GCSE Unit 2  Use of a calculator is allowed 
1. 
Four of the interior angles of a sevensided polygon are 114^{o} , 150^{o} , 160^{o} and 170^{o}. The other three interior angles of this polygon are equal. Calculate the size of each of the other three interior angles. [5]
 
2.  (a) Express 144 as the product of its prime factors in index form. [3]
(b) Given that 60 = 2^{2} x 3 x 5, find: (i) the highest common factor (HCF) of 144 and 60, [1] (ii) the lowest common multiple (LCM) of 144 and 60. [1]
 
3.  (a) Solve the inequality given below. [2]
7n < 5n + 11 (b) Give the largest integer value for n that satisfies this inequality. [1]
 
4.  A solution to the equation
Use the method of trial and improvement to find this solution correct to 1 decimal place.
 
5.  Carys has a Monday to Friday job and a weekend job. Working Monday to Friday and working weekends are independent events. In any given week, the probability that Carys works every day from Monday to Friday is 0.65 . The probability that she works both days during a weekend is 0.2 . (a) Complete the following tree diagram. [2]
(b) Calculate the probability that next week Carys will work every day from Monday to Sunday. [2]
 
6.  An allotment has two rectangular flower beds A and B.
Flower bed A is x metres long and y metres wide.
The perimeter of flower bed A is 18 metres.
Use an algebraic method to calculate the area of flower bed B.
 
7.  Factorise x^{2}  x  20, and hence solve x^{2}  x  20 = 0 [3]
 
8.  A sketch of the graph of the straight line y = 7x + 2 is shown below.
(a) What are the coordinates of the point A, where the line cuts the yaxis?
(b) When h is equal to 1 unit, what is the value of k?
(c) Which of the following equations is an equation of a straight line that is perpendicular to y = 7x + 2?
 
9. 
Calculate the length AD. [3] Find the size of the angle x. [5]
 
10.  (a) Make c the subject of the following formula. [2]
(b) Solve 3x^{2} + 4x  18 = 0, giving your answers correct to two decimal places.
 
11.  ABCD is a rectangle, P, Q, R and S are the midpoints of the sides.
(a) Prove that triangles APS and CRQ are congruent. [3]
(b) Use your proof in part (a) to decide what is the special name given to the quadrilateral PQRS.
 
12.  The square and the sector of a circle shown below have equal areas.
Calculate the size of angle x. [3]
 
13. 
 
14.  30 students in a Year 11 class have decided which subjects they are going to study next year.
The universal set ε contains all the students in the class. [2]
(b) Given that a student, chosen at random, has decided to study French, what is the probability that this student has also decided to study German? [2]
 
15.  Circle the correct answer for each of the following questions.
(a) tan 30^{o} is equal to,
(b) cos 150^{o} is equal to,
(c) The graph
can be represented by the equation
where a and b are both positive numbers.
 
16.  Using the axes below, sketch the graph of y = sin x + 3 for values of x from 0^{o} to 360^{o}. [2]
 
17. 
Calculate the area of triangle ACD. [6]
 
18.  A factory produces a very large number of beads which are either coloured red or coloured blue. The beads are identical in all other respects. The probability of a randomly chosen bead being red is 0.7. The beads are randomly packed in boxes of 20 beads.
