GRADE 12 Mathematics - fs2.beta.obami.comfs2.beta.obami.com/Portal/b14bd756-b01d-48c8-becb-a1630171da42/938818c... · (Round off your answers to the first decimal place) [9] 7. Find

Dr SL Sproule 1

GRADE 12

Mathematics

Contents

Learning outcome 3: Trig, transformation and analytic geometry (page 2)

Learning outcome 4: Statistics (page 16)

Conceptual questions (page 27)

Dr SL Sproule 2

Learning outcome 3:

Trigonometry, transformation and analytic geometry

Unit 1: Trigonometry in triangles

Standard stuff

1. If sin = 5/13; 90<<270 determine, without the use of a calculator, the value of:

a. cos [4]

b. cos x, where x and are supplementary [3]

c. cos ( – 30) [7]

2. If tan 25 = t, express in terms of t:

a. tan 335 [3]

b. cos 25 [3]

c. tan 50 [3]

3. If cos 42 = p express each of the following in terms of p

a. cos 222 b. cos (–138) c. sin 318 d. cos 84

4. The diagram shows a circle with radius 2 units.

Use the given information to determine the

following without a calculator:

a. x

b. sin and hence

c. tan(360 )

d. State the values of a and b.

Tough stuff

5. Without a calculator evaluate 10

13sincos

AA if 180 360A and

5

12Atan .

6. If 2

1 21

sin tanA A calculate the value(s) of sin A without calculating A [7]

7. If sin 2x = 8

15 and x [45 ; 90] determine the value of cos x [7]

8. Answer the question without a calculator. In ∆ABC, C is an obtuse angle. Calculate

the value of sin A if sin B = 3/5 and sin C = 12/13 [10]

Dr SL Sproule 3

Unit 2: All sorts of trigonometry

Easy stuff

1. If 30 , 50 70A B and C find

the value of each of the following without

the use of a calculator:

a. tan7 sin( 40 )

sin( )

A B

A B C

b. sin(360 2 )tan(180 ).tan(90 )

3 sin

AB B

A

2. Evaluate to 3 decimal places:

a. tan71,2

b. 4,1sin37

sin113

c. 1

2sin 144cos

A if AA

d. cos2 59,4if

e.

2sin 80 59,42

if

3. In the figure ˆ 25BOX and OB = 2 units.

Given ˆ ˆ2AOX BOX and 2OA OB

Find the following to one decimal place:

a. the x-coordinate at B.

b. the difference between the y-

coordinates of A and B.

Tough stuff

4. The following statements are given:

A. sin + cos = 1

B. sin + cos < 1

C. sin + cos > 1

Which of the above statements is/are true in

each of the following cases:

a. when 0 < < 90

b. when 90 < < 180

5. If sin (x + 30) = ½ sin x prove that

31

1xtan

[6]

6. Detemine sin 15 without the use of a

calculator

7. Given that cos2 x + cos x = p [3]

Determine the value of p if cot x = sin x

8. Determine the value(s) of k, without

using a calculator if 8

k = sin 105 [8]

9. P(x; y) is a point on the circumference of

the circle with centre (0; 0) and radius r

units. POA =

Use the diagram and the definitions of the

trigonometric functions to prove that:

a. cos2 + cos

2.tan

2 = 1

b. For which positions of P is the identity in

a not valid

10. If tan 1, where 0 360

a. solve for [4]

b. for what values of is tan 1

and sin cos [3]

11. If sin 2a = 1/7, compute the numerical

value of sin4 a + cos

4 a.

12. Find all the positive angles x such that

3x is one of the non-right angles of a

right triangle and sin 2x = cos 3x

St John’s College 4

Unit 3: Trigonometry simplification and identities

Easy stuff

Evaluate, without using a calculator the value of:

1.

70cos100cos20cos80sin

)20sin(190sin340cos10cos [8]

2. tan(90 )sin(180 ) tan(360 )

cos240 tan 225

x x x

[10]

3. 2sin (90 ) tan(360 ).sin(180 ) sin( 90 )

cos(180 )

x x x x

[8]

4. sin (90 – A). sin3 (180 – A) – tan (180 – A). cos

3 (-A). cos (360 – A) [5]

5. cos(50 + ) cos (20 + ) + sin(50 + ) sin(20 + ) [3]

6. sin(180 ).tan50 .tan220 .tan(90 )

cos(360 ).sin210

7. Prove the following :

a. 0 2

2 2

sin . sin(180 ) 1 cos

cos cos

[3]

b. cos(180 ).sin(90 ) tan(180 ).tan 1 1 [4]

c. 2cos

cos .tan sin 1sin

xx x x

x

Standard stuff

8 a. Prove that 2 21 cos sinA A for [0 ;90 ]A .

b. Simplify to one trigonometric ratio:

2

1( cos )cos

tan.

c. Write as a single trigonometric ratio: 2 2

tan sin

cossin cos

.

Prove that:

9. cos2 cos 1 1

sin 2 sin tan

B B

B B B

[5]

10. sin 3A = 3 sin A – 4 sin3 A [7]

11 a. (cos2 cos )cos 2 1

(cos 1)cos .sin tan sin

x x x

x x x x x

[10]

b. Determine the values of x [0;180] for which this identity is not valid [3]

12 a. Simplify: cos260 cos170

sin190 sin10 cos350

[4]

b. Simplify: sin(90 – ) sin3 (180 – ) – tan (180 – ) cos (360 – ) cos

3 (–) [5]


c. If it is further given that tan 80 = k and = 40 write both question 12a and b

in terms of k [6]

13 a. Prove that xsinxcos

xsinxcos

x2cos

x2sin1

[7]

b. Hence find the value of

15sin15cos

15sin15cos without the use of a calculator [6]

14. Prove that 2

12

1 2sinsin2

1tan

tan

AA

AA

[7]

15. Prove that 1 sin cos

tan 2cos2 cos sin

A AA

A A A

[9]

Tough stuff

16. Prove that Atan1A2cosA2sin

1A2cosA2sin

[6]

Unit 4: Trigonometry equations

Easy stuff

1. Solve for x in the following equations:

a. sin 0,8326 [0 ;360 ]x and x b. cos2 0,44 2 [180 ;360 ]x and x

c. 35,2 sin 0

tanand x

x d. 2tan 1 0 [0 ;360 ]x and x

2. Solve for x [0; 360]

a. sin x = ½ b. cos x = –0,345

c. tan x = 3 d. 6cos x – 3 = 1

e. 1 = –2,168.sin x

3. If cos2 0,34 0 2 180with find the following to one decimal place:

a. b. 2tan c.

1

2cos( 44,9 )

4. Find the value of Q if sin( 10 ) cos 50 ( 10 ) [90 ;270 ]Q C where C and Q

Standard stuff

5. Solve for x [0 ; 360] 2

5sin 5cos 2tan

x xx

[9]

6. Solve for x, where x (-180 ; 180), 3cos2x + sin x cos x = 1

(Round off your answers to the first decimal place) [9]

7. Find the general solution of the equation rounded off to two decimal places

10 sin A – 6 cos A = 3 cos2 A – 5 sin A. cos A [7]


Tough stuff

8. Solve for x, where x [-180 ; 180], without the use of a calculator

2 sin 2x – 2 cos x +2 2 sin x = 2 [8]

9. Determine the general solution of the equation: cos (2x + 30) = sin (x – 60) [7]

10. Determine the general solution of the equation: 1

tan (2 + 60) = tan(3 90)

[5]

11. Without using a calculator solve the following equation in the interval θ [-360 ; 360]

4 5

2tantan sin

[12]

Unit 5: 2–D and 3–D Trigonometry

Easy stuff

1. In the triangle 0ˆ 90ACB ; AB = 1unit

and cos B = n. Write the following in

terms of n:

a. BC b. AC

c. sin B d. tan A

2. In the figure AB = 75,3 metres, 0110BMA and M is the centre of the

circle through A and B. Calculate the

following correct to two decimal places:

a. the length of AM

b. the area of AMB

3. In any ∆PQR, Pcos.qr2rqp 222

In the diagram AB = 3 cm , B = 120° ,

BC = 5 cm , DC = 8 cm and ˆ 81,8DAC .

a. Calculate AC

b. Calculate D to one decimal place

c. Which side or angle(s) should be

calculated to see whether quadrilateral

ABCD is a trapezium or not? (Do not

actually calculate the angles!)

4. An aeroplane leaves an airport P and flies

16km on a bearing of 37° East of North

to airport A. It then flies due West 13km

to Airport B.


a. Give the size of A .

b. How far is airport B from airport P?

c. On what bearing must the aeroplane fly

in order to return to airport P?

5. In the diagram AB represents a vertical

cliff which is 112metres high. From the

top of the cliff (point A), two boats C

and D are sighted at angles of

depression of 740 and 66° respectively.

B, C and D are in the same horizontal

plane.

Calculate the distance between the two boats.

Standard stuff

6. PQ and PS are equal chords of length a

QS = QR. QPS =

Show that:

a. QS = )cos1(2a [3]

b. Area ∆QRS = – a 2 sin 2 (1 – cos ) [8]

7. ABCD represents a square section of a

steep ramp which makes an angle of 60

with the horizontal plane ABEF and 30

with the vertical plane DCEF. The side of

the square is p metres. A man climbing the

ramp, starting at point A, chooses path AC

rather than AD as it is not quite so steep.

The angle made by this path with the

horizontal plane is shown in the diagram

as . Calculate the size of , rounded off

to the first decimal place. [7]

8. The given figure represents the roof of the

barn. The beams AB and AC are both

equal to b. The beam AF is perpendicular

to BC. The triangles ABC and EGD are

congruent and perpendicular to the

horizontal plane GBCD, which is a

rectangle. B is joined to D. BAC = 30

and DBC = 60

a. Prove that, BC2 = )32(b2

b. Hence prove that CD = 336b [10]


9. PS represents tha leaning tower of Pisa. It

is learning at 5 from the vertical VS. The

tower leans directly towards a person

standing at A. The angle of elevation of

the top of the tower from A is 20. AS is

horizontal. A plumb line is lowered from

P to touch AS at K. KS = 5m

Calculate the distance of A from S [6]

From B the angle of elevation to P is 25. If

AKB = 60 and AKB is horizontal,

calculate the distance AB. [10]

10. In the figure, a diameter PQ of the circle

is produced to R such that QR = QS = x

and QPS =

a. Find the size of RQS in terms of [2]

b. Prove that RS2 = 2x

2(1 + sin ) [4]

c. If RS = 12 and x = 2, show without a

calculator that:

i. = 30 [3]

ii. PQ = 4 [2]

11. A, B and C are three points on the circle

with centre O such that AB = BC = 3/2

AO. Let AO = x

a. Calculate the size of AOB, rounded off

to the nearest degree. [5]

b. If AOB = 97 and x = 10cm, calculate

the length of AC (rounded to the nearest

whole number) [5]

Tough stuff

12. Show that the area of a quadrilateral is

equal to one half the product of its

diagonals multiplied by the sine of the

included angle. {That is the acute angle

between the two diagonals}

13. If AD bisects angle BAC prove that

AC

AB

DC

BD

Dr Sproule, Penryn College 9

Unit 6: Trigonometry graphs

Easy stuff

1. On the same system of axes sketch the following graphs for the interval [0 ;360 ]x :

xsin2y and xcosy

Use the graphs to answer the following questions:

a. Determine two possible values of x for which 1xcosxsin2 and indicate where you

found these by using the letters A and B on your graph.

b. If (150°; y) lies on the graph of xsin2y , calculate the value of y and indicate where

this lies on your graph using the letter C.

2. On one set of axes sketch the graphs of the following for the interval [0 ;360 ] :

cos2y and tany

Use the graphs to answer the following questions:

a. For which values of does cos2 increase as increases?

b. What is the minimum value of cos2 ?

c. What are the equations of the asymptotes of tany ?

d. What is the period of tany ?

e. What is the amplitude of cos2y ?

f. Indicate on your graph using the letters A, B, C etc. to show the solutions to the equation

cos2tan .

g. Determine any two solutions to 2tancos2 .

3. Figure 1 depicts a wheel with radius OP, which rotates in an anti-clockwise direction about point

O. PQ is perpendicular to OQ with Q on the x-axis. As P rotates, PQ changes size.

The graph in figure 2 shows the length of PQ as increases from 00 through 360

0.

a. Write an equation of the curve in figure 2.

b. What is the radius of the wheel?

c. What would the equation of the curve be if the radius of the wheel was 3 units?

4a. Solve for A where A [0 ; 180] and 2 sin A = tan A [7]

b. Now draw sketch graphs of the functions f and g on the interval [-180 ; 180] where

f(x) = tan x and g(x) = 2 sin x. Indicate clearly any asymptotes, intercepts on both

axes as well as coordinates of any point(s) of intersection between the two graphs [10]

c. Use the answers in (a) and (b) to calculate the value(s) of B in tan B 2sin B where

B [-180 ; 180] [4]


5. On the same set of axes draw the curves of:

f(x) = cos (x + 30)

g(x) = sin x – 1 on x [-180 ; 180]

Label the curves clearly and show any intercepts with the axes [6]

Standard stuff

Question 6

f = {(x; y) | y = 1 + sin x} and g = {(x; y) | y = cos 2x}

a. Without using a calculator, determine algebraically the values of x for which

f(x) = g(x) if x [-180 ; 180] [10]

b. For which value(s) of x will f(x) = 0 if x [-180 ; 180] ? [2]

c. What is the range of f ? [2]

d. Sketch the graphs of f and g on the same set of axes for x [-180 ; 180] [8]

e. Use your graphs to write down the values of x for which f(x).g(x) < 0,

b. for x [-180 ; 180] [3]

Question 7

f = {(x; y) | y = cos (2x – 90)} and g = {(x; y) | y = tan x}

a. Give the period of f [1]

b. Give g(-45) and g(45) [2]

c. Draw sketch graphs of f and g on the same system of axes for the interval

[-90 ; 90]. Show the intersection with the axes and the maximum and

minimum values where applicable [7]

d. By using the graph solve 2sin x. cos x – tan x 0 for x where x [-90 ; 90] [7]

Question 8

The accompanying graph shows the curves of the following functions for x [-180 ; 180]

f(x) = 2 tan ax and g(x) = b cos (x – c)

Use the graph to answer the following questions

a. Give the values of a, b and c [5]

b. Give the period of f [2]

c. Give the minimum value of g(x) [2]

d. Determine the approximate values for m and n if f g = {(m; n)} [2]

e. Give in terms of the sine function, the equation of the curve g which is obtained after having

shifted the y-axis by 45 to the left, while the x-axis remains in the same position. [2]

-3

-2

-1

0

1

2

3

-180 0 180

y

x

g

f (45;2) (90;2)

(-90; -2)


Question 9

Sketch graph for x [-180 ; 180] of f and g are given, where:

f : x a cos (x + b) g : x c sin x

9.1 From the given sketch graphs deduce the value of:

a. a b. b c. c [3]

9.2 P(-14,64 ; k) and Q(m ; -0,51) are approximate values of the points of intersection

of f and g. Write down, rounded off to two decimal places, the values of:

a. k b. m [2]

9.3 For what values of x will:

a. f(x) – g(x) < 0 [4]

b. f(x).g(x) 0 [4]

9.4 If the graph of the function f moved 30 to the left, give:

a. the defining equation of the new curve in the form, y = … [2]

b. the value of x where this graph has a minimum value on x [-180 ; 180] [1]

Unit 7: Analytic Geometry

Easy stuff

1. Refer to the diagram. A (4; 3), B (2; 7), C(-2; 5) and D (0; 1) are points in a Cartesian Plane.

a. Calculate the length of BD, leaving answer in simplest surd form. (3)

b. Show that CA = BD (2)

c. Show that the co-ordinates of M, the midpoint of BD, are ( 1; 4) (3)

d. Prove that AM BD (5)

e. Prove that A, M and C are collinear (3)

f. State, giving a reason, which type of quadrilateral ABCD is. (2)

-2

-1

0

1

2

-180 -135 -90 -45 0 45 90 135 180

y

x

P

Q

f

g


2. Write answers to one decimal place.

a. Calculate the angle which the line passing through A (-2; -2)

and B (3; 4) makes with the positive x-axis. (2)

b. Calculate the inclination of the line passing through the points C (-3; 3) and D (2; 4) (2)

c. Calculate the gradient of a line with inclination:

(i) 54,7°

(ii) 145,5° (2)

3. If A (-2; 3), B (1; 4), C (-4; 1) and D (x; 4), calculate the value of x if:

a. AB CD b. AB CD (7)

4. The straight line PQ with equation 1yx2 cuts the y-axis at Q and the straight line PR with

equation 12y2x3 cuts the x-axis at R. Calculate:

a. the coordinates of Q and R.

b. the coordinates of P

c. the coordinates of M, the midpoint of QR

d. the equation of PM.

5. A(0 ; 1), B(-2 ; -4), C(8 ; 1) and D(d ; 6) are the vertices of a parallelogram.

a. Calculate the gradient of BC.

b. Hence find the equation of AD and use it to find the value of d.

c. Calculate the equation of the altitude AE of ABC if E is on BC.

d. Find the angle of inclination of BE.

e. B lies on the circumference of a circle whose centre is at the origin. Find the equation of

that circle.

6. Show that the points (1 ; 1), (-2 ; -8) and (0 ; -2) are collinear.

7. Refer to the figure.

Given : Circle centre (0 ; 0 ) with

equation 2522 yx .

CA and CB are tangents to the

Circle at A( a ; 0 ) and B( -3 ; -4 )

respectively.

a. Write down the value of a. (1)

b. Calculate the gradient of BO. (2)

c. Show that the equation of BC is

2543 yx . Show all your working. (3)

d. Write down the x - coordinate of C. (1)

e. Calculate the y - coordinate of C. (2)

f. Calculate the coordinates of E, the midpoint of AB. (2)

g. Does E lie on the line through O and C ? Show your working to justify your answer.(3)


8. Refer to the figure. ABCO is a rectangle. The

length of AO = 6 and M ( 5 ; a ) is the midpoint

of the diagonal AC.

Write down :

a. the value of a (2)

b. the coordinates of B (2)

9. Given circle centre the origin O. AB is a tangent to the circle at P ( -4 ; 2 ). PO produced meets

the circle at D. BC is a tangent to the circle at C and BC AB

a. Determine the equation of the circle (2)

b. Determine the equation of OP (2)

c. Determine the equation of AB (3)

d. Find the x - intercept of AB (1)

e. Use symmetry to write down the

coordinates of C and D (2)

f. Calculate the length of CD (3)

10. Given : Circle with equation 1822 yx and the straight line 6 yx .

a. Calculate the coordinates of the point(s) where the circle and the straight line intersect

each other. (5)

b. Is the straight line a tangent to the circle or not? Give a reason for your answer. (2)

c. Find the angle of inclination of the straight line and the positive x–axis. (3)

11. a. Calculate the gradient of the line joining (2;3) ( 2; 3)F and G (1)

b. Calculate the gradient of the line perpendicular to 3 2 12y x (2)

c. Rectangle PQRS is given with vertices : ( 5 ; 2); ( 5;3); ( ;3); (4; )P Q R x S y

Calculate the values of x and y (3)

12. Given the vertices of a triangle : ( 4; 1), (2;3) (6; 3)A R and M

A ( -4 ; -1 )

R ( 2 ; 3 )

M ( 6 ; -3 )

X

Y

O


a. Calculate the coordinates of S , the midpoint of AM. (2)

b. Determine the equation of line RS. (3)

c. Find the length of RA, answer correct to ONE decimal digit. (3)

d. Show that ARM is right-angled. Show your working. (4)

e. Calculate the area of ARM , answer correct to ONE decimal digit. (4)

f. Calculate the angle of inclination of RM with the positive direction of the x – axis (2)

13. Given : 052 yx and 2522 yx

These two graphs intersect at P and Q, with P on the y-axis

a. Find the coordinates of P (2)

b. Calculate the coordinates of Q (5)

c. If QR is the tangent to the circle at Q, determine the equation of QR (5)

14. Study the Cartesian Plane and the points plotted very carefully:

Write down the letter(s) of points or lines which satisfy the following conditions:

a. a line parallel to CF (1)

b. a line perpendicular to ED (1)

c. a line with length = 53 (2)

d. a line with gradient = 1 (1)

e. a line with an angle of inclination with the x – axis of 34,99° (2)

f. 4 points that form a parallelogram (2)

g. a line with midpoint

2

1;

2

3 (2)

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

.A

.B

.C

.E

.D

O .G

.F

x

y


15. A circle with centre the origin is drawn. P (-3 ; -1) is given. PA is a tangent to the circle at P.

Q is symmetrical to P with respect to the y – axis

P ( -3 ; -1 ) R

A

x

y

O

Q

a. Write down the coordinates of Q (1)

b. Show your working to find the equation of the circle (2)

c. Show your working to find the equation of PA (4)

d. Calculate the Area of PAQ (4)

16. a. Sketched below are the lines 73 xy and 035 yx Calculate the size

of the angle correct to 2 decimal places (6)

b. ABCD is a trapezium

A ( -4 ; 3)

B ( x ; 6 )

C ( 4 ; y )

D ( -2 ; -1)

AD parallel to BC

(1) Since AD || BC, find an equation in x and y (3)

(2) If you are given that yx 2 as a second equation,

calculate the values of x and y (3)


Learning outcome 4: Statistics

Unit 8: Calculations

Easy stuff

1.

2.

b. Calculate the standard deviation of the TV sets per household

3.


4.

b. Calculate the standard deviation of the number of calls per day

Standard stuff

(d) Estimate the standard deviation of the population of students

7.

(c) Estimate the standard deviation of the leaves collected in the sample


8.

a) Estimate the mean score in the mathematics competition

b) Calculate the standard deviation of the scores in the mathematics competition

9.

10.


11.

Tough stuff

12.

13.


Unit 9: Graphs

Easy stuff

1.

2.


Standard stuff

3.

4.

5.

Tough stuff

6.


7.

8.

9.


10.

11.

Definition:


12.

13. The cumulative frequency polygon below shows the times taken to travel to a city centre school

by a group of children.


Unit 10: Graph interpretation 14.


15.

16. The bar chart shows the matches won, drawn and lost by five football teams at one stage in the

1986/87 season

(a) What percentage of their games has Norwich won?

(b) Why are all the bars not the same height?

(c) Has Luton or Coventry won a greater percentage of their games?

(d) Which of the five teams is ahead in the log table for the league?


Conceptual questions

These questions should take you between 30 seconds and 2 minutes each to answer.

1. Solve for x

a) 2

3( 3) 4x

(3) b) 3 3x (1)

c) 3 2 0xx 3 (3)

2. Determine x and y if: (x – 1)² + (y + 3)² = 0

3. Evaluate: bLimax

4. Without solving the equations, which of the following equations have real roots? Motivate your

answers.

a) 052 xx

b) 025 xx

c) 052 xx [6]

Now solve the equation(s) that have real roots [2]

5. Determine k so that the turning point of the parabola y = x² – 8x + k is a point on the x-axis.

6. For what values of [– 360; 360] is sin . cos > 1

7. Find two fractions that are evenly spaced between these two a

anda 2

73

8. If one root of the equation ax² + bx + c = 0 is the reciprocal of the other root what is the

relationship between a and c?

9. If x

x

3

2

is Real determine the value of x

10. When is

cos

sintan undefined?

11. If the line y = mx + c cuts the positive x and y axes solve for m and c.

12. What is the average of the first fifteen Natural numbers?

13. sin 1 cos

1 cos tan sin .cos

Why is this statement not defined at = 90?

14. Write down the third term of the geometric sequence x; x ; __ ; …

15. What is the minimum value of f(x) = (x – 4)(x – 2) ?

16. When does the series (x + 1) + (x + 1)² + … converge?

17. If cos 62 = m determine the values of sin 208 in terms of m.

18. Write a number that is double log 3 9 as a log

19. Determine the LCM of log 5 25 ; log 2 32 and log 3 27 and write the answer as a log base 10

20 a. If the period of 2

tan xy is halved what is the new equation?

b. If the amplitude of y = sin 2x is doubled what is the new equation?

c. If the period of y = ½ cos 2x is doubled what is the new equation?


21. Given statements A, B and C

A. sin x + cos x = 1

B. sin x + cos x < 1

C. sin x + cos x > 1

Which statement(s) is / are true if:

a) 0 < x < 90 b) 90 < x < 180

22. Write down the new equation of f(x) = 3x when it is reflected in the:

a) x-axis b) y-axis

c) line y = x d) line y = –x

Multiple choice questions

1. – log a b

a) log a –b (b) log 1/a b (c) log b a

2. If sin A + cos A = 1,1 then sin A. cos A =

a) 0,150 (b) 0,105 (c) 0,605 (d) 0,550

3. If 90 < A < 180 and 270 < B < 360 which one of the following statements is true?

a) cosA . cosB > 0 (b) sinA . cosA > 0 (c) sinA . sinB > 0 (d) sinB . cosA > 0

4. The staight line y = mx + c cuts the positive x-axis and the negative y-axis if:

a) m > 0 and c > 0 (b) m < 0 and c > 0 (c) m < 0 and c < 0 (d) m > 0 and c < 0

5. Which statement if false?

a) sin (–A) = – sin A (b) cos (360–A) =

cos (90–A)

(c) tan (180+A) =

tan (360+A)

(d) cosec A =

cosec (180–A)

6. Which statement is true? If the axis of symmetry of y = ax² + bx + c is positive then:

a) a < 0 and b < 0 (b) a < 0 and b > 0 (c) a < 0 and c < 0 (d) a > 0 and b > 0

GRADE 12 Mathematics - fs2.beta.obami.comfs2.beta.obami.com/Portal/b14bd756-b01d-48c8-becb-a1630171da42/938818c... · (Round off your answers to the first decimal place) [9] 7. Find

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