Identify
Is it an expression, equation or function?
1) -(x-5)+41x2
2) 3x3+x-56=8
3) f(x)=ax+b
4) y=65x2-5x+4
1) Expression
2) Equation
3) Function
4) Function
Solve:
a) 35k-12k=9
b) -4(2+7m)=56
c) 4(5x+8)-3(2x+1)=2(-×-7)
a) x=0.391 (3s.f.)
b) x=-2.29 (3s.f.)
c) x=-2.69 (3s.f.)
For the following straight lines:
Determine the gradient, the y- intercept, and increase or decrease steepness:
a) y=5x+4
b) y/(-x+1)=3
a) m=5; n=4; inceasing line
b) m=-3; n= 3; decreasing line
Addition or multiplication:
a) (2x+3)(-x+1)+4
b) 7(×2+67)(4-2x)
c) 7x(4x-2)-8(34-5x)
a) Addition
b) Multiplication
c) Addition
a) x2-9=0
b) -143+x2=1
c) 4x2=64
a) x1=3 x2=-3
b) x1= 12 x2=-12
c) x1= 4 x2= -4
For the following quadratics, determine the concavity, y- intercept and the x coordinate of the vertex:
a) y= 3x2+7x+1
b) y= -4x2-5x-2
a) positive, y=1, xv=-7/6
b) negative, y=-2, xv=-5/8
Linear, quadratic or cubic?
a) 7m(4+2m)+3
b) 5t+11+56t=2t-77
c)(2x+7)x(5x-1)
a) Quadratic
b) Linear
c) Cubic
Solve:
a) (x-5)(x-7)=0
b) 7(x+8)(3x-1)=0
a) x1=5 x2= 7
b) x1= -8 x2= 1/3
For the following quadratics determine the vertex:
a) (x-7)2+8=0
b) (x+9)2-1=0
a) V(7, 8)
b) V(-9, 1)
Region or linear inequality?
a) 5x>-6x+8
b) y-4<5x-7
c) 4(x+1)<2x+3
a) Linear inequality
b) Region
c) Linear inequality
Solve:
a) x2+6x+9=0
b) x2+12x+36=0
a) x=-3
b) x=-6
For the following cubics, determine the concavity, the y- intercept, and the roots:
a) y=(x-5)(x+4)x
b) y=(x+5)(x-2)(-x+8)
a) positive, y=-20, x1=5, x2=-4, x3=0
b) negative, y=-80, x1=-5, x2=2, x3=8
Linear function, quadratic function or cubic function?
Show pictures
a) b) c)
Solve the following equations:
1) 3x(4-5x)-x2+1=0
2) 81x-6-3x+4=-7x+35
3) (x-4)(x+1)x=0
1) x1= 0.826 (3 s.f.) x2=-0.0756 (3s.f.)
2) x= 0.435 (3s.f.)
3) x1=4 x2=-1 x3=0
Sketch the following graphs:
a) y=x2
b) y=3x-1
c) y=(x-1)(x-2)(x+3)
Show graph on the board.