Foundation Maths-Exam Paper-June 2014 - Final FPB 2

8/17/2019 Foundation Maths-Exam Paper-June 2014 - Final FPB 2

1/7

Foundation Mathematics

3 June 2014

Examination Paper

Answer ALL questions.

Clearly cross out surplus answers.

Any reference material brought into the examination room must behanded to the invigilator before the start of the examination

Calculators ARE permittedGraph paper is required

Time: 2 hours


2/7

Questions continue on the next page

Page 2 of 7

Foundation Mathematics June 2014 Final © NCC Education Ltd 2014

CANDIDATES MUST ANSWER ALL QUESTIONS

QUESTION 1 Marks

a) Simplify the following:

i) − × 1

ii)

× − 1

iii) 3 ÷ 1

b) Simplify the following:

i)

×

1

ii) ÷

4 1

iii) 7 ÷ 13 1

c) Factorise the following:

i) 6 +214 2

ii) 20 2

d) Simplify the following:

i)

+

2

ii) 4

4

2

e) Transpose the following formula to make the subject:

= √ + 7

2

f) Solve the following equation and find the value of :

2 6 = + 6

2


3/7

Questions continue on the next pagePage 3 of 7


g) Solve the quadratic equation:

11 + 28 = 0

by factorising.

2

Total 20 Marks

QUESTION 2 Marks

a) Solve the following quadratic equation by using the Quadratic Formula:

9 + 2 3 = 0

(You may leave your answer in surd form)

2

b) Solve graphically the simultaneous equations

= 3 2 and = 1 0 for 0 ≤ ≤ 5

Use the graph paper provided.

7

c) Calculate the gradient of the following curves at the point where = 1 , usingdifferentiation.

i) = 2 +

3

ii) = 2 + 1 3

d) A particle moves metres in seconds so that = 2 + 9 1

i) Find the velocity, , after 2 seconds 3

ii) Find the acceleration, , after seconds. 2

Total 20 Marks


4/7



QUESTION 3 Marks

a) i) Using differentiation, find the coordinates of the turning point on the curve =3 6

4

ii) Identify the turning point found in part i) above as either a maximum or minimum

turning point.

2

b) Integrate the following expression:

√ 3

2

c) The gradient of the curve which passes through the point (2, 9) is given by 10 3.Find the equation of the curve.

3

d) Evaluate the following definite integrals:

i) (54 + √ )ⅆ

3

ii) ∫ 2 + 3 + 2 ⅆ 3

e) Find the area bounded by the curve, = 8 + 3 1 the - axis and the lines =1 and = 2

3

Total 20 Marks


5/7



QUESTION 4 Marks

a) The acceleration of a moving body at the end of seconds from the commencement ofmotion is 12 5 m/s2.

i) Find the velocity at the end of 3 seconds if the initial velocity is 10 m/s. 3

ii) Find the distance travelled by the body at the end of 2 seconds. 3

b) Sara and Jackie both work in the same office.The probability that Sara will be late on a Monday morning is 0.25The probability that Jackie will be late on a Monday morning is 0.3

i) Draw a probability tree diagram to show all the possible outcomes for Mondaymorning.

8

ii) Use your tree diagram to find out the probability that at least one person is on time. 2

c) You are given a box containing 6 books. How many ways can you arrange 2 of themon a shelf?

2

Total 18 Marks


6/7



QUESTION 5 Marks

a) 30 students complete a short test. The students are marked out of 10. The results arerecorded below:

8 6 7 10 8

9 7 7 9 74 9 3 7 5

2 5 6 4 9

8 6 8 7 10

0 7 8 4 9

i) Summarise this data as a frequency distribution table. 2

ii) Construct a bar chart to illustrate this data. 4

iii) What is the modal mark? 1

iv) Calculate the mean. You may leave your answer as a fraction. 3

v) Calculate the range. 1


7/7

End of examination

Page 7 of 7


b) The masses of 100 male students were recorded to the nearest kg and are shown inthe following table:

Mass(kg)Number ofstudents

(Frequency)

50 < 60 20

60 < 70 50

70 < 80 30

i) Copy and complete the following table which calculates the cumulative frequencyof the data presented above.

Mass (kg) Number ofstudents

(Frequency)

Cumulativefrequency

50

Documents

Foundation Maths-Exam Paper-June 2014 - Final FPB 2