Elective Maths 20

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Question 1 of 20

1. Question
The point P(-1,3) undergoes an anticlockwise rotation through 60⁰ about the origin. Find the coordinates of its image.
- $\left(-\frac{3}{2}-\frac{\sqrt3}{2},-\frac{1}{2}+\frac{3\sqrt3}{2}\right)$
- (-3 ,- 1)
- (3, 1 )
- $\left(-\frac{1}{2}-\frac{3\sqrt3}{2},-\frac{3}{2}+\frac{\sqrt3}{2}\right)$
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Question 2 of 20

2. Question
A point P has image (0,5) under the transformation N: (x, y) (x- y, 2x+3y). Find the co-ordinates of P.
- (-1 ,- 1)
- (-1,1)
- (1 ,- 1)
- (1,1)
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Question 3 of 20

3. Question
What is the single transformation for a reflection in the x-axis followed by a rotation through 90⁰ anticlockwise about the origin O?
- Reflection in the y-axis
- Reflection in the line y =- x
- Reflection in the line y = x
- Rotation through 1800 about the origin
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Question 4 of 20

4. Question
A linear transformation is defined by P: (x, y) (-y, 5y -2x). What is the image of the point (-2,3) under the transformation P?
- (2,19)
- (-2,19)
- (-3,11)
- (-3,19)
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Question 5 of 20

5. Question
The linear transformations A and B are defined by A : (x, y) (x+ y, 2x- y) and B : (x, y) (x’, y’). When a point is transformed under A followed by B, it remains unchanged. Find the point (x’,y’).
- ( 2x – y, x+ y )
- [latex]\left(\frac{-x-y}{3},\frac{-2x+y}{3}\right)[/latex]
- [latex]\left(\frac{2x-y}{3},\frac{x+y}{3}\right)[/latex]
- [latex]\left(\frac{x+y}{3},\frac{2x-y}{3}\right)[/latex]
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Question 6 of 20

6. Question
The linear transformation T is given by T: (x, y) $\rightarrow$ (-x, x+ y). Find the image of the point (1 ,- 1) under T.
- (-1,0)
- (-1,1)
- (0,1)
- (1,1)
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Question 7 of 20

7. Question
Find the image of the point P(8, – 2) under an enlargement from the origin O, with a scale factor of 2.
- (-4,16)
- (-2,8)
- (8, – 2)
- (16, – 4)
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Question 8 of 20

8. Question
A linear transformation T is defined by T: (x, y) (3x-2y, 4x +5y). Find the image of (2, – 1) under T.
- (4 ,- 13)
- (4,3)
- (8,3)
- (8,13)
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Question 9 of 20

9. Question
Find the point whose image under the linear transformation S : (x, y) $\rightarrow$ (3x, 2y) is (-3,8)
- (3,8)
- (1,4)
- (-1,4)
- (-9,16)
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Question 10 of 20

10. Question
Find the point whose image is (-6, – 12) under the linear transformation x’=2x-5 $y^1=4x-3y$
- (-3, 0)
- (-3,1)
- (0,3)
- (1,3)
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Question 11 of 20

11. Question
A linear transformation is defined by $\begin{matrix}x\prime\ =\ y\\y\prime\ =-\ x\\\end{matrix}$ .Find the image of the point (-4, 5) under the transformation.
- (5,4)
- (5,-4)
- (4,5)
- (-5,4)
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Question 12 of 20

12. Question
The deviations between two ranks are 1,1,-1,1,0,-3,1,-2,1 and 3.
- 0.20
- 0.733
- 0.879
- 0.979
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Question 13 of 20

13. Question
Given that n=10 and $\sum{d^2=20}$ , calculate the Spearman’s rank correlation coefficient.
- 0.121
- 0.733
- 0.879
- 0.979
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Question 14 of 20

14. Question
The line of best fit in a scatter diagram passes through the points (2,-3) and (10,9) in the x – y plane. What will be predicted value for y when x= 4?
- -3
- 0
- 3
- 6
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Question 15 of 20

15. Question
A negative correlation coefficient implies that
- the association is definitely weak
- there exists no linear association
- the two sets of variables are decreasing together
- a set of increasing variables are associated with decreasing ones.
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Question 16 of 20

16. Question
The regression line of marks obtained in physics (y%) on marks obtained in Mathematics (x%) for student in a class is 3x – 4y + 8=0. Find the mean mark for the two subjects for a candidate who obtained 71% in Physics.
- 63.1%
- 72.0%
- 78.0%
- 81.5%
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Question 17 of 20

17. Question
The regression line of marks obtained in physics (y%) on marks obtained in Mathematics (x%) for student in a class is 3x – 4y + 8=0. If a student obtained 84% in Mathematics, find the mark she obtained in Physics.
- 81%
- 65%
- 63%
- 61%
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Question 18 of 20

18. Question
The regression line of marks obtained in physics (y%) on marks obtained in Mathematics (x%) for student in a class is 3x – 4y + 8=0. Find the regression coefficient of y on x.
- 4
- 4/3
- ¾
- – ¾
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Question 19 of 20

19. Question
Which of the following statements is/are true about scatter diagrams?

I. Knowledge about the relationship between the variables enables us to predict and control event.

II. The independent variable is the variable which is not affected by changes in the other.

III. The main purpose of a scatter diagram is to determine whether there is any pattern among the points.
- III only
- I and II only
- II and III only
- I, II and III
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Question 20 of 20

20. Question
The equation of the line of best fit for two variable X and Y, where X is the independent variable, is given by Y= 4.2X – 0.3, Predict the value of Y when X=7.1
- 30.12
- 29.82
- 29.52
- 29.10
Correct

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