domain and range of the functions , and . (6)

[31]

Question 2


Country Currency Symbol Exchange Rate (units per R1)

Switzerland Franc Swiss Franc 0.1697New Zealand Dollar NZD 0.21

Japan Yen Y 16.03

2

1

-1

-2

-2 2

A ( 1 ; 1 )

h

g

Consider the functions and

2.1 Sketch the graphs of and on the same system of axes, showing ALL intercepts with the axes and relevant turning points (7)

2.2 Use your sketch to find the values of if;

2.2.1 (3)2.2.2 s(x) – t(x) = -3 (2)2.2.3 (3)2.2.4 s(x) < t(x ) (2)

2.3 Write down the equation of if results from shifting 2 units up. (2)[19]

Test 6: FUNCTIONS 2Time: 1 hours Marks: 50

Question 1

Sketched below are the functions and and A, the

point of intersection, is ( 1 ; 1 )

1.1 Find the values of , and (3)

1.2 What is the equation of the asymptote of (2)

1.3 What is the range of (2)

1.4 What is the equation of if is the reflection of in the y-axis (2)

[6]

Question 2Given the two functions and

2.1 Sketch the graphs of and on the same system of axes, showing the co-ordinates of all intercepts with the axes. (6)

2.2 Calculate the co-ordinates of the points at which (4)2.3 Read from your graph, the values of for which . (2)

2.4 Draw a dotted line on your sketch, showing graph of . The intercepts

on the axes must be shown. (3)[15]

Question 3

3.1 Determine the equation of a linear function f (x) = mx + c, if and (2)


y

x 0

f

2

P (3 ; 9)

3.2 Draw a sketch graph of . Clearly indicate the asymptotes. (3)

3.3 A sketch graph of is shown.

3.3.1 What is the length of line segment PR? (4)

3.3.2 For which values of x is ? (2)

3.3.3 Compare the shapes of

and (2)

[13]Question 4

4.1 Sketched below are graphs of and for

O>x

^y

C(1;6)

B(4;0)

A(0;2)

4.1.1 Given that cuts the -axis at and that lies on both graphs, calculate the values of and (4)

4.1.2 It is further given that cuts the -axis at the point . Calculate the values of and . (4)

4.1.3 Write down the equation of the horizontal asymptote of (2)

4.2 In the sketch f is the graph of the function + q

4.2.1 Calculate the value of a and q if the point P(3 ; 9) lies on the graph. (4)

4.2.2 Write down the equation of the asymptote of f. (2)


Y

X-3 R

P

O

[16]

Test 7 : Analytical GeometryTime: 1 hours Marks: 50

Question 1

S(x ; 3 )

R( -1 ; 1 )

Q( 4 ; 6 )

P( -5 ; 9 )

1.1 Find the gradient of line PQ (3)1.2 If it is given that , find the value of x in the point S (5)1.3 1.3.1 Assuming that , find the gradient of line SR (2)

1.3.2 What does this tell us about SR? Explain. (2)1.4 Join PR

1.4.1 What type of triangle is ? Show all working. (5)1.4.2 Find the area of (3)

[20]Question 2


y

x

D ( -2 ; k )

C ( 4 ; 6 )

B ( -8 ; 2 )

A ( -3 ; 7 )

2.1 Calculate the gradient of BC (3)2.2 D(-2; k) lies on BC. DA AC. Find the value of k. (4)2.3 Find the length of BC. (3)2.4 Assuming the value of k is 4, calculate the area of ABC. (5)

[15]

Question 3

Sketched below is . The co-ordinates of the vertices are as indicated on the sketch.

3.1 Calculate the co-ordinates of the mid-points D and E of AB and AC respectively. (4)3.2 Show that DE // DC (3)3.3 Given the points and , show that

PARM is a parallelogram by proving both pairs of opposite sides parallel. (4)3.4 The vertices of a rhombus , . Prove that:

the diagonals RO and HM bisect each other. (4)[15]

Test 8: Trigonometry 1 Time: 30 minutes


Marks: 25

Question 1

In each of the following right-angles triangles, write down the value of the required trigonometric ratio (leave your answers as ratios) and calculate the size of the angle marked :

1.1 Find the value of and the size of angle

(3)


(3)


(3)

[9]

Question 2

2.1 If sin = , determine each of the following without the use of a calculator:

(Hint: Use a sketch) ( < 90o)

2.1.1 cos 2.1.2 tan 2.1.3

2.1.4 sin 2 2.1.5 cos 2 2.1.6 sin 2 + cos 2 (8)

2.2 Make a conjecture about

a) (2)

b) sin 2 + cos 2 (2)

2.3 Simplify the following expressions without the use of a calculator and show ALL the workings:

(5)[17]

Test 9 : Trigonometry 2 Time: 1 hour


7

8

7

5

3

4

30

20 E

DC

B

A

Marks: 50

Question 1

Use a calculator to determine (correct to ONE decimal place), ( < 90o) in each of the following:

1.1 3 cos = 51.2 3 tan = 5 1.3 5 sin (2 + 10o) – 4 = 0 (10)

Question 2In the sketch below, is right angled at C, BD = 3 units, and . Also, BCDE is a rectangle.calculate the lengths of

2.1 BC (4)

2.2 CD (4)

2.3 AD (6)

2.4 Angle DBA (3)[17]

Question 3

With reference to the figure alongside:

3.1 Write down two ratios for cos 34. (4)

3.2 If CD = 8,3 cm, calculate the value of BD (4)

3.3 Write down a trigonometric definition for .(2)

[11]Question 4In the figure alongside MN NR, MRN = 42o, MN = 8 units, PR = 5 units and PR NR.

4.1 Calculate NR. (4)

4.2 Calculate MR (4)

4.3 Calculate PN (4)

[12]

Test 10: Trigonometry 3Time: 1 hour


B

AD

C34

42o

M

N

P

R

D1

D2

3 m

yx

Marks: 50

Question 1

A shark spotter is standing at lookout point 25m above the waters edge. He spots a shark in the water at an angle of depression of . If the swimmer that is also in the water is 5m from the foot of the lookout spot, how far is the shark from the swimmer?

[6]Question 2

A laser speed trapping device is mounted on a pole that is 3m high. The device measures the initial angle of depression of a car (x) and then measures the angle of depression again 1 second later (y).

These measurements are used to work out how much distance the car has covered in 1 second and then to determine whether or not the driver is breaking the speed limit.

2.1 Show that the initial distance from the camera is given by: and the distance

from the camera, one second later, is given by (3)

2.2 If and , calculate the distance (in metres) covered by the car


25m

5m

50

313

12

D

C

BA

in 1 second. (3)

2.3 If the speed limit is 60 km/hour, determine whether or not the motorist is exceeding the speed limit. Show all calculations. (If you were unable to do 6.1, assume that the car covered 20,51 m in 1 second.) (2)

[8]

Question 3

In the diagram, AC=13 units, AB = 12 units and BD = 4 units. and are right-angles.

3.1 Calculate the measurement of CB and BD. (4)

3.2 Now determine the value of:

3.2.1 (1)3.2.2 (1)3.2.3 (3)

3.3 Use you calculator to determine the size of angle A, correct to one decimal place. (2)

[11]

Question 4

Sketched are graphs of and

Write down the:4.1 value of ; (1)4.2 period of ; (1)

4.3 values of and (2)


4

2

-2

50 100 150 200 250 300 350

y

x

g

f

x

y

-90 -60 -30 0 30 60 90 120 150 180

-2

-1

1

2 g

f

4.4 range of (1)4.5 values of for which . (3)

[8]

Question 5

The following graphs have been drawn below: and + q

5.1 Determine the value of a and q. (2)5.2 Write down the values of x for which . (2)5.3 Write down the period of f. (1)5.4 Write down the equations of the asymptotes of f (2)5.5 For which values of x is f(x) = 0 (3)

[10]

Question 6Below is a sketch of and

6.1 Write down the amplitude of and (2)6.2 What is the range of (2)6.3 What is the period of (1)6.4 Determine the values of and (2)

[7]


Test11: StatisticsTime: 1 hour Marks: 50

Question 1

1.1 At a recent interschool athletics event, the following distances were recorded for all the participants in the girls long jump: 3,1m; 3,2m; 5,0m; 3,6m; 4,1m; 2,9m; 3,2m; 4,3m; 4,9m; 3,9m; 2,8m; 4,6m. Calculate the

1.1.1 mean, (3)1.1.2 median and (2)1.1.3 mode (1)

1.2 The amount of time, in minutes, that a group of Grade 10 learners spent on their cellular phonein a week was measured and recorded below. Use classwidths of 20 minutes

82 102 108 142 150 170

145 115 154 121 128 126

147 92 137 158 81 146

177 152 152 130 88 132

1.2.1 Construct a frequency table for this data set (5)1.2.2 Calculate the estimated mean time (5)1.2.3 What is the modal class? (1)1.2.4 What percentage of learners used their cellular phones for 2 hours or more

in the week? (2)1.2.5 What comment can you make regarding the use of cellular phones amongst

this group of learners? (2)[20]

Question 2

2.1 The marks in a class test of 15 girls in Mrs Mbusi’s Science class s given below. The test is out of 50 marks:43 42 31 32 22 13 44 38 25 50 9 1525 35 41

2.1.1 Determine the mean, median and mode of the marks. (3)2.1.2 Calculate interquartile range for the class (3)2.1.3 Draw a box and whisker plot to represent the marks (2)


2.2 Consider the box-and-whisker diagrams below representing the marks of two Grade 10 classes in a test out of 50

2.2.1 Write down the five number summary for 10B (3)2.2.2 What is the inter quartile rage for 10A (1)2.2.3 What is the median mark for 10B (1)2.2.4 What percentage of marks in 10A lies between the highest mark and the median (1)2.2.5 Which class in your opinion did the best? Give a reason (2)

[16]

Question 3

The pulse rate of patients at a clinic was measured and the results tabulated in a frequency table shown below3.1 Complete the frequency table (4)

Pulse rate Tally marks Frequency150≤x< 160. 3160≤x< 170. //// ///170≤x< 180. 13180≤x< 190. ////

Use the frequency table to determine:

3.1.1 How many patients were measured on that day? (1)3.1.2 the estimated mean (2)3.1.3 the modal class (1)

3.2 A music shop records the sales of CDs over a two year period. The monthly sales figures are given below:

204 255 310 283 288 393 282 359 364 172 158407 458 299 109 307 272 283 285 367 479 280382 258 111

3.2.1 Complete the frequency table below (4)

Class interval Tally marks Frequency Class midpoint Frequency x class midpoint

100 //// 4 150 600

24503150


4010 20 30 50

10A

10 B

Total Total

3.2.2 Determine the mean monthly sales to the nearest whole number (2)[14]

Test 12: ProbabilityTime: 1 hour Marks: 50

Question 1

1.1 A fair die is rolled once. 1.1.1 Write down the sample space (2)1.1.2 what is the probability of getting the following:

(a) The number 6 (1)(b) A number less than 3 (2)(c) the number 3 or 6 (2)(d) the number 3 and 6 (1)

1.2 . A bag contains 7 red marbles and 5 green marbles. One marble is drawn out of the bag. Determine the probability that it is:

1.2.1 a red marble (1)1.2.2 a green marble (1)1.2.3 a yellow marble (1)1.2.4 a red or green marble (2)1.2.5 not a red marble (2)

[15]

Question 2

Two dice are rolled simultaneously. 2.1 Write down the sample space (3)2.2 Determine the probability that :

(a) the number 2 is obtained (2)(b) the sum of the numbers equals 8 (2)(c ) one of the numbers is an odd number(d) both of the numbers are factors of 6 (2)

2.3 Mandy spins the spinner in figure 1 and Louisa spins the spinner in figure 2.

2.3.1 Calculate the probability for each one to get a 3 (2)2.3.2 Who has the greater chance of getting a 2? Give a reason for your answer (2)2.3.3 Who has the greater chance of getting a 1? Give a reason for your answer. (2)

[15]


15

2

34

3Figure 1

1

4

2

23

Figure 2

Question 3

There are 120 grade 10 learners at a school. 55 learners offer Mathematics and 80 offer Life Sciences. There are 25 learners who does not offer Mathematics or Life Sciences3.1 Represent the information in a Venn diagram (4)Use the Venn Diagram to calculate the probability that a randomly chosen learner:3.2 offer Mathematics only (2)3.3 offer Life Science only (2)3.4 offer Mathematics and Life Sciences (2)

[10]

Question 4

In a staff of 20 teachers a survey was conducted to establish how many drink coffee and how many drink tea.. The following was found: 3 staff members did not drink either coffee or tea; 11 drank coffee and 8 drank tea4.1 Represent this information in a Venn diagram. Let C={staff members who drink coffee} and

T={ staff members who drink tea}. Let the number of staff members who drink both coffee and tea = x. (4)

4.2 Calculate the value of x (2)4.3 If a staff member is chosen randomly, calculate the probability that s/he drinks

a. Only coffee (1)b. Only tea (1)c. Coffee and tea (1)d. Coffee or tea (1)

[10]


Test 13 : MeasurementTime: 1 hour Marks: 5

Question 1

1.1 In the figure, the cube and the cylinder have equal volume. If two sides of the cube are doubled, and the diameter of the cylinder is doubled, will the volumes of the resulting prisms still be equal? Show all calculations.

(5)

1.2 Consider the figures below and in each case determine:

1.2.1 the surface area and the volumeof the prism 1.2.2 the surface area and the volume

of the cylinder

1.2.3 Determine the surface area if the edge of the base of the prism is doubled.

1.2.4 Determine the volume of the cylinder if the radius is doubled.

(10)[15]


18 cm18 cm

30 cm

15 cm

24 cm

y

y

xx

x

5cm

8cm

h

h

R Q

P

12 12

12

Question 2

Dylan made a right square pyramid out of plaster for an art project as shown alongside. Each side of his pyramid's base measures 8 cm. The height of the slant triangle of this pyramid measures 5 cm.

2.1 What is the area, in square cm’s, of the base of Dylan’s pyramid? (2)

2.2 What is the total surface area, in square cm’s, of Dylan’s pyramid? Show your working. (5)

2.3 What is h, the height, in cm’s, of Dylan’s pyramid? Show or explain how you got your answer. (4)

2.4 Using the height you determined in part 2.3, what is the volume, in cubic cm’s, of Dylan’s pyramid? Show your working. (3)

[14]

Question 3

3.1 PQR is an equilateral triangle, with the measurement of each side equal to 12cm.

3.1.1 Use any appropriate method to show that the perpendicular height of the triangle is 10,39cm. (3)

3.1.2 Hence, calculate the area of the triangle. (2)

3.2 A triangular pyramid is constructed using four triangles that are the same as the triangle in 3.1 (i.e. an equilateral triangle with sides measuring 12cm).

3.2.1 Calculate the perimeter of the base of the pyramid. (1)

3.2.2 Explain how you know that the height of the slanted triangles is 10,39cm. (1)

3.2.3 Calculate the total surface area of thepyramid. (3)

[10]


Question 4

A product designer is designing a set of three open baskets according to the following specifications:

The capacity of the baskets: large basket = 1,5lmedium basket = 1,25lsmall basket = 1,0l

4.1 Has the same scale factor been applied when reducing the basket capacity from large to medium and from medium to small? Substantiate your answer with calculations. (3)

4.2 Convert the capacity of each basket to ( ). (3)

4.3 The designer decides that the large basket should be 15cm long and 12cm wide. Show that the height of the basket will be 8.3cm. (3)

4.4 The baskets fit inside each other with a 0,5cm gap all around. What is the length and breadth of the medium basket? (2)

4..5 The small basket will be covered with decorative paper. Calculate the area of paper required to cover the bottom and sides of the small basket. (The dimensions of the small basket are length = 13cm, breadth = 10cm and height = 7,7cm.) (3)

[14]


Test14 : GeometryTime: 1 hour Marks: 50

Question 1

1.1 In the diagram below, AB and DC are two parallel lines cut by two transversal lines at X, Y and Z respectively.

1.1.1 Determine giving reasons, the value of x in the diagram: (6)1.1.2 Name one pair of co-interior angles (1)1.1.3 Name one pair of alternate angles (1)1.1.4 Complete: If two parallel lines are cut by a transversal, then the co-interior angles are .......(1)1.1.5 Complete: The size of angle XYD = , Reason ..................... (2)

1.2 Determine with reasons, the value of y ( XY) in the diagram below. Given that AB = 4 units and BC = 3 units. X and Y are the midpoints of AB and BC respectively. (5)

[16]


A

B

C

DY

X

Z x60o

x - 20o

A

B C

X

Y

y

=

=

4

3

Question 2

Question 3


2.1

2.2

3.1

6

6

10

12

Question 4


3.2

4.1

4.2

12

8

8

PROJECTS AND INVESTIGATIONS

INVESTIGATION: Functions Marks: 50

1 Draw the graphs of each of the below by means of point-by-point plotting .

(18)2 Now indicate whether it is a straight line, parabola, hyperbola or any other function by filling the

algebraic equations in the correct column in the table below:

Straight line Parabola Hyperbola Other

(4)3 What do the equations representing straight line graphs have in common? (3)

4 What do the equations representing parabolas have in common? (3)

5 What do the equations representing hyperbolas have in common? (3)

6 Write down 4 other formulas that each make : straight lines, parabolas or hyperbolas . (4)

7 Is the graph of a line, a parabola or some other shape? Explain. (3)

8 Is the graph of a line, a parabola or some other shape? Explain (3)

9 What do you notice about the graphs of the following equations:

, , , (4)


1.1 1.7 1.13

1.2 1.8 1.14

1.3 1.9 1.15

1.4 1.10 1.16

1.5 1.11 1.17

1.6 1.12 1.18

10. Make a conjecture about the effect of the ‘+2’. (3)

Project: Finance Marks: 50

Section A – Exchange Rates ( 2 marks for each correct answer =30)

The table below shows the average Rand (R)/US dollar ($) exchange rate from 2000 to 2007. The figure given under the column “Exchange Rate” is how many Rands were required to get one US Dollar.

YEAR EXCHANGE RATE2000 6.94

2001 8.58

2002 10.52

2003 7.57

2004 6.45

2005 6.37

2006 6.78

2007 7.06

1 In 2006, a book published in America cost $15.00. How much would you expect to pay for the book in South Africa?

2 You go to a bookshop and see the book on the shelf. It costs R136.00. Is this more or less than you expected? Suggest some reasons for the difference between the price you expected to pay and the marked price of the book.

3 In which year would you expect the book to cost the least? Substantiate your answer.

4 In 2007, A T-shirt made in South Africa costs R95.00. The shirt is exported to America. How much would it cost in $?

5 If you were running a clothing factory where the clothes were made from imported American cotton, in which year would the exchange rate have been best for you and in

which year would it have been worst? Explain.

6 If you were running a business that exported South African chocolates to America, in which year would the exchange rate have been the best for you and in which year would have been the worst? Explain.

7 The banks only give a few exchange rates in the same format as the table above, i.e. how many Rand you need to buy one unit of foreign currency ($, €uros (€) and British Pounds (£)). All other exchange rates are quoted in the amount of foreign currency that can be purchased with R1.00. In 2007, the Rand/Australian dollar (A$) exchange rate was R1.00 to A$ 0.17. If you went to the

bank with R100, how many Australian dollars would you be able to get?

8 How much would you need in R to get A$ 1? Is this a better or worse exchange rate than the Rand/Dollar exchange rate in 2007? Explain your answer.

9 Work out the exchange rate between Rands and US dollars in the same format as the exchange rate for Australian dollars, i.e. work out how many US dollars you can get for R1.00.


10 Using the 2007 exchange rates for Australian dollars and US dollars, work out how many Australian dollars you would need to get 1 US dollar.

11 In December 2007, the price of crude oil, which is used to make petrol, was $92.00 per barrel. How much did South Africa pay for a barrel of oil and how much did Australia pay for a barrel of oil?

12 In 2007, the exchange rate between the Rand and the British pound was R14.13 to 1£. The Rand/US dollar exchange rate was R7.06 to 1$. Estimate the exchange rate between the US dollar and the British pound.

13 You are visiting America and decide to buy a Big Mac burger for lunch. It costs $3.20. What is the Rand equivalent of the Big Mac Burger. (Use the 2007 exchange rate given in the table above.)

14 While you are eating your Big Mac, you compare what you have just paid in Rands for your burger with what you would have paid in South Africa (R15.50). Is the Big Mac more or less expensive in America?

15 Experiment with exchange rates, using any method you think suitable, to work out a Rand/Dollar exchange rate that would result in the price of a Big Mac in America being equivalent to the price that you pay for a Big Mac in South Africa. Does the official Rand/Dollar exchange rate undervalue or overvalue that Rand?

Section B – Inflation and Interest (20)

1 In 2000, a pair of track shoes costs R450. The inflation rate is 5,4%. What would you expect the shoes to cost in 2007? (3)

2 The table below gives that actual annual inflation rates from 2000 to 2007. Use the table to work out the 2007 price of the track shoes. How does this compare with your answer in 1. Explain why your answers are different. (4)

YEARINLFATION

RATE (%)2000 5,42001 5,72002 9,22003 5,82004 1,42005 3,42006 4,72007 7,7

3 You decide to buy a cellphone costing R890. You have saved R320 towards the cost of the cellphone and your parents have agreed to lend you the balance at 8,5% per year simple interest. You will pay your parents back in equal monthly payments for a period of 2 years. Work out your monthly repayments. (4)

4 Instead of borrowing money, you decide that you are going to save for two years and then buy your new cellphone.

4.1 You invest the R320 that you have in a special savings account which pays 8% per annum interest, compounded monthly. Calculate the balance in this account after 2 years.

4.2 After six months, you deposit R170 into an ordinary savings account, at 7.5% interest per


K

Q

S

R

P

annum, compounded six monthly. Six months later, you deposit R160 and six months later you deposit R170 into the same account. Calculate the balance in this account at the end of two years

(3)4.3 During the two-year period that you are saving, the rate of inflation is 6,7% per annum.

What will the cost of the cellphone be at the end of the two years? (3)

4.4 Using your results from questions 4.1 – 4.3, determine whether or not you will have enough money to pay cash for the cellphone. (3)

Grade 10 Project: Shape, Space and Measurement Marks: 75

1 On a sheet of unlined paper, construct line AB = 9cm. Now construct line DC so that DC is parallel to AB and equal to AB. Join B to C and A to D. (2)

1.1 What type of quadrilateral is ABCD? (1)

1.2 Write down four conjectures about ABCD that involve either equal lines or equal angles. (4)

1.3 Confirm each conjecture by measuring the lines or angles and write down the measurements. (4)

[11]

2 Using a compass, construct a circle with a radius of 5cm. Label the centre of the circle K. (1)

2.1 Draw any two diameters of the circle and label them PQ and RS as shown in the diagram. (2)

2.2 How long is PQ? Explain how you know this without measuring PQ. (2)

2.3 Which other lines equal PK? Give a reason for this. (2)

2.4 Join points P, R, Q and S. What type of triangle is

PKR? Give a reason. (2)

2.5 What type of triangle is PKS? Give a reason. (2)

2.6 Prove that . (4)

2.7 Are there any other angles that are ? If so, name them. (2)

2.8 Do you think that you have proved that quadrilateral PRQS is a rectangle. Explain. (2)

[19]


( 0 ; 0 )

3 On the grid provided, plot points F(1;1) and G(6;1). (1)

3.1 What is the length of FG? (1)

3.2 Plot point E so that FE is the same length as FG and the coordinates of E are integers, but FE is not parallel to the y-axis. What are the coordinates of E? Explain the method you used to plot E. (3)

3.3 Plot point H so that EFGH is a rhombus. What are the coordinates of H. (1)

3.4 Which property of a rhombus did you use to draw EFGH? (1)

3.5 Draw the diagonals FH and DE. Using coordinate geometry, prove that the diagonals bisect each other. (3)

[10]

4 What is the definition of a regular polygon? Using your definition of a regular polygon, decide which of the following are regular polygons. In each case, you must state which requirements of your definition are true (if any) and which are not true (if any). Make use of diagrams to illustrate your answers.

4.1 Scalene triangle (2) 4.2 Rhombus (2)

4.3 Isosceles trapezium (2) 4.4 Isosceles triangle (2)

4.5 Square (2) 4.6 Kite (2)

4.7 Parallelogram (2) 4.8 Equilateral triangle (2)[16]


E

D CB

A

side adjacent to

side opposite

hypotenuse

side adjacent to

side opposite

RQ

P

5 On the grid paper, plot the points A(-1;2) B(0;-5) and (4;7). Join the points. (4)

5.1 What type of triangle is ABC? (1)

5.2 Prove the conjecture you have made in 5.1. (5)

Note: The coordinates of A, B and C are all integers and no integer is used more than once. Use this rule to answer the next question.

5.3 On the grid, plot points J, K, L and M so that JKLM is a kite. Give the coordinates of the four points you have plotted. (4)

5.4 Prove that JKLM is a kite. (5)[19]

Grade 10 Project: Trigonometry Marks: 85

You are reminded of the definitions of sine, cosine and tangent, abbreviated as sin, cos and tan:

In the right angled triangle below:

,

,

,

Task 1

1.1 Name all the similar triangles in the sketch above. (3)


1.2 Given that BD = 8 units, DC = 4 units and units, calculate the lengths of all the other line segments in the sketch. Leave your answers in surd form (5)

1.3 Express , and in as many different ways as possible.

For example (15)

1.4 Given that , express and in as many different ways as possible. (15)

[38]

Task 2

The three circles have radii 2, 3 and 5 units.

4

2

-2

-4

-5 5D

C 3

C 2

C 1

B 3

B 2

B 1

A 3

A 2

A 1

2.1 Read, as accurately as possible, the co-ordinates of the points marked: and hence complete the following table (work correct to 1 decimal place).:

x co-ordinate

y co-ordinate

1A

1C


(10)

2.2 Write any observations about what you have read and calculated using the co-ordinates of the nine points. (9)

[19]Task 3

3.1 Measure , and and use your calculator to determine the sine, cosine and tangent of each of these three angles. (6)

3.2 How, if at all, are the ratios determined in the previous question related to the values in the table completed in task 2? (2)

3.3 Use your calculator to investigate

3.3.1. the maximum and minimum values (if they exist) of , and for any values of (try multiples of ) (10)

3.3.2 the value/s of for at least 5 of values of (use , some positive values and some negative values). (2)

3.3.3 the values of , and for at least 5

values of (4)

3.4 Write any observations about the results you obtained through your calculator work. (4)

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