R4Rt5

|x[pic] |[pic] |[pic] |[pic] |[pic] |

|Frequency |12 |10 |17 |11 |

a) Use this information to show that the bar representing the group 10-12 must be 6cm wide and 20cm high. (hint – don’t forget that there are no gaps between bars on a histogram so the 10-12 bar is actually 9.5-12.5!)

b) Find the height of the other two bars

PURE MATHS

2 Find the equation of the line through (2, – 3) and (5, 15) in the form ax + by + c = 0 where a, b and c are integers

3 Find the equation of the line passing through (2, 5) which is parallel to the line

2x – y = 6. Write your answer in the form ax + by + c = 0 where a, b and c are integers.

4 Complete the square of the following quadratics by first writing them as [pic] then completing the square inside the square brackets and finally expanding out the square brackets. Hence state the turning point.

(a) [pic] (b) [pic]

5 Find an equation of the straight line which passes through the origin and which is perpendicular to the line 4y – 3x + 2 = 0. Write your answer in the form

ax + by + c = 0 where a, b and c are integers.

6 Solve the quadratic inequality [pic] (Note: no, you cannot square root both sides of an inequality!!) ALWAYS USE A SKETCH WHEN SOLVING QUADRATIC INEQUALITIES!

7 Solve the following equations

(a) [pic] (b) [pic] (c) [pic]

8 The tangent to a circle at P is always perpendicular to the radius joining P to the centre of the circle. Use this information to find the equation of the tangent to the circle [pic] at the point (–3, 4), giving your answer in the form

ax + by + c = 0 where a, b and c are integers.

[pic]

9

a) Find the length of BC

(b) Find the area of the triangle

(c) Find the angle at C

10 The following is the...