The rule below can be used to work out the cost, in pounds, of renting a computer projector.

Add two to the number of hours required

Multiply your answer by 20

The cost of renting a PC projector for n hours is C pounds.

Write down a formula for C in terms of n.

b) The rule below can be used to convert degrees Centigrade to Fahrenheit.

Multiply your temperature in centigrade by 9, then divide your answer by 5

Add 32 to your answer.

The temperature in centigrade is C. The conversion in Fahrenheit is F.

Write down a formula for F in terms of C

c) Using the formula in b), convert 100 centigrade to Fahrenheit

ANS

The formula v = u + at gives the final velocity of an object as it accelerates.

a) Find the value of v when:

u = 100, a = –10 and t = 8.5

b) The formula v^{2} = u^{2} + 2as gives the final velocity of an object as it accelerates over a distance s.

Find v when: u = 5, a = 2 and s = 6

Find u when: v = 9 , a = 4.25 and s = 2

ANS

a) Expand and Simplify (y + 5)(y – 4)

b) Expand and Simplify (2a + 5)(3a – 2)

c) Expand and Simplify (2a^{2} + 2)(a – 2a^{2})

d) Expand and Simplify (a + 3)^{2}

ANS

a) Write down the integer values of x that satisfy the inequality

– 4 ≤ x < 2

b) Solve the inequality 5a – 16 < 8 – a

c) Solve the inequality 4x ≥ x + 5

d) Solve the inequality x > 3x + 10

ANS

a) Make a the subject of the formula

4x = 3a + y

b) Make z the subject of the formula

3x = 5z^{2} – 4y

c) Make x the subject of the formula

6x – 3y = ax^{2} – 4

d) Make z the subject of the formula

ANS

a) Solve 5t – 6 = 2t + 12

b) Solve 8 + x = 2(3 + 2x)

c) Solve 5(4x – 4) = 5(2x + 9)

d) Solve 7(x + 3) = 11x – 15

ANS

a) The equation
**x ^{3} + 5x – 4 = 52**

has a solution between 3 and 4

Use a trial and improvement method to find this solution.

Give your answer correct to 1 decimal place.

b) The equation
**x ^{3} – 3x^{2} + 7 = 6**

Has a solution between 2 and 3.

Using trial and improvement find the solution to 1 decimal place.

ANS

a) What is the reciprocal of 7?

b) Simplify

(y^{9})/
y^{3}

c) Simplify a^{10} × a^{–5}

d) Simplify fully (3a^{3}b^{4})^{5}

e) Simplify fully 5h^{4} × 4h^{2} ÷ 2h^{3}

ANS

a) Complete the table of values : y = 3x – 2

x | –2 | –1 | 0 | 1 | 2 | 3 |

y | –8 | –2 |

b) Now get some graph paper and draw the graph of y = 3x – 2

c) What is the gradient of y = 3x – 2

d) Find the equation of the line passing through (6,5) and perpendicular to the line y = 3x + 4.

e) Find the equation of the line passing through (6,5) and (4,9)

f) Complete the table for: y = x^{2} + 4x– 1

x | –5 | –4 | –3 | –2 | –1 | 0 | 1 |

y | –1 | –4 | –5 |

g) Get some graph paper and draw the graph of x^{2} + 4x– 1

h) Complete the table for: y = x^{3} + 2x – 1

x | –2 | –1 | 0 | 1 | 2 |

y | –4 | 11 |

i) Get some graph paper and draw the graph of y = x^{3} + 2x – 1

ANS

a) Complete the table for: 2y + 3x = 9

x | –1 | 0 | 1 | 2 | 3 |

y |

b) Now complete the table for: y = x + 2

x | –2 | –1 | 0 | 1 | 2 |

y |

c) Get some graph paper and draw the graph of y = x + 2 and 2y + 3x = 9

d) Using the graphs find the solution to the simultaneous equations

y = x + 2 and 2y + 3x = 9

e) Draw the graphs for these simultaneous equations and use them to find the solutions

x^{2} + y^{2} = 9

y = x + 1

Look at the angles in the above 4 sided shape.

a) Write an equation in terms of b, as simply as possible for these angles

b) Solve the equation in a) to work out the value of b

Look at the angles in the triangle

c) Write an equation in terms of x for these angles

d) Solve the equation in c) to work out the value of x

e) Show that the area of the shape above is given by the expression 10 x^{2} + 15x – 12

ANS

a) Solve the simultaneous equations

5p + 3q = 25

3p + 3q = 21

b) Solve the simultaneous equations

6x + 5y = 15

5x – 5y = 40

c) Solve the simultaneous equations

6x – 4y = 19
12x + 12y = 18

d) Solve the simultaneous equations

2x – 3y = - 5
3x + 2y = 38

e)Solve the simultaneous equations

y = x^{2} – 6x + 24

6x – y = 12

ANS

a) Factorise x^{2} + 7x +10

b) Factorise x^{2} + 14 x – 15

c) Solve x^{2}+ 10x – 39 = 0

d) Simplify fully

ANS

a) Factorise x^{2} + 10x + 24 by completing the square

b) Hence solve x^{2} + 10x + 24 = 0

c) Factorise y^{2} – 12y + 5 by completing the square.

d) Hence solve y^{2} – 12y + 5 = 0 correct to 2 d.p.

ANS

Solve x^{2} – 7x - 9 = 0 using the quadratic formula. Answer to 3 sf

b) Solve x^{2} + 7x + 1 = 0 using the quadratic formula

ANS

Solve the equation:

a)

b)