User:Adamsaleel

Infinite product
$$\frac{A^{24}}{2^{\frac{2}{3}}\pi^2{e^2}}=\left(\frac{2}{1}\right)^{\frac{1}{2}} \left(\frac{2^2}{1\cdot3}\right)^{\frac{2}{2}}\left(\frac{2^3\cdot4}{1\cdot3^3}\right)^{\frac{3}{4}}\cdots$$

Euler constant
$$\gamma=\lim_{x\to\infty}\frac{xe^{\frac{\alpha\gamma}{x}}-e^{\frac{\beta\gamma}{x}}\Gamma\left(\frac{1}{x}\right)}{\alpha-\beta+1}$$

Special condition

$$\gamma=\lim_{x\to\infty}\frac{xe^{\frac{1}{x}}-e^{-\frac{1}{x}}\Gamma\left(\frac{1}{x}\right)}{3}$$

pi
\

$$\sqrt{\frac{\pi}{2}}=\lim_{n \to \infty}\left[(8n-1)(8n-3)\right]^{\frac{1}{4}}\prod_{k=1}^{2n-1} \left(\frac{1}{2k}\right) ^{(-1)^{k-1}}$$

$$\sqrt{\frac{\pi}{2}}=\lim_{n \to \infty}\frac{\left[(8n+1)(8n+3)\right]^{\frac{1}{4}}}{4n+1}\prod_{k=1}^{2n} \left(\frac{1}{2k}\right) ^{(-1)^{k-1}}$$

Others
$$\lim_{n \to \infty}{\sum_{k=2^n}^{2^{n+r}-2^{r-1}}\left(\frac{1}{k}\right)-\frac{1}{2^{n+r+1}-1}}=r\ln2$$

$$\lim_{n \to \infty}\sum_{k=3^n}^{3^{n+1}-2}{\frac{1}{k}}=\ln3$$

$$\lim_{n \to \infty}\sum_{k=(2i+1)^n}^{(2i+1)^{n+1}-(i+1)}{\frac{1}{k}}=\ln(2i+1)$$

$$\frac{\pi^2}{6}=\sum_{n=1}^{\infty}\frac{1}{\sum_{i=1}^{2n-1}(-1)^{i-1}\left(2n+1-i\right)^2i^3}$$

$$=\sum_{n=1}^{\infty}\frac{1}{\sum_{i=1}^{2n-1}(-1)^{i-1}\left(2n+1-i\right)i^2}$$

$$\lim_{n \to \infty}\left[2+\frac{2}{3}+\frac{2}{5}+\cdots+\frac{2}{2^n-1}+\ln\left(\frac{1}{2^{n+1}-1}\right)-\frac{1}{2^{n+1}-1}\right]=\gamma$$

Special case aln3
$$\lim_{n \to \infty}\sum_{k=3^n}^{3^{n+1}-2}{\frac{1}{k}}=1\ln3$$

$$\lim_{n \to \infty}\sum_{k=3^n}^{3^{n+2}-[2+3]}{\frac{1}{k}}=2\ln3$$

$$\lim_{n \to \infty}\sum_{k=3^n}^{3^{n+3}-[2+3+3^2]}{\frac{1}{k}}=3\ln3$$

$$\lim_{n \to \infty}\sum_{k=3^n}^{3^{n+4}-[2+3+3^2+3^3]}{\frac{1}{k}}=4\ln3$$

$$\lim_{n \to \infty}\sum_{k=3^n}^{3^{n+a}-\left(2+\sum_{i=1}^{a-1}3^i\right)}{\frac{1}{k}}=a\ln3$$

General case aln(2i+1)
$$\lim_{n \to \infty}\sum_{k=(2i+1)^n}^{(2i+1)^{n+a}-\left(i+1+i\sum_{j=1}^{a-1}(2i+1)^j\right)}{\frac{1}{k}}=a\ln(2i+1)$$

General case ln(2i)
$$\sum_{k=(2i)^n}^{(2i)^{n+1}-(i+1)}\frac{1}{k}=\ln(2i)$$

$$\sum_{k=(2)^n}^{(2)^{n+a}-(1+2^{a-1})}\frac{1}{k}=a\ln(2)$$

$$\sum_{k=(4)^n}^{(4)^{n+a}-(1+2^{2a-1})}\frac{1}{k}=a\ln(4)$$

Continued fractions
$$\frac{e+1}{e-1}-{\frac{2}{e-1}}\left(\sum_{j=1}^{2n-1}(-1)^{j+1}\sqrt[2n]{e^j}\right)=\frac{1}{4n+\frac{1}{12n+\frac{1}{20n+\frac{1}{28n+\cdots}}}}$$

Let n = 1, yields

$$\frac{e+1}{e-1}-{\frac{2\sqrt{e}}{e-1}}=\frac{1}{4+\frac{1}{12+\frac{1}{20+\frac{1}{28+\cdots}}}}$$

Radical 2 odd
$$\frac{a-\sqrt[2k-1]{a}}{\sqrt[2k-1]{a^2}-1}=\sqrt[2k-1]a+\sqrt[2k-1]{a^3}+\sqrt[2k-1]{a^5}+\cdots+\sqrt[2k-1]{a^{2k-3}}$$

$$\frac{a\sqrt[2k-1]{a}-\sqrt[2k-1]{a^2}}{\sqrt[2k-1]{a^2}-1}=\sqrt[2k-1]{a^2}+\sqrt[2k-1]{a^4}+\sqrt[2k-1]{a^6}+\cdots+\sqrt[2k-1]{a^{2k-2}}$$

$$\frac{a+(a-1)\sqrt[2k-1]{a}-\sqrt[2k-1]{a^2}}{\sqrt[2k-1]{a^2}-1}=\sum_{j=1}^{2k-2}{\sqrt[2k-1]{a^j}}$$

$$\frac{a-(a+1)\sqrt[2k-1]{a}+\sqrt[2k-1]{a^2}}{\sqrt[2k-1]{a^2}-1}=\sum_{j=1}^{2k-2}(-1)^{j+1}{\sqrt[2k-1]{a^j}}$$

Radical 3 even
$$\frac{a-\sqrt[2n]{a^2}}{\sqrt[2n]{a^2}-1}=\sqrt[2n]{a^2}+\sqrt[2n]{a^4}+\sqrt[2n]{a^6}+\cdots+\sqrt[2n]{a^{2n-2}}$$

$$\frac{(a-1)\sqrt[2n]{a}}{\sqrt[2n]{a^2}-1}=\sqrt[2n]{a}+\sqrt[2n]{a^3}+\sqrt[2n]{a^5}+\cdots+\sqrt[2n]{a^{2n-1}}$$

Radical 1 (mixed)
$$\frac{1}{2}{\times}\frac{\sqrt[5]2+1}{\sqrt[5]2-1}-\frac{5}{2}=\sqrt[5]4+\left(\sqrt[5]{\frac{1}{5}}+\sqrt[5]{\frac{4}{5}}\right)^{\frac{1}{2}}{\times\sqrt[5]{125}}$$

$$\frac{1}{2}{\times}\frac{\sqrt[3]2+1}{\sqrt[3]2-1}-\frac{1}{2}=2\sqrt[3]2+\left(4\sqrt[3]{\frac{2}{3}}+5\sqrt[3]{\frac{1}{3}}\right)^{\frac{1}{8}}{\times\sqrt[3]{9}}$$

$$\frac{1}{2}{\times}\frac{\sqrt[3]2+1}{\sqrt[3]2-1}-\frac{1}{2}=\left(\sqrt[3]{\frac{1}{9}}+\sqrt[3]{\frac{4}{9}}+\sqrt[3]{\frac{16}{9}}\right)^{\frac{3}{2}}$$

$$X=\frac{1}{4}\left(1-\frac{\sqrt[3]2+1}{\sqrt[3]2-1}\right)+\frac{2}{\sqrt[3]2}=-\frac{16813}{500000}$$; Rational number!!!

$$Y=\left(\frac{9}{2\sqrt[3]4}-\frac{9}{4}\right)^{\frac{1}{3}}=\frac{41813}{500000}$$; Rational number!!!

$$X+Y=\frac{1}{2}$$

$$\left(1-\frac{\sqrt[3]2-1}{\sqrt[3]2+1}\right)^3=\frac{8}{3}\left(\sqrt[3]2-1\right)$$

$$\frac{a-1}{2}\left(\frac{\sqrt[3]a+1}{\sqrt[3]a-1}-1\right)=2\sqrt[3]a+\left[\left(a^2-7a+1\right)+\left(6a-3\right)\sqrt[3]a+\left(6-3a\right)\sqrt[3]{a^2}\right]^{\frac{1}{3}}$$

$$\frac{a-1}{2}\left(\frac{\sqrt[3]a+1}{\sqrt[3]a-1}-1\right)=2+2\sqrt[3]{a^2}-\left[\left(a^2-7a+1\right)+\left(6a-3\right)\sqrt[3]a+\left(6-3a\right)\sqrt[3]{a^2}\right]^{\frac{1}{3}}$$

$$\frac{a+1}{2}\left(1-\frac{\sqrt[3]a-1}{\sqrt[3]a+1}\right)=\left[\left(a^2-7a+1\right)+\left(6a-3\right)\sqrt[3]a+\left(6-3a\right)\sqrt[3]{a^2}\right]^{\frac{1}{3}}$$

$$\frac{a-1}{4}\left(\frac{\sqrt[3]a+1}{\sqrt[3]a-1}-1\right)-\frac{a+1}{4}\left(1-\frac{\sqrt[3]a-1}{\sqrt[3]a+1}\right)=\sqrt[3]a$$

$$\frac{a-1}{4}\left(\frac{\sqrt[3]a+1}{\sqrt[3]a-1}-1\right)+\frac{a+1}{4}\left(1-\frac{\sqrt[3]a-1}{\sqrt[3]a+1}\right)=1+\sqrt[3]{a^2}$$

Ramanujan
General of ramanujan's nested radical

Stage:1

$$\frac{\sqrt[n]k+1}{\sqrt[n]k-1}=\frac{2}{k-1}\left(\frac{k+1}{2}+\sqrt[n]{k}+\sqrt[n]{k^2}+\sqrt[n]{k^3}+\cdots+\sqrt[n]{k^{n-1}}\right)$$

$$\frac{\sqrt[2n]k-1}{\sqrt[2n]k+1}=\frac{2}{k-1}\left(\frac{k+1}{2}-\sqrt[2n]{k}+\sqrt[2n]{k^2}-\sqrt[2n]{k^3}+\cdots+\sqrt[2n]{k^{2n-1}}\right)$$

$$\frac{\sqrt[2n-1]k-1}{\sqrt[2n-1]k+1}=\frac{2}{k+1}\left(\frac{k-1}{2}+\sqrt[2n-1]{k}-\sqrt[2n-1]{k^2}+\sqrt[2n-1]{k^3}+\cdots+\sqrt[2n-1]{k^{2n-2}}\right)$$

Sum

$$\frac{\sqrt[n]k+1}{\sqrt[n]k-1}=\frac{2}{k-1}\left(\frac{k+1}{2}+\sum_{j=1}^{n-1}\sqrt[n]{k^j}\right)$$

$$\frac{\sqrt[2n]k-1}{\sqrt[2n]k+1}=\frac{2}{k-1}\left(\frac{k+1}{2}+\sum_{j=1}^{2n-1}(-1)^{2j-1}\sqrt[2n]{k^j}\right)$$

k = 5

Yields ramanujan's equation

$$\frac{\sqrt[4]5+1}{\sqrt[4]5-1}=\frac{1}{2}\left(3+\sqrt[4]{5}+\sqrt[4]{5^2}+\sqrt[4]{5^3}\right)$$

Fibonacci
$$a^2+b^2=c^2$$

$$a^4+b^4=2\left(c^2+ab\right)^2-\left(a+b\right)^4$$

$$a^4+b^4=\left(a+b\right)^4-2ab\left(2c^2+3ab\right)$$

$$\left(a+b\right)^2=ab+\frac{a^4+b^4+\left(a+b\right)^4}{a^2+b^2+\left(a+b\right)^2}$$

$$2\left(a+b\right)^2=ab+\frac{\left(a+b\right)^4-\left(a^4+b^4\right)}{\left(a+b\right)^2-\left(a^2+b^2\right)}$$

$$G_n=G_{n-1}+G_{n-2}$$

G1 = i and G2 = j

i & j ɛ {1,2,3,4,...}

$$G_1+G_2+G_3+\cdots+G_n=G_nG_{n+1}+G_1(G_1-G_2)$$

Formulae

$$\frac{F_n^4+F_{n+1}^4+F_{n+2}^4}{2}=\left(F_n^2+F_{n+1}F_{n+2}\right)^2$$

$$\sum_{i=1}^{k}F_i^4+\sum_{i=1}^{k}F_{i+1}^4+\sum_{i=1}^{k}F_{i+2}^4=2\left(F_{i-1}F_{i}+\sum_{i=1}^{k}F_iF_{i+1}\right)^2$$

Assessement for years 1 - 2
Q1.

Add

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

Q2.

Subtract

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

Q3.

Mulitply

2 × 4 =

5 × 6 =

2 × 4 × 1 =

1 × 1 =

3 × 0 =

Q4.

Division

6 ÷ 2 =

10 ÷ 5 =

8 ÷ 8 =

Q5.

Put the numbers in order of smallest size first.

a. 6, 1, 0, 3

b. 18, 10, 15, 11

Q6.

Shade three portions of the shape

a. _______ | | | | |  | | | | |  |_|_|_|_| Shade 8 portions of the shape

b. _______________ |_|_|_|_|_|_|_|_|  |_|_|_|_|_|_|_|_|

Assessement for years 7 - 8
Q1. a. Find the sum of -10 and 20

b. Find the product of zero and six

c. Find the difference of -2 and 3

Q2.

Work out the following a. - 2 + 8 =       b. - 5 + 5 =        c. - 5 + 0 = d. - 2 - 8 =       e. - 1 + 2 - 1 + 3 - 3 = f. - 2 × 8 =       g. - 2 × (-4) =     h. 12 ÷ (-3) =

Q3.

Work out the following

a. $$\frac{1}{4}+\frac{2}{5}$$

b. $$\frac{3}{4}-\frac{2}{5}$$

c. $$\frac{2}{3}\times{\frac{1}{3}}$$

d. $$\frac{1}{4}\div{\frac{2}{5}}$$

Q4.

Write the following

a. Four square numbers greater than 1

b. Three cube numbers less than 100

c. Five prime numbers between 4 and 20

Q5.

Work out the following

a. 23

b. 50

c. $$\sqrt{9}$$

d. 2-3

e. $$4^{\frac{1}{2}}$$

f. $$\sqrt[3]{8}$$

g. $$8^{\frac{2}{3}}$$

Q6.

Find the answer

a. 15 - 9 ÷ 3 =

b. 2 ÷ 2 - 2 =

c. (16-6) ÷ 2 + 5

Q7.

Work out the following

a. 0.4 × 0.6

b. 12 ÷ 2.4 =

c. 12.0054 + 0.00542

Q8.

£20 is divided in the ratios 2 : 3 : 5

a. Work out the amount of the smallest ratio

b. Find how much more is the largest amount from the smallest amount

Q9.

a. What is 20% of £600.00?

Q10.

Draw the following triangles and label with its appropriate symbols

a. An isoscle triangle

b. An equlateral triangle

c. A scalene triangle

d. A right angle triangle

Q11. .    | .  8m |. 10m |    .     |_______.        6m

a. Find the area of the triangle

b. Find the perimter of the triangle

Q12.

Simplify the following

a. 5y + 5x - y

b. $$2x\times4y$$

Q13.

Expand and simplify

a. $$2(3x+3)+4$$

b. $$4(4y+1)+2(2y+3)$$

Q14.

Solve the for x

a. x - 8 = 1

b. 2x + 4 = 10

c. x2 = 16

Q15.

a. True or false 3 > 4

b. True or false 3 ≤ 3

Q16. e   / 60 ________ /_________  →               /  f    / ____/______________ →    /

a. Find angles e and f

Q17.

y = 2x - 1

a. Fill in the table

b. Plot the graph y ↑ |    8-|       |     6-|       |     4-|       |     2-|    ___|__________________________________→       |   1   2   3   4   5   6   7      x

Q18.

Shoe sizes 5, 2, 2, 1, 3, 4

a. Find the mean size

b. Find the median size

c. Find the modal size

d. Find the range of size

Q19.

John tosses a coin

a. Calculate the probability that it lnads on a head first

Q20.

The probability Henry comes to school late on monday morning is 65%

a. Find the probability that Henry comes to school on monday early.

Q21.

John did a survey, he wants to find out how many people like the following colours

Here is a table and graph showing John's survey

People ↑ 11-|        |      10-|                             |--|          |                             |  |       8-|                             |  |         |                             |  |       6-|        |--|                 |  |         |        |  |                 |  |       4-|  |--|  |  |                 |  |         |  |  |  |  |                 |  |       2-|  |  |  |  |                 |  |    _____|__|__|__|__|_________________|__|______________  →         |  Red   Blue  Green  Purple  Yellow     Colours

a. Fill in the table and the graph.

b. How many more people like yellow colours than red colours

c. How many people are there in John's survey

Assessement for years 9 - 10
Q1.

Work out

a. 31.2 × 0.12

Q2. Computer _______________     |               |       _________      |               |      |         |      |               |      |  Offer  | |              |      | 20% Off | |_______________|     |_________|         __________         \_- - - _/

Price £2400.00

a. Work out the sale price

Q3.

a. Change 0.12 into fraction with the lowest term

Q4.

Evaluate

a. 90        b. 9-1        c. 92       d. $$\sqrt9$$

e. $$\sqrt[3]8$$       f. 271/3

Q5.

Work out

a. $$1\frac{4}{5}-1\frac{2}{5}$$

b. $$\frac{1}{5}+\frac{2}{3}$$

c. $$1\frac{1}{2}\times{\frac{2}{3}}$$

Q6.

Work out

a. $$\left(3\times4-4\div2\right)^2+1$$

Q7.

Simplify

a. 6x + y -5x + 3y

b. 6x2 - 5 + 3x2 + x + 2

Q8.

Expand and simplify

a. $$2(5x-1)+3(x+1)$$

b. $$(2x+3)^2$$

Q9.

Factorise the following

a. x - xy

b. 2x2 - 4x

Q10.

Solve for x

a. 5x - 2 = 8

b. -3x - 5 = -5x + 5

c. $$\frac{x}{3}-1 = 2$$

Q11.

List all the possible values of x

a. - 1 < x < 3

Q12.

Solve the following inequalities

a. 3y - 5 > 4

Q13.

Solve the simultaneous equation

x - y = 3 2x + y = 12

Q14.

The formula c2 = a2 + b2

Given a = 3m and b = 4m

a. Find the value of c

Q15.

Rearrange the formula y = mx + c to make x the subject of the formula

Q16.

Triangle ABC is an isoscle B. .  .             .       .           .           .         .               . ___ X        .___________________.__|____ A                    C Angle A =  30°

a. Find angles X and B

Q17. 6m ________                 |        |              |        | 4m |       |          10m |        |_____ |             |              |              |              |______________|

8m

a. Calculate the the area of the L shape

b. Calculate the perimeter of the L shape

Q18.

a. Name the follwing shapes.

a                                             _____________ .-.                     .                 |             |       .     |     .                    .|.                |             |      .      |h. . | .            a |             | .      |       .                .  |h. |            |    .________|________.              .___|___.             |_____________|             b                           b                        b

--                           --

b. Write down the formulae for each shape to work out the area.

a                                             _____________ .-.                     .                 |             |       .     |     .                    .|.                |             |      .      |h. . | .            a |             | .      |       .                .  |h. |            |    .________|________.              .___|___.             |_____________|             b                           b                        b

Area =                        Area =                   Area =

Q19.

A circle has a radius of 4mm

a. Calculate the area of the circle

b. Calculate the circumference of the circle

Q20.

Here is a list of the size of a quantity

10, 6, 8, 4, 2

a. Calculate the mean size

b. Calculate the median size

c. Calculate the range of the size

Q21.

a. Calculate the mean weight

b. Find the modal weight

Q22.

A bag contain 5 green, 4 blue and 2 black marbles

a. Calculate the probability that a black marble is chosen at random.

b. Calculate the probability that a green and a blue marbles chosen at random

Assessement for years 11
Q1.

Fig.1 below is a right angle triangle

a. Find lenght c. Round the answer to 3 d.p. |. 5m |. c     |. |___.      3m Fig.1

b. Work out the area of this triangle

Q2.

Work out the following

a. $$2\frac{2}{5}+\frac{2}{3}$$

b. $$2\frac{2}{5}\times{1\frac{2}{3}}$$

Q3.

Expand and simplify

a. $$\left(x-2\right)^2-x-2$$

b. $$2\left(2x-1\right)-2x\left(x-1\right)$$

Q4.

Factorise the following

a. $$x^2-2x+1$$

b. $$x^2-1$$

c. $$x\left(x-2\right)+2\left(x-2\right)$$

Q5.

Find the HCF and LCM of 24, 32 and 42

Q6.

Add

a. $$\frac{2}{x+1}+\frac{3}{x-1}$$

Solve for x

b. $$\frac{2}{x+1}+\frac{3}{x-1}=2$$

Q7.

£34.00 travel fair has increased by 23% from last year. Work out the price before the increase.

Q8.

The sequence 3, 7, 11, 15, ...

a. Find the nth of the sequence

b. Work out the 25th of the sequence

c. Show that 50 is not a term in the sequence

Q9.

Diagrams below are mathematically similiar .       |.        | .                 .        27m |. |.        |   .             y |. |   .              |  .        |_____.             |___.          15cm               5m

a. Find the lenght of y

Q10.

Three children of David, Bob, Steve and John shared a sum in the ratios 2 : 5 : 8

Steve received £450 from the sum.

a. Calculate the sum of the sum money shared by the children.

b. How much more did John get more than Bob?

c. Calculate the amount of John in percentage.

Q11.

Work out and write the answer in standard form

a. $$\left(12.4\times10^4\right)+\left(15\times10^3\right)$$

Q12.

a. Change 360km/h into m/s

b. 4m2 into mm2

Q13.

Solve the following simultaneous equations 3x - 2y = 5 2x + 4y = 14

Q14.

Rearrange the formula to make angle B the subject.

a. $$A=\frac{1}{2}acsinB$$

b. Evaluate the angle B, given A = 10, a = 5 and c = 8

Q15.

Solve the equtions to fin the value for x

a. 2x - 5 = 15

b. -3x - 4 = -6x + 2

c. -3(x - 1) + 2(2x + 3) = 10

d. $$\frac{2}{3}+\frac{2x + 1}{6}=7$$

Q16.

Below is a straight line graph

Y     ↑ |  12-|            .      |              10-|         . B(x2,y2) |           8-|      .            |    6-|   .  A(x1,y1) |   4-|      |    2-|         |    0-|---1---2---3---4---5---6---7---8---→ X      |

a. Write down the co-ordinates of points A and B

b. Find the equation of this straight graph

Q17.

Simplify the following indices

a. $$3^{-5}\times3^{12}$$

b. $$3^{2}\div3^{-2}$$

c. $$(2^{-2}x^{-3}y^2)^{-2}$$

d. $$\frac{x^4\times{x^{-2}}}{x^{-4}\times{x^2}}$$

Q18.

Evaluate the following

a. 40

b. 4-1

c. 41/2

d. 43/2

e. 82/3

f. $$\left(4^{\frac{3}{2}}\right)^2$$

Q19.

Solve the following inequalities

a. 2x - 3 ≥ 5

b. 5x + 3 > 7x + 5

Q20.

List all the possible values of x in this inequality

a. -2 < x ≤ 1

Q21.

Expand and simplify the following

a. $$\sqrt{3}\left(\sqrt{3}-1\right)+2\left(\sqrt{3}+1\right)$$

b. $$\left(\sqrt{2}+1\right)\left(2\sqrt{2}-1\right)$$

Q22.

Use the quadratic formula to solve the quadratic equation, round the answers to 2 s.f.

Quadratic formula

$$x=\frac{-b\pm{\sqrt{b^2-4ac}}}{2a}$$

a. 2x2 - 4x + 1 = 0

Q23.

Below is a right angle triangle

A                  .| . |               .  |            c. | b                 .    | .    |            .______|           B   a    C

Given angle B = 30°, lenght b = 10m.

a. Find lenght a, give the answer to 2 s.f

Q24.

Steve invested £2000.00 in a saving account at a compound interest of 1.5% per year.

a. Work out the interest he earns after 10 years period.

Q25.

The rectangle below has an area of 35m2

(2x-1)m _________    |         |     |         |     |         | (2x+1)m |        |     |_________|

a. Show that 4x2 - 36 = 0

b. Work out the lenght and height of the rectangle

Q26.

In a bag there are 6 colur sweets. Three are reds and the rest are blues

a. Calculate the probability that Steve eats both red sweets.

Q27.

Below is table shows record time in seconds for an event

a. Find the mean time for the event

Q28.

Below is a triangular shape

.|                   . | 4m . |               .| .___|              . |    /             .  |  /  10m .___|/            3m

a. Calculate the surface area

b. Calculate the volume

Q29.

Estimate

a. $$\frac{5.9\times4.01}{11.98}$$

Q30.

Use a calculator, work out and write down all the digits on your calculator

a. $$\frac{\sqrt3-\sqrt2}{\sqrt5}$$

Q31.

y = 2x - 3 and y1 = 7 - 3x1

a. Fill in the table and plot the eqautions on the graph below

↑   y | |  10-|      |    8-|      |    6-|      |    4-|      |    2-|    ____|_____________________________→ -1   |   1   2   3   4   5   6    x   -2 | |  -4 |      |   -6 |      |