2U Mathematics Fun Run (1 Viewer)

[Forbidden.]

Enjoy​

1) Change 0.8 to simplest form

2) Write 0.88888.. as rational number

3) 0.06x0.09

4) Solve 4^-3 into fraction

5) Absolute of -2

6) Factorise 6x²+13x+5

7) Expand 1000+8t³

8) If a=-4 n=18 d=3 Find T if T=a+(n-1)d

9) Solve |2x-3|=x+4

10) Solve |2x+5/(3)|<2

11) Find b if b^-2/3=1/9

12) Complete the square of y²+y=0

13) Find x in 3x²-5x+1=0

14) Solve simultaneously 5p+2q+18=0 & 2q-3q+11=0

15) Find y if (y+10)⁰+(2y)⁰+(y+10)⁰=180⁰

Note: ⁰ means degrees ...

16) State the properties of a rhombus

17) Find the sum of interior angles of a regular pentagon

18) If f(x)=3x²-x+1 Find f(4) and f(1)

19) If f(x)=x²-x Find f(x)-f(-x)

20) Solve (x²-8x+15)/(x²-3x-10) when lim x-->5

21) Solve (h³+2h³-7h)/h when lim x-->0

22) Is f(x)=x³ an even or odd function ?

23) Is f(x)=x⁴-9x²+7 an even or odd function ?

24) Find x- and y- intercepts of y=2x²-5x-12

25) Find domain and range of y=x-2

26) Solve (2x-4)/2

27) State the formula for the circle

28) Find the equation of the circle if centre is (4,-1) and the radius is 6 units

29) Find the centre and radius of the circle if x²+y²-6y+5=0

30) State the domain and range of y=|x|/x

31) Is the graph xy=1 continuous or discontinuous ?

32) Describe the locus of a person climbing down the ladder

33) Does (5,2) lie in the region of y<x+1 ?

34) Find the exact value of sin 90

35) Find the exact value of cos 60

36) Find t if cot(2t+5)=tan(3t-15)

37) If sin x=5/7, find cosec x

38) Round 23⁰12^'22^" to the nearest minute

39) Find the angle x if the adjacent side is 14.9 and the hypotenuse if 21.3

40) The angle of elevation of a tree from a point 50m out its base if 38⁰14^'

41) An attack helicopter is flying very slowly at 700m above ground. A hidden missile emplacement is positioned to aim 55 degrees into the air from the ground. Assuming the missile is launched at very high speed, how close must the helicopter be from the air in order to be at point blank range of the emplacement ?

42) A girl rides her motorbike through her property, startign at her house. If she rides south for 1.3km, then rides west for 2.4km, what is her bearing from her house to the nearest degree ?

43) Which quadrant is tan positive ?

44) Find the exact value of sin 225

45) Prove cos²x-1=-sin²x

46) Prove 3+3tanx=3/(1-sin²x)

47) State the formula for the area of a non-right angled triangle

48) Find the gradient of the line joining (2,9) to (7,-1)

49) Prove the points (3,-1), (5,5) and (2,-4) are collinear

50) The gradient of a line is 3/5. Find to the nearest whole degree, the angle the line makes with the positive direction of the x-axis

51) Find the gradient, to 2 significant figures, of the straight line that makes an angle of 42 degrees 51 minutes with the x-axis

52) Find the gradient, y-intercept as well as the general form of 5x-4y=15

53) Find the gradient, y-intercept as well as the general form of (x/2)+(y/3)=1

54) Find the equation of the straight line passing through the point (3,4) with gradient m=2

55) A line has gradient 1/2 and passes through the point (5,-1). Find the co-ordinates of the point which cuts the y-axis

56) Find the equation of the line through the point (8,-3) with gradient 1/4. Express the answer on general form

57) Find the equation of the straight line passing through (3,6) and (-1,9)

58) Find the equation of the line with x-intercept 1 and y-intercept 3

59) Find the gradient of the straight line parallel to the line joining (3,5) and (-1,2)

60) Show that the lines 6x-5y+1=0 and 6x-5y-3=0 are parallel

61) Show that the lines 7x+3y+2=0 and 3x-7y=0 are perpendicular

62) The points A(-2,0), B(1,4), C(6,4) and D(3,0) form a rhombus. SHow that the diagonals are perpendicular

63) Find the point of itnersection of straight lines y=2x+1 and 5x-3y+6=0

64) Find the equation of the line through the point of intersection of 8x+3y=0 and 7x+2y-5=0 and also through the point (-1,-2)

65) Find the perpendicular distance between (1,2) and 3x+4y+2=0

66) The perpendicular distance between the point (x,-1) and the line 3x-4y+7=0 is 8 units. Find the value of x

67) Show that the line 3x-4y+12=0 does not cut the cirlce x²+y²=1

68) Diffrentiate from first principles to find the gradient of the tangent to the curve x²+x at the point (2,6)

69) Find the gradient of the tangent at any point on the curve y=5x²-x-1

70) Diffrentiate x(2x+1)

71) Diffrentiate from first principles to find the gradient of the tangent to the curve f(x)=2x²-3x at the point x=4

72) Diffrentiate 2x^1/2-3x^-1

73) Diffrentiate 1/3x⁶(x²-3)

74) Diffrentiate d/dx(1/5x-2)

75) Diffrentiate d/dx(1/(x⁴-3x³+3x))

76) Diffrentiate y=3x(5x+7)

77) Diffrentiate y=(2x²+x-7)⁵(3x-4)⁷

78) Diffrentiate y=(x/2x²-x)

79) Find the discriminant of the quadratic equation x²-3x+1=0 and determine whether it has real roots, is rational or equal

80) Find the discriminant of the quadratic equation x²+9x-2=0 and determine whether it has real roots, is rational or equal

81) For what values of p will the expression 5x²-4x+p will always be positive ?

82) Reduce 5^2x-5^x-20=0 to a quadratic equation

83) Reduce 4x⁴+11x²-3=0 to a quadratic equation

84) Reduce 4^x-10.2^x+16=0 to a quadratic equation

 

[Riviet]

You can't do a single one of them?!

 

[Riviet]

Here are the answers to the first 10:

1) 4/5

2) 8/9

3) 0.0054

4) 1/64

5) |-2|=2

6) 6x²+3x+10x+5=3x(2x+1)+5(2x+1)=(3x+5)(2x+1)

7) I think you meant factorise: (10+2t)(100-20t+4t²)

8) T=-4+(18-1).3=-4+51=47

9) Case 1: 2x-3=x+4 => x=7
Case 2: -2x+3=x+4 => x=-1/3

10) -2 < (2x+5)/3 < 2
-6 < 2x+5 < 6
-11 < 2x < 1
-11/2 < x < 1/2

 

[Forbidden.]

You can't do a single one of them?!

I can, the aim of this "fun run" is to test your 2U maths preliminary knowledge, and of course i know them ... if i did not know the answers to any of them, i wouldn't be doing 2 unit


You are correct for all of those first 10

Try some more, like the ones on linear graphs ... Because many post-HSC students don't master it ...

 

[gamecw]

84-76

84) (2^x - 8)(2^x - 2)
83) (4x^2 - 1)(x^2 + 3)
82) (5^x - 5)(5^x + 4)
81) p has to be greater than 4/5
80) equal or rational? i dont get what its sayin...
discriminant = root (81+8) = root 90, hence it has real roots, roots r not equal and they r not rational?
79) dicriminant = root (9-4) = root 5
hence it has real roots, roots r not equal and they r not rational
78) -2/(2x-1)^2
77) 5.(4x+1).(2x^2+x-7)^4.(3x-4)^7+21.(2x^2+x-7)^5.(3x-4)^6
76) 30x+21

 

[Mark576]

I have the answers for questions 11 - 15

11) b = 27

12) y^2 + y + 1/4 = 1/4

(y + 1/2)^2 = 1/4

y = 0 or -1

13) 3x^2 - 5x + 1 = 0

Using the quadratic formula:

x = (5 +/- sqrt 13)/6

14) q = 11, p = -8 (maybe the second equation was supposed to start with 2p, rather than 2q?)

15) y = 40

NOTE: i'm only in year 10, so forgive me if i've done something wrong.