Following are model questions for AP Board Junior Intermediate Mathematics students. The questions are framed as per the new syllabus of the Govt. of AP. The duration of the test is 3 hours. There will be three sections in the question paper. Here are some model questions:
1. Find the value of ‘y’, if the line joining the points (3, y) and (2, 7) is parallel to the line joining the points (−1, 4) and (0, 6).
2. Find the distance between the parallel lines 5x − 3y − 4 = 0 and 10x − 6y − 9 = 0
3. If (3, 2, −1), (4, 1, 1) and (6, 2, 5) are three vertices and (4, 2, 2) is the centroid of a tetrahedron, find the fourth vertix.
4. Find the angle between the planes x + 2y + 2z − 5 = 0 and 3x + 3y + 2z − 8 = 0
5. Find the equation to the locus of a point, which forms a triangle of area 2 with the points (1, 1) and (−2, 3).
6. A straight line passing through the point A(−2, 1) makes an angle of 30° with the positive direction of X − axis. Find the points on the straight line whose distance from A is 4 units.
7. Find the derivative of tan 2x from the first principles.
8. A point P is moving on the curve y = 2×2. The x coordinate of P is increasing at the rate of 4 units per second. Find the rate at which the y coordinate is increasing when the point is at (2, 8).
9. Find the angle between the lines whose direction cosines are given by the equation 3l + m + 5n = 0 and to 6mn − 2nl + 5lm = 0 .
10. Find the value of x, if the slope of the line passing through (2, 5) and (x, 3) is 2
11. Transform the equation x + y + 1 = 0 into the normal form.
12. Show that the points (1, 2, 3), (2, 3, 1) and (3, 1, 2) form an equilateral triangle.
13. Find the angle between the planes 2x − y + z = 6 and x + y + 2z = 7
14. A(2, 3) and B(−3, 4) are two given points. Find the equation of the locus of P, so that the area of the triangle PAB is 8.5 sq.units.
15. Find the points on the line 3x − 4y − 1 = 0 which are at a distance of 5 units from the point (3, 2)
16. Find the derivative of sin 2x from the first principle.
17. At any point t on the curve x = a (t + sin t); y = a (1 − cos t), find lengths of tangent and normal
18. A wire of length l is cut into two parts which are bent respectively in the form of a square and a circle. Find the lengths of the pieces of the wire, so that the sum of the areas is the least.