GRADE 11 P1

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GRADE 11 FINAL ASSESSMENT PAPER 1

NOVEMBER 2015 TOTAL: 150 TIME: 3 hours

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INSTRUCTIONS 1. This question paper consists of 10 questions. 2. Answer all the questions. 3. Clearly show all calculations used to solve problems. 4. You may use an approved scientific calculator, unless

stated otherwise. 5. If necessary, round off answers correct to two decimal

places. 6. Diagrams are not necessary drawn to scale. 7. Number the answers according to the questions. 8. Write neatly and legibly.

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QUESTION 1:

1.1 Solve for x:

1.1.1 (-x + 4)(x + 5) = 0

(2)

1.1.2 x2 - 6x = 3, correct to two decimal places.

(4)

1.1.3 x + 5 - 3 = 4

(4)

1.1.4 3x2 - 2x - 8 0

(4)

1.2 Solve the equations simultaneously:

(x - 2 y)(2x + y) = 12 and 7 y - x + 9 = 0

(6)

1.3 Solve for x:

3

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2(x - 2) 2 = 108

(3)

1.4 Use the solution for k - 3 = 2 to solve x if 3x - 31-x - 2 = 0 . (6) k [29]

QUESTION 2:

2.1 Simplify without using a calculator:

32003 - 32001

(4)

32003

2.2 f (x) = x - 3 x +1

2.2.1 For which value(s) of x will f (x) be undefined?

(2)

2.2.2 For which value(s) of x will f (x) be non real?

(2)

2.3 Simplify the expression:

10 x.252x.8x

(4)

40 x

[12]

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QUESTION 3:

The perimeter of a square is 16x.

3.1 Determine the length of a side for the square.

(2)

3.2 Hence, determine the area of the square if x = 2 cm. (3) [5]

QUESTION 4:

4.1 Use the given number pattern: -9 ; -3 ; 10 ; 30 ; 57 ; ..... 3 432

4.1.1 Determine the general term for the given pattern.

(4)

4.1.2 Which term will be 297?

(4)

4.1.3 Determine the general term for the first differences.

(3)

4.2 Use the following number pattern: 1 ; 3 ; 7 ; 15 ; 31

4.2.1 Determine the general term for the given number pattern. (2)

4.2.2 Calculate the value of the eighth term.

(2)

[15]

QUESTION 5:

5. Use the given picture pattern to answer the questions.

Figure 1

Figure 2

5.1 Determine the nth term for the given pattern. 5.2 How many matches will be used for T20?

Figure 3

(3) (2)

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5.3 Determine the biggest number of matches needed if the pattern will use less

than 518 matches.

(2)

[7]

QUESTION 6:

6. Given: f (x) = - 8 - 3 x+2

6.1 Write down the equations of the asymptotes for f .

(2)

6.2 Calculate the x- and y-intercepts of f .

(3)

6.3 Sketch the graph of f .

(3)

6.4 If y = -x + k the equation of the symmetry of f , determine the value of k.

(2)

6.5 What is the domain and the range for f .

(4)

6.6 Determine the equation of h where h is the reflection of f in the x-axis.

(2)

[16]

QUESTION 7:

7. The diagram represents g(x) = -4.2 x+2 + 4 .

7.1 Determine the coordinates of A, B and C.

(6)

7.2 Determine the average gradient between B and C.

(4)

7.3 Find the equation of h where h is the reflection of g in the Y-axis.

(2)

7.4 For which value(s) of x will g(x) = h(x) ?

(2)

7.5 Determine the x-intercept of h .

(2)

[16]

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