Foundation Mathematics for Engineering| Algebra| Foundation Studies| Teesside University| FME-TMA1

Questions 1

Remove (Open) the brackets and simplify the following:

  • 7x+6\left(x-y\right)-3\left(x-2y\right)

  • x\left(x-y\right)+3y\left(x+y\right)

  • \left(y-x\right)\left(2x+4y\right)

Question 2

Evaluate the following:

  • Evaluate S to 2 decimal places, where the radius r=10 cm and the height h=500 mm

S=2\pi r^2+2\pi rh

  • Evaluate \frac{2x^2-y^3+2xyz}{2yz}, where x=1, y=-2, z=-1

Question 3

Transpose the following formulae:

  • P=\frac{RT}{V}\:\:\:\:find\:T

  • K=\frac{mv^2}{2g}\:\:\:\:\:\:find\:v

  • y=\frac{a+x}{5-bx}\:\:\:\:\:\:find\:x

Question 4

  • Solve the following equations and check your answers by substitution:

    • 4-2x=16

    • 10\left(2+y\right)=5\left(1-y\right)

    • \frac{3t}{2}-\frac{10}{4}=8

    • 3x^2-9=3

  • Solve the following simultaneous equations:

3p-4q-11=0
5p+9q+13=0

Question 5

  • Factorise and solve the following quadratic equations

    • x^2-5x-6=0

    • 3x^2-7x+2=0

  • Solve the following quadratic equation using quadratic formula:

    • 3x^2+6x-10=0

Question 6

  • Given the equation y=ae^{-kx}::

    • Evaluate a when x=0.36, k=3 and y=25.1.

  • Solve the equation for x:  9.1=10e^{-2.1x}

 

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