Calculator Techniques

1. Calculator Techniques

2. Equations
Solve the value of X and Y : 2X + 7Y = 4 & X + 2Y = 1
(Ans: -1/3 and 2/3)
In 5 years, Ana’s age will be twice as the age of her
friend Jun. Five years ago, she was three times as old
as his friends. Find their present ages (Ans: 35 and 15
yrs old)

3. Solve the quadratic equation : 6X2 – 7X – 5 = 0 (
Ans: 5/3 & -1/2 )
Find the value of 15X2 -11X -12 = 0 (Ans. 4/3 & - 3/5 )
Solve the cubic equation: X3 +2X2 -5X -6 = 0
(Ans: 2, -1 & -3)
Solve the value of X3 +2X2 -X -2 = 0 (Ans: 1, -1 & -2)
Find the values of X, Y and Z:(ans:X= 3,Y= 1,andZ= 2)
3X -3Y -Z = 4
X +9Y +2Z = 16
X -Y +6Z = 14

4. Progression Problem
Arithmetic Problem:
In the sequence 921, 821, 721, 621,….. What is the 7th
term of the sequence?
Find the 30th term of 2, 6, 10, 14,….
Find the 22nd term in the AP if the 4th term is 8 and
the 10th term is 29.

5. Progression Problem
 Geometric Problem:
 If the 3rd term of GP is 20, and the 6th term is 160, what is the
1st term?
 The 4th term of a GP is 216 and the 6th term is 1944. Find the
8th term?

6. Probability and Statistics
 Mean, Median, Mode and Standard deviation:
 Find the mean, median and mode of the set of number: 2, 5,
6, 2, 15. (Answer: mean: 6, median: 5, mode: 2, and standard
deviation: 4.77)
 Find the mean and standard deviation from the data: 8, 4, 9,
15, 25, 12, and 7. (Answer: mean: 11.43 and standard
deviation: 6.43)

7. Combination
 In how many ways can a committee of 4 people be chosen
from a group of 10 people (answer: 210)
 Evaluate the combination of 50 objects taken 5 at a time
(answer: 2118760)
 In how many ways a Dean choose 2 of 15 faculty members to
review a student grade appeal? ( answer: 105)

8. Permutation
 If15 people won prizes in the state of lottery, in how many
ways can these 15 people win first, second, third, fourth and
fifth prizes. (Answer: 360,360 ways)
 How many 4 digits number can be formed without repeating
any digit from the following: 1,2,3,4 and 6? (Answer:120ways)
 In how many ways can a set of 6 distinct books be arranged in
bookshelf? (Answer: 720ways)

9. Remainder Theorem
 Find the remainder when 4Y3 +18Y2 +8Y -4 is divided by
2Y+3. (Answer 11)
 The polynomial X3 +4X2 -3X +8 is divided by X-5, then the
remainder is? (Answer: 218)

10. Sum of Coefficient
 If the second term is constant K:
 What is the sum of the coefficients of the expansion (2X-1)20
 What is the sum of the coefficients of the expansion ( X +2Y )4
 What is the sum of the coefficient of the expansion (3X -1)3
S = (coeff. X + coeff Y)n
S = (coeff. X + K)n –(K)n

11. Determinant
 Find the determinant : Answer: 228
 Simplify Answer:

12. Components of a Force
 Find the X and Y component of the forces 200: (Answer:
X=173.21 & Y=100

13. Components of a Force
 Find the resultant forces and the angle:

14. Complex
 Evaluate ( 6-9i )( 12+7i )
 Find the value of (1+ i )6
 Simplify the expression i1997+ i1999 Ans: 2i

15. Trigonometry
 Find the radius and angle in standard position, when the
terminal side contains the point (-3, -4)? (Answer: R= 5,
angle= -126.8698)
 Given the polar equation r = 5sin X. Determine the
rectangular coordinates (x,y) of a point in the curve when
X=30 degrees. (Answer: X=2.165 & Y=1.25)

16. Analytic Geometry
 If (-2,-4) is the midpoint of (6, -7) and (X,Y), Then the values of
X and Y are: (Ans:B)
a. X=2 & Y=1 c. X=10, & Y=-1
b. X= -10 & Y=-1 d. X= -8 & Y=-1
 The segment from (-1,4) to (2, -2) is extended three times its
own length. The terminal point is: (Ans: D)
a. (11,-24) c. (11,-18)
b. (-11,-20) d. (11,-20)

17. Center Point
 Determine the center of the parabola: X2 -8X -4Y2 +64Y = 256
(Ans: (4,8) )
 What are the coordinates of the center of the curve X2 +Y2 -2X -4Y
-31 =0 (Ans: (1,2))

18. Volume
 What is the volume of a frustum of a cone whose upper base
is 15cm diameter and lower base is 10cm with an altitude of
25cm? (Ans: 3108.87 cm3)
 A conical vessel has a height of 24 cm and a base diameter
of12 cm. It holds water to depth of 18 cm above the vertex.
Find the volume?( Ans: 381.70)
Store Value of A, B and C