5.1 Hwk Answers due 29 Sept 15

To be done neatly in the front of your books
TOTAL 22 marks

1. The plots shows the curve $y=x^2+4x-1$

   

   1. Use the formula to solve the equation $x^2+4x-1=0$ giving your answers to 2 d.p. $$(x+2)^2 - 5 = 0 \\ x = -2 \pm \sqrt{5} \\ x=0.24 \text{ or } -4.24$$
   2. $x^2+4x-1=k$ has no solutions, where k is an integer. Use the plot above to find the maximum value of k $$k = -6$$

   [4 marks]

2. Complete the square $x^2+8x-4$ and use your answer to solve $$x^2+8x-4=0 \\ (x+4)^2 - 20 = 0 \\ x=-4 \pm \sqrt{20} \\ x=-4 \pm 2\sqrt{5}$$

   [3 marks]

3. Y varies indirectly as the square root of x. If y=7 when x=4, then:
   1. Find a formula for y in terms of x $$y=\frac{k}{\sqrt x} \\ k = 7 \times 2=14 \\ \therefore y=\frac{14}{\sqrt x}$$
   2. Find y when x=10 to 3 s.f. $$y = 14 \div \sqrt{10} = 4.43$$
   3. Find x when y=2.2 $$x=(\frac{14}{y})^2 = (\frac{14}{2.2})^2 = 40.5$$

   [4 marks]

4. Find the image of the point (-2, -3) under the transformation represented by M $$\begin{pmatrix} 4 & -3 \\ -5 & -7 \end{pmatrix} \begin{pmatrix} -2 \\ -3 \end{pmatrix} = \begin{pmatrix} 1 \\ 31 \end{pmatrix} \\ \text{Point is } (1,31)$$

   [2 marks]

5. Find the 2x2 matrix which represents a reflection in the x axis. $$\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$$

   [2 marks]

6. Write $2x^2+6x -3$ in the form $a(x+b)^2 +c$. $$2(x+\frac{3}{2})^2 - \frac{15}{2}$$

   [3 marks]

7. Draw up a table of values for $-2 \leq x \leq 3$ for the function $y=x^3 -2x^2+x-3$ and use it to sketch the curve neatly (and with appropriate scales). $$\begin{array}{|c|c|c|c|c|c|c|} \hline \ x & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline \ y & -21 & -7 & -3 & -3 & -1 & 9 \\ \hline \end{array}$$

   

   [4 marks]

6.6 FM Progress Homework due 5.10.15

Total: 25 marks. Show all working out. Those not showing mathematical rigour will be penalised.

1. Factorise fully $6x^2-7x-20$

   [2 marks]

2. Complete the square: $y=5-2x-3x^2$ and use your answer to sketch y, indicating clearly any points where the curve crosses the axes

   [4 marks]

3. Sketch $y=(3-x)(2x+5)^2$ indicating any intersections with the axes

   [4 marks]

4. $$y^2=x^2+x \\ y=2x+k \\ $$ Find the values of k such that the hyperbola and the line do not meet.

   [4 marks]

5. Find the centre and radius of the circle that passes through A(9,3), B(13,-5) and C(-5,-11)

   [5 marks]

6. Solve: $$\frac{3}{27^{5-x}}=\sqrt{81^{5-2x}}$$

   [3 marks]

7. Simplify as far as possible: $$\frac{15}{\sqrt 5} - \frac{6}{\sqrt 7 - \sqrt 5}$$

   [3 marks]

   ANSWERS

4.2 Homework due Mon 28.9.15

Complete neatly in the front of your books. Calculator allowed but working must be shown. Total: 21 marks

1. A teacher has a 3% pay increase to £18,200. What was his previous salary?

   [3 marks]

2. £3000 is deposited in a bank account with an interest rate of 3.1% p.a., what will the balance be after 8 years?

   [2 marks]

3. Without a calculator, find the value of $$\frac{5.6 \times 10^{-5}}{8 \times 10^{-8}}$$ Give your answer in standard form.

   [2 marks]

4. Solve $$\frac{3x-2}{2}=\frac{4-x}{4}$$

   [3 marks]

5. Solve $3(2x+3)-4(5-3x)=1$, leaving your answer as a fraction

   [3 marks]

6. Find the gradient of the line between A(-1,4) and B(3,-8) and hence find the equation of the line

   [4 marks]

7. Pete's son is a third of his age. 8 years ago, Pete was four times his son's age. How old is Pete today? Show your method clearly. Guesses get nothing!!

   [4 marks]

ANSWERS

5.1 Homework due Tue 29.9.15

To be done neatly in the front of your books
TOTAL 22 marks

1. The plots shows the curve $y=x^2+4x-1$

   

   1. Use the formula to solve the equation $x^2+4x-1=0$ giving your answers to 2 d.p.
   2. $x^2+4x-1=k$ has no solutions, where k is an integer. Use the plot above to find the maximum value of k

   [4 marks]

2. Complete the square $x^2+8x-4$ and use your answer to solve $x^2+8x-4=0$, leaving your answers in surd form

   [3 marks]

3. Y varies indirectly as the square root of x. If y=7 when x=4, then:
   1. Find a formula for y in terms of x
   2. Find y when x=10 to 3 s.f.
   3. Find x when y=2.2

   [4 marks]

4. Find the image of the point (-2, -3) under the transformation represented by M $M = \begin{pmatrix} 4 & -3 \\ -5 & -7 \end{pmatrix}$

   [2 marks]

5. Find the 2x2 matrix which represents a reflection in the x axis.

   [2 marks]

6. Write $2x^2+6x -3$ in the form $a(x+b)^2 +c$.

   [3 marks]

7. Draw up a table of values for $-2 \leq x \leq 3$ for the function $y=x^3 -2x^2+x-3$ and use it to sketch the curve neatly (and with appropriate scales).

   [4 marks]

4.2 Homework due 21.9.15

Complete neatly in the front of your books. Calculator allowed but working must be shown. Total: 23 marks

1. A milkman has a 12% pay increase to £15,000. What was his old salary?

   [3 marks]

2. The number of insects on a corpse increases by 25% every hour. At 9am there were 1000 insects on the corpse.
   1. How many insects were there at 10am?
   2. How many insects were there at 11am?
   3. Roughly how many insects will there be by midday?

   [6 marks]

3. A pair of trainers costs £35 AFTER a discount of 45%. How much were they before the discount?

   [3 marks]

4. A paperboy has his wage increased by 15% to £6.65 per hour. What was his wage before it was increased??

   [3 marks]

5. Without a calculator, find the value of $$\frac{3.2 \times 10^{-4}}{4 \times 10^6}$$ Give your answer in standard form.

   [2 marks]

6. Change $\frac{3}{25}$ into standard form showing ALL your working

   [2 marks]

7. Show all your working out for:
   1. $3\dfrac{2}{3} - 1\dfrac{6}{7}$
   2. $1\dfrac{2}{5} \times 4\dfrac{3}{8}$

      [4 marks]

5.1 Homework Due Tue 15.9.15

To be done neatly in the front of your books
TOTAL 20 marks

1. The plots shows the curve $y=-\frac{1}{3}x^2+3x+1$

   

   1. Use the formula to solve the equation $-\frac{1}{3}x^2+3x+1=0$ giving your answers to 2 d.p.
   2. Use the formula to find the solutions to 2 significant figures $-\frac{1}{3}x^2+3x+1=3$
   3. $-\frac{1}{3}x^2+3x+1=k$ has no solutions, where k is an integer. Use the plot above to find the minimum value of k

   [6 marks]

2. By factorising only, solve: $12x^2+23x-24=0$

   [3 marks]

3. The volume of a balloon is directly proportional to the cube of its radius. A balloon of radius 5cm has volume $525cm^3$:
   1. Find a formula for v in terms of r
   2. Find the volume of the balloon when the radius is 15cm
   3. What is the radius of a balloon with volume $2560cm^3$?

   [4 marks]

4. Find the image of the point (4, -5) under the transformation represented by M $M = \begin{pmatrix} 3 & -2 \\ 1 & -1 \end{pmatrix}$

   [2 marks]

5. Find the 2x2 matrix which represents a rotation 90 degrees anticlockwise around the origin.

   [2 marks]

6. A line passes through the points A(-1,5) and B(4, -5). By first finding the gradient of AB, write down the equation of the line in the form y=mx+c

   [3 marks]