GCSE Unit 2 | Use of a calculator is allowed |
1. |
Four of the interior angles of a seven-sided polygon are 114o , 150o , 160o and 170o. The other three interior angles of this polygon are equal. Calculate the size of each of the other three interior angles. [5]
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2. | (a) Express 144 as the product of its prime factors in index form. [3]
(b) Given that 60 = 22 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]
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3. | (a) Solve the inequality given below. [2]
7n < 5n + 11 (b) Give the largest integer value for n that satisfies this inequality. [1]
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4. | A solution to the equation
Use the method of trial and improvement to find this solution correct to 1 decimal place.
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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]
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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.
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7. | Factorise x2 - x - 20, and hence solve x2 - x - 20 = 0 [3]
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8. | A sketch of the graph of the straight line y = 7x + 2 is shown below.
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(a) What are the coordinates of the point A, where the line cuts the y-axis?
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(b) When h is equal to 1 unit, what is the value of k?
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(c) Which of the following equations is an equation of a straight line that is perpendicular to y = 7x + 2?
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9. |
![]() Calculate the length AD. [3] Find the size of the angle x. [5]
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10. | (a) Make c the subject of the following formula. [2]
(b) Solve 3x2 + 4x - 18 = 0, giving your answers correct to two decimal places.
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11. | ABCD is a rectangle, P, Q, R and S are the mid-points 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.
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12. | The square and the sector of a circle shown below have equal areas.
![]() Calculate the size of angle x. [3]
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13. | ![]()
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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]
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15. | Circle the correct answer for each of the following questions.
(a) tan 30o is equal to,
![]() (b) cos 150o is equal to,
![]() (c) The graph
![]() can be represented by the equation
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where a and b are both positive numbers.
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16. | Using the axes below, sketch the graph of y = sin x + 3 for values of x from 0o to 360o. [2]
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17. |
![]() Calculate the area of triangle ACD. [6]
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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.
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