II. MATERIAL
6. Data sources consulted
6.1. FAO sources
? Q3. If |2x − 5| = 8, what is x?
3.11 Inequalities
Q1. How many valuesx might have for the inequality: 1 ≤ x < 3?
Q2. If 1
p > 1, what is the range of value of p?
Q3. What do following inequalities suggest about the values ofa, and b?
(A) ab > 0 (B) ab < 0 (C) ab = 0 (D) a
b > 0 (E) a
b < 0
Q4. For which values ofx, will the inequality |2x − 1| < 5 be true?
Q5. Solve the |x + 2| < 7 inequality for x.
Q6. Solve the inequality |1 − 2x| < 9 for x.
Q7. Solve the inequality 5x − 1
−6 ≤ 1 − 2x
3 forx.
Q8. If 1< x < 3, then which of the following could be true?
I. x2< 2x II. x2=2x III. x2> 2x
(A) I only (B) II only (C) III only (D) I and II only
(E) All three
Q9. What does the inequalityab2c < 0 suggest for the values of a, b and c?
Q10. If 8> x > 3 and 4 < y < 6, what is the range of values of (x − y)?
Q11. If 6< x < 12 and y = x + 4, what is the greatest possible integer value of (x + y)?
Q12. For what values ofx, the inequality: x2> −6x − 5?
Q13. For what values ofx, the inequality: x2> 6x − 5?
3.12 Percents
Q1. 24 is 8% of what number?
Q2. If an industrial worker rejects 0.03% of screws as defective, how many screws does he examine to reject 300 screws?
Q3. What percent of 17 is 30 percent of 289?
Q4. How much you have to pay for an item priced $800, and discounted at 40%?
Q5. An item was sold at $100; it was bought for $120. What is the percent loss?
Q6. An item was bought at $100 after a discount of $20 on Marked Price. What is the percent discount on the Marked Price?
Q7. IfX is more than Y by 110%, and Z is less than X by 10%, then X is what % of Z?
Q8. If a number is first increased by 20%, and then decreased by 20%, is the resulting number equal to the original number?
Q9. A shopkeeper increased the price of his articles by 25%. What is the maximum percent discount should he offer so that he does not run into losses?
3.13 Ratio & Proportion
Q1. If 0.25 : 5 :: x : 4, then x=?
Q2. Two numbers are respectively 20% and 50% more than the third number. What is the ratio of the two numbers?
Q3. If $529 be divided into three parts, proportional to 1 2 : 2
3 : 3
4, then what is the value of the third part?
Q4. A and B together have $240. If 3
5 of A’s amount is equal to 2
5 of B’s amount, how much does B have?
Q5. Two number are in the ratio of 3 : 5. If 9 is subtracted from each, new numbers are in the ratio of 12 : 23. What is the value of the larger number?
Q6. IfA : B : C = 2 : 3 : 4, then find A B : B
C : C A.
Q7. A 60 liters mixture has milk and water in the ratio of 2 : 1. If the ratio is to be reversed, then what quantity of water should be added?
Q8. The sum of three numbers is 190. If the ratio of the first to second is 2 : 3 and that of the second to the third is also 2 : 3, then the third number is:
Q9. The salaries of A, B and C are of ratio of 2 : 3 : 5. If the increments of 15%, 10% and 20%
are made to their respective salaries, then find the new ratio of their salaries.
Q10. If three numbers are in the ratio of 2 : 3 : 5, and the sum of their squares is 1368, what is the value of the first number?
3.14 Simple Interest
Q1. Find the simple interest on $8000 borrowed at 503 % for 27 months.
Q2. Brian took a loan for 6 years at the rate of 5% per annum on simple interest, If the total interest paid was $1230, what was the principal?
Q3. If a sum becomes four times of itself in 15 years, find simple rate of interest.
Q4. Brian borrows $5000 for 2 years at 4% p.a. simple interest. He immediately lends whole money to Suzy at 254% p.a. for 2 years. Find the gain for Brian.
Q5. A lent $5000 to B for 2 years and $3000 to C for 4 years on simple interest at the same rate of interest and received $2200 in all from both of them as interest. What is the rate of interest per annum?
3.15 Compound Interest
Q1. Find the compound interest on $7500 at 4% per annum for 2 years, compounded annually.
Q2. Simple interest on a certain sum for 3 years at 8% per annum is equal to half the com-pound interest on $4000 for 2 years at 10% per annum. What is the sum placed on simple interest?
Q3. If the difference between simple interest and compound interest compounded annually on a certain sum of money for 2 years at 4% per annum is $1, find the sum.
Q4. What will be an effective annual rate of interest corresponding to nominal rate of 20% per annum, compounded half yearly?
Q5. If a sum of money invested at compound interest amounts to $800 in 3 years and to $840 in 4 years, what is the rate of interest per annum?
3.16 Functions
Q1. Givenf (x) = 2x − 7, for what value of x, does 3f (x) − 3 = f (2x − 6)?
Q2. For all positive integersp, [p] = −|√
p| when p is odd and [p] = p
5 whenp is even. What is the value of [25] × [10]?
Q3. If[m] is the greatest integer less than or equal to m, what is the value of [−2.2] + [2.6] + [6.2]?
Q4. An operation # is defined by the equationa#b = (a + b)
(a2+b2), for all numbers a and b. If a#c = 0, then what is the value of c in terms of a?
Q5. Givenf (x) = 2x
2x − 1, for what value ofx, does f (f (x)) = −1?
Q6. Givenf (x) = 2x
2x − 1 andg(x) = 2x − 1
2x , for what value ofx, does f (g(x)) = 3?
Q7. Iff (x) = 2x +√
x, what is the value of f (p2−10p + 25)?
Answer Key
Numbers and Digits
1.1: Irrational; 1.2: Irrational; 1.3: Rational; 1.4: Rational; 1.5: Irrational
2: 646
99 3: 524
999 4: 0 5: n = {0, 1, 2, 3, 4, 5} 6: 78
Even/Odd and Consecutive Integers
1: Indeterminable 2: Indeterminable 3: Yes 4: No 5: Yes
6: Indeterminable 7: Indeterminable 8: A, B, D, & E 9: Indeterminable 10: Yes Divisibility
1: 37 2: Yes 3: Indeterminable 4: Yes 5: Yes
6: Yes 7: Indeterminable 8: Yes 9: 6 10: Yes
11: 24 12: 0
Simplification
1: 241 2: 1 3: 0.0725 4: −218 5: 31000
6: 0.2 7: 4 8: y: Largest 9: 5 & 6 10: 3 & 4
z : Smallest
Exponents
1: 14 2: 12 3: 227 4: E 5: 5
6: 85 7: 6 8: {−3, −4} 9: {2, 3, 4}
Factors/Multiples and LCM/HCF
1: Cannot say 2: Yes 3: 6 4: D 5: {12, ±1}
6: 14 7: 5n
Fraction
1:
45 43
2
2: 1/3 3.A: 45
44 3.B: 45
44 3.C: 91
92
3.D: 114 111
Rationalization of fraction
1: −
√2
3 2:
√30 2 Linear and Quadratic Equations
1: x = 1
5, &y = −2
5 2: x = −4, & y = 6 3: −3 or −1
2 4: 4 or 1 5: −8 or 1
6: 8 or 2 7: 5
2 or −2 8: One 9: Two
Absolute numbers
1: x = ±2 2: 1 3: −3
2 or 13 2
Inequalities
1: Infinite 2: 0< p < 1 3.a:a > 0, & b > 0 3.b: a > 0, & b < 0 3.c: a = 0, ora < 0, & b < 0 ora < 0, & b > 0 &/orb = 0
3.d: a > 0, & b > 0 3.e:a > 0, & b < 0 4: −2< x < 3 5: −9< x < 5 6: −4< x < 5 ora < 0, & b < 0 ora < 0, & b > 0
7: x ≥ −1 8: E 9: a & c have 10: 4> x − y > −3 11: 27 opposite signs;
sign ofb cannot be determined
12: x > −1 or x < −5 13: x < 1 or x > 5 Percents
1: 300 2: 1,000,000 3: 510 4: $480 5: 16.67%
6: 16.67% 7: 111.11% 8: No; less by 4% 9: 20%
Ratio & Proportion
1: 1/5 2: 4:5 3: 207 4: 144 5: 55
6: 8:9:24 7: 60 liters 8: 90 9: 23 : 33 : 60 10: 12
Simple Interest
1: $3000 2: $4100 3: 20% 4: $225 5: 10%
Compound Interest
1: $612 2: $1750 3: $625 4: 21% p.a. 5: 5%
Functions
1: x = 5/2 2: −10 3: 5 4: −a 5: −1/6
6: 2 7: 2p2−19p + 45;
2p2−21p + 55.