BRAINSTORM GROUP (BSG) MAT112 TEST (2021/22)

Answer all question

1. Find the distance between the two points 14. Find the equation of the line parallel to 3y = 5x +
(𝑎 + 𝑏, 𝑎 − 𝑏) and (𝑏 − 𝑎, 𝑎 + 𝑏). 7 and passing through A(2, 3).
A. 2√𝑎2 + 𝑏 2 B. √𝑎2 + 𝑏 2 A. 5y - 3x + 1 = 0 B. 5y + 3x - 1 = 0
C. 2√𝑎2 − 𝑏 2 D. 2(𝑎2 + 𝑏 2 ) C. 3y -5x + 1 = 0 D. 3y + 5x + 1 = 0
2. Find the distance PQ given Q(4, 3) and P(2, 2). 15. If the 3y1 = -4x + 7 and 2y2 = 6x + 12. Find the
value of 𝑡𝑎𝑛𝜃, where 𝜃 is the angle between line.
A. 2√5 B. 2√2 C. √5 D. 2 13 13 9
3. Find the midpoint coordinate of the line joining A. -13 B. C. − D.
9 9 13
the point M(-4, 3) and N(6, 7). 16. Find the distance between (a² + b², c² + d)
A. (5, 1) B. (1, 5) C. (2, 3) D. (-1, 5) and ( −(a² + b²), −c² + d).
4. The perpendicular bisector of line PQ cuts line A. √𝑎4 + 𝑏 4 + 4𝑐 4 + 2𝑎2 𝑏 2
1
PQ at ___, given P(-3, ), Q(4, 5). B. 2√𝑎4 + 𝑏 4 + 𝑐 4 + 𝑑2 + 2𝑎2 𝑏2 + 2𝑐 2 𝑑
2
1 11 7 9 1 11 7 9
A. ( , ) B. (− , − ) C. ( , ) D. ( , ) C. 2√𝑎4 + 𝑏 4 + 𝑐 4 + 2𝑎2 𝑏2
2 2 2 4 2 4 2 4
5. Given P(x, 2x) and Q(2x, 1) and PQ = √2. Find x. D. 2√𝑎4 + 𝑏 4 + 𝑐 4 − 2𝑎2 𝑏2
1 17. What is the perpendicular distance between
A. B. 1 C. -1 D. 2
5 point (1, 3) and line 12y + 5x = -4.
6. Find the distance between point A(3k, 6k) and 31 27 31 45
A. − 13 B. 13 C. 13 D. 13
B(3k, -3k).
A. 3k B. 5k C. 8k D. 9k 18. Find the equation of line passing through Z(2, 3)
7. Find the coordinate of the point that divide A(2, - and perpendicular to line y = 4.
2) and B(4, 5) in the ratio 1:3. A. 𝑦 = 2𝑥 + 3 B. 𝑦 = 2𝑥 − 3
5 1 5 1 C. 𝑥 = 3 D. 𝑥 = 2
A. (2, 4) B. (2, − 4)
19. Find the equation of a line through the origin and
1 5 3
C. (2, 2) D. (4, -1) bisecting the angle between the positive x- axis
8. Obtain the point that divide X(-3, 5) and Y(4, 5) and negative y-axis.
in the ratio 2:3. A. 𝑦 = 𝑥 B. 𝑦 = −𝑥
1 1
A. (5, 1) B. (− , 5) C. ( , 5) D. (-1, -5) C. 𝑦 = 2𝑥 D. 2𝑦 = 𝑥
5 5 20. What is the linear form equation of a line passing
2 1
9. Find the distance between point A( , ) and through (-2, 5) where dy/dx = 10.
3 3
4 4 A. 𝑦 − 10𝑥 − 25 = 0 B. 𝑦 − 10𝑥 + 25 = 0
B(− 3, 3).
C. 10𝑦 − 𝑥 − 25 = 0 D. 10𝑦 − 𝑥 + 25 = 0
A. 0 B. 5 C. √3 D. √5
21. The two lines ay = (b + 1)x + c and (b + 1)y = -
10. Find the slope of line passing through M(5, -2)
ax + c are
and N(-4, -6).
4 9 4 9 A. curves B. circular
A. 9 B. − 4 C. − 9 D. 4 C. parallel D. perpendicular
11. If the slope of the line passing through A(2, 3) 22. The line 2y + 3x – 14 = 0 and 7y – 2x – 24 = 0
1
and B(-2, k) is − . Find the value of k. intersect at point P. Find the coordinates of P.
4
A. 2 B. -2 C. 4 D. -4 A. (-4, -2) B. (4, -2)
12. Find the slope intercept form of equation of the C. (-4, 2) D. (4, 2)
increase in x
line passing through M(2, 3) and N(-2, 4). 23. If m = increase in y, which of the following is
𝑥 7
A. 4y + x − 14 = 0 B. 𝑦 + = equivalent to m [where α is the angle between
4 2
7 𝑥 7 𝑥 the line and x-axis].
C. 𝑦 = 2 − 4
D. 𝑦 = 2
+ 4 A. sinα B. cosα C. tanα D. cotα
13. Find the equation of the line passing through (1, 24. The intercept form equation of straight line is
3) and (5, -2). given by
A. -4y = 5x + 17 B. 4y = 5x + 17 𝑥 𝑦 𝑥 𝑦
A. 𝑎 + 𝑏 = 0 B. 𝑎 − 𝑏 = 1
C. 4y = 5x - 17 D. -4y = 5x – 17 𝑦 𝑥 𝑥 𝑦
C. 𝑎 − 𝑏 = 0 D. 𝑎 + 𝑏 = 1
25. Two perpendicular lines PQ and QR intersect at C. 4𝑦 − 7𝑥 = 18 D. 4𝑦 − 7𝑥 = −18
(1, -1). If the equation of PQ is x – 2y + 4 = 0, 35. Find the equation of tangent to the circle of
Find the equation of QR. equation 2𝑥 2 + 2𝑦 2 − 3𝑥 + 4𝑦 − 32 = 0 at (2, 3).
A. x – 2y + 1 = 0 B. 2x + y – 1 = 0 A. 16𝑦 + 5𝑥 = 58 B. 16𝑦 + 5𝑥 = −58
C. x – 2y + 3 = 0 D. 2x – y – 1 = 0 C. 16𝑦 − 5𝑥 = 58 D. 16𝑦 − 5𝑥 = −58
7
26. Find the tangent to a line of gradient 5 at point 36. Find the center and radius of a circle whose
(2, 3). equation is 𝑥 2 + 𝑦 2 − 6𝑥 − 8𝑦 + 5 = 0.
A. 5𝑦 − 7𝑥 + 10 = 0 B. 5𝑦 − 7𝑥 − 1 = 0 A. (−3, 4), 𝑟 = √10 B. (3, 4), 𝑟 = √10
C. 7𝑦 − 5𝑥 − 29 = 0 D. 7𝑦 − 5𝑥 − 1 = 0 C. (−3, 4), 𝑟 = 2√5 D. (3, 4), 𝑟 = 2√5
27. Find the value of k for which lines 3𝑦 = 4𝑥 − 1 37. ________ is defines as the set of all points in a plane
and 𝑘𝑦 = 𝑥 + 3 are perpendicular and parallel to that are equidistant from a fixed point.
each other. A. circle B. parabola C. ellipse D. hyperbola
A.
3 4
𝑎𝑛𝑑 − B.
3
𝑎𝑛𝑑 −
3 38. _______ is defines as the locus of a point moving in
4 3 4 4 a plane such that its distance from a fixed point is
4 3 3 4
C. − 3 𝑎𝑛𝑑 4 D. 4 𝑎𝑛𝑑 3 equal to its distance from a fixed line.
28. Find the equation of the circle with center (3, -2) A. circle B. parabola C. ellipse D. hyperbola
and radius 2 units. 39. What is the focus of the parabola 𝑦 2 = 32𝑥.
A. 𝑥 2 + 𝑦 2 − 6𝑥 + 4𝑦 + 9 = 0 A. (4, 0) B. (8, 0) C. (16, 0) D. (32, 0)
B. 𝑥 2 + 𝑦 2 + 6𝑥 − 4𝑦 + 9 = 0 40. What is the vertex of the parabola (𝑦 − 4)2 =
C. 𝑥 2 − 𝑦 2 − 6𝑥 + 4𝑦 + 9 = 0 20(𝑥 + 2).
D. 𝑥 2 + 𝑦 2 − 6𝑥 − 4𝑦 + 9 = 0 A. (–2, 4) B. (2, –4) C. (2, 0) D. (4, 0)
29. Find the equation of the circle with center origin, 41. Find the equation of the tangent to the parabola
radius 3 units. 𝑦 2 = 8𝑥 at point (2, 4).
A. 𝑥 2 + 𝑦 2 − 3 = 0 B. 𝑥 2 + 𝑦 2 + 9 = 0 A. 𝑦 − 𝑥 − 2 = 0 B. 𝑦 + 𝑥 − 2 = 0
C. 𝑥 2 + 𝑦 2 − 9 = 0 D. 𝑥 2 + 𝑦 2 + 3 = 0 C. 𝑦 + 𝑥 + 2 = 0 D. 𝑦 − 𝑥 + 2 = 0
30. Find the equation of the circle whose center is (5, 42. Find the equation of the normal to the parabola
-4) and which passes through (-3, 2). 𝑦 2 = 18𝑥 at point (2, 6).
A. 𝑥 2 + 𝑦 2 + 8𝑦 − 10𝑥 − 59 = 0 A. 3𝑦 + 2𝑥 − 22 = 0 B. 3𝑦 − 2𝑥 − 22 = 0
B. 𝑥 2 + 𝑦 2 + 10𝑦 − 8𝑥 − 95 = 0 C. 3𝑦 + 2𝑥 + 22 = 0 D. 3𝑦 − 2𝑥 − 22 = 0
C. 𝑥 2 + 𝑦 2 + 8𝑦 + 10𝑥 + 59 = 0 43. Find the focus and vertex of the parabola 𝑦 2 =
D. 𝑥 2 + 𝑦 2 + 8𝑦 − 10𝑥 − 95 = 0 12𝑥.
31. Find the center and radius of a circle whose A. F(3, 0), V(0, 0) B. F(12, 0), V(3, 0)
equation is 𝑥 2 + 𝑦 2 − 6𝑥 + 4𝑦 − 3 = 0 C. F(12, 0), V(0, 0) D. F(3, 0), V(3, 0)
A. (-3, -2) and R = 16 B. (3, -2) and R = 4 44. The locus of a point which moves so that it is
C. (-3, 2) and R = 4 D. (-2, 3) and R = 16 equidistant from two intersecting straight lines is
32. Find the center and radius of a circle whose A. Perpendicular bisector of the two lines
equation is 36𝑥 2 + 36𝑦 2 − 24𝑥 − 36𝑦 − 23 = 0 B. Angle bisector of the two lines
1 1
A. ( , ) and R = 1
1 1
B. (− , − ) and R = √2 C bisector of the two lines
3 2 3 2
1 1 1 1 D. Line parallel to the two lines
C. (− 3, − 2) and R = 1 D. (3, − 2) and R = √2 45. What is the acronyms of the group that organize
33. Find the equation of the normal to the circle of this test?
equation 𝑥 2 + 𝑦 2 + 3𝑥 + 5𝑦 − 18 = 0 at (1, 2). A. BCG B. BSC C. BSP D. BSG E. BST
A. 5𝑦 + 9𝑥 − 1 = 0 B. 9𝑦 − 5𝑥 − 1 = 0
C. 5𝑦 − 9𝑥 − 1 = 0 D. 5𝑦 + 9𝑥 + 1 = 0
34. Find the equation of tangent to the circle of
equation 𝑥 2 + 𝑦 2 + 2𝑥 − 3𝑦 − 13 = 0 at (1, -2)
A. 7𝑦 − 4𝑥 = 18 B. 7𝑦 − 4𝑥 = −18
 ANSWER
1 A 16 C 31 B
2 C 17 D 32 A
3 B 18 D 33 C
4 C 19 B 34 B
5 B 20 A 35 A
6 D 21 D 36 D
7 B 22 D 37 A
8 B 23 D 38 B
9 D 24 D 39 B
10 A 25 B 40 A
11 C 26 B 41 A
12 C 27 C 42 A
13 D 28 A 43 A
14 C 29 C 44 B
15 C 30 A 45 D