1
What is the value of -2x^2 + 18x − 13 when x = -8?
Medium
A
-285
B
-239
C
-292
D
-250
Explanation -2(-8)^2 + (18)(-8) + (-13) = (-128) + (-144) + (-13) = -285.
2
How many solutions does |x + 13| = −11 have?
Medium
A
Exactly 2 solutions
B
No solution
C
Exactly 1 solution
D
Infinitely many solutions
Explanation An absolute value can never equal a negative number, so |x + 13| = −11 has no solution.
3
What is (6.9 × 10^9) ÷ (2.3 × 10^8) in scientific notation?
Medium
A
3.0 × 10^1
B
3.0 × 10^17
C
3.0 × 10^2
D
3.5 × 10^1
Explanation Divide the mantissas (6.9 ÷ 2.3 ≈ 3.0) and subtract the exponents (9 − 8 = 1), adjusting the mantissa as needed: 3.0 × 10^1.
4
What is (6.2 × 10^5) × (2.0 × 10^3) in scientific notation?
Medium
A
1.24 × 10^10
B
1.24 × 10^9
C
2.24 × 10^9
D
1.24 × 10^15
Explanation Multiply the mantissas (6.2 × 2.0 = 12.4) and add the exponents (5 + 3 = 9), adjusting so the mantissa stays between 1 and 10: 1.24 × 10^9.
5
A geometric sequence has first term 4 and common ratio 2. What is the 5th term?
Medium
A
58
B
71
C
56
D
64
Explanation aₙ = a₁ × r^(n−1) = 4 × (2)^4 = 64.
6
f(x) = -x − 7 if x < -8, and f(x) = 3x − 14 if x ≥ -8. What is f(-12)?
Medium
A
8
B
2
C
5
D
9
Explanation Since -12 < -8, use f(x) = -x − 7: f(-12) = 5.
7
What is (4.5 × 10^4) ÷ (2.3 × 10^3) in scientific notation?
Medium
A
2.46 × 10^1
B
1.96 × 10^2
C
1.96 × 10^7
D
1.96 × 10^1
Explanation Divide the mantissas (4.5 ÷ 2.3 ≈ 1.96) and subtract the exponents (4 − 3 = 1), adjusting the mantissa as needed: 1.96 × 10^1.
8
Simplify: 6^10 ÷ 6^4
Medium
A
6^40
B
6^-6
C
6^14
D
6^6
Explanation When dividing powers with the same base, subtract the exponents: 6^10 ÷ 6^4 = 6^(10-4) = 6^6.
9
Convert the mixed number 15 1/2 to an improper fraction.
Medium
A
32/2
B
33/2
C
16/2
D
31/2
Explanation 15 1/2 = ((15 × 2) + 1) / 2 = 31/2.
10
A population of 4375 grows by 20% each year. What will the population be after 3 years?
Medium
A
7493
B
7651
C
7636
D
7560
Explanation Population after 3 years = 4375 × (1 + 20/100)^3 = 7560.
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11
The digits of 1895 sum to 23. Based on this, is 1895 divisible by 3?
Medium
A
Yes
B
No
C
Cannot be determined
D
Only if n is even
Explanation A number is divisible by 3 if and only if its digit sum is divisible by 3. Here the digit sum is 23, which is not divisible by 3.
12
Solve for x: x/-12 + 6 = 9
Medium
A
-39
B
-28
C
-36
D
-35
Explanation x/-12 = 9 − (6) = 3, so x = -12 × 3 = -36.
13
What is 37/50 expressed as a decimal?
Medium
A
0.64
B
0.84
C
0.74
D
0.79
Explanation 37 ÷ 50 = 0.74.
14
A rectangle has length (x + 5) and width (x + 14). If the area of the rectangle is 532 square units, what is the value of x (where x is a positive number)?
Medium
A
10
B
16
C
11
D
14
Explanation (x + 5)(x + 14) = 532. Testing x = 14: (19)(28) = 532, which checks out (the other algebraic root is negative and not valid here).
15
How many solutions does the equation 6x + -13 = 3x + 0 have?
Medium
A
No solution
B
Infinitely many solutions
C
Exactly one solution
D
Exactly two solutions
Explanation Since the coefficients of x differ, the equation has exactly one solution.
16
What is the solution set of |x + 31| > 5?
Medium
A
x < -36 or x > -26
B
-36 < x < -26
C
x > -26
D
x < -38 or x > -24
Explanation |x + 31| > 5 means x is farther than 5 from -31, giving x < -36 or x > -26.
17
If f(x) = -3x − 9 and g(x) = 6x + 7, what is g(f(-3))?
Medium
A
7
B
5
C
11
D
12
Explanation f(-3) = 0, so g(f(-3)) = g(0) = 6(0) + 7 = 7.
18
Round 184.171 to the nearest tenth.
Medium
A
184.3
B
184.2
C
184.1
D
184.0
Explanation Rounding 184.171 to the nearest tenth gives 184.2.
19
For the function f(x) = √(x − (-65)), what is the smallest value of x in the domain?
Medium
A
-68
B
-61
C
-69
D
-65
Explanation The expression under the square root must be ≥ 0: x − (-65) ≥ 0, so x ≥ -65. The smallest such value is -65.
20
What is the highest power of 13 that divides 76! (76 factorial) exactly?
Medium
A
5
B
2
C
3
D
7
Explanation Using Legendre's formula, the exponent of 13 in 76! is floor(76/13) + floor(76/169) + ... = 5.
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21
Express 22,000 in scientific notation.
Medium
A
2.2 × 10^5
B
2.2 × 10^3
C
22.0 × 10^3
D
2.2 × 10^4
Explanation Move the decimal point so only one nonzero digit remains before it: 22,000 = 2.2 × 10^4.
22
What is the cube root of 27?
Medium
A
3
B
5
C
4
D
7
Explanation 3^3 = 27, so the cube root of 27 is 3.
23
Simplify: 2^8 × 2^5
Medium
A
4^13
B
2^13
C
2^3
D
2^40
Explanation When multiplying powers with the same base, add the exponents: 2^8 × 2^5 = 2^(8+5) = 2^13.
24
What is the value of -7x^2 + 9x + 8 when x = -8?
Medium
A
-512
B
-509
C
-490
D
-510
Explanation -7(-8)^2 + (9)(-8) + (8) = (-448) + (-72) + (8) = -512.
25
What is the greatest common divisor (GCD) of 28 and 56?
Medium
A
28
B
42
C
37
D
17
Explanation The largest integer dividing both 28 and 56 evenly is 28.
26
What is 60% of 40% of 1370?
Medium
A
328.8
B
322.8
C
342.8
D
356.8
Explanation 60% of 40% of 1370 = (60/100) × (40/100) × 1370 = 328.8.
27
Round 151.6376 to the nearest tenth.
Medium
A
151.5
B
151.7
C
152.0
D
151.6
Explanation Rounding 151.6376 to the nearest tenth gives 151.6.
28
What is |-22| − |-26|?
Medium
A
-6
B
-10
C
-3
D
-4
Explanation |-22| − |-26| = 22 − 26 = -4. (Note this is generally different from |-22 − (-26)|.)
29
By selling an item for Rs. 188, a trader incurs a loss of 50%. What was the cost price?
Medium
A
367
B
376
C
381
D
384
Explanation Cost price = SP / (1 − 50/100) = 188 / 0.5000 = Rs. 376.
30
Does the parabola y = -3x^2 + 11x − 5 open upward or downward?
Medium
A
Cannot be determined
B
Downward
C
Upward
D
It is a straight line
Explanation Since a = -3 is negative, the parabola opens downward.
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31
Solve for x: 19/3 = 228/x
Medium
A
36
B
38
C
34
D
37
Explanation Cross-multiplying: 19 × x = 3 × 228, so x = 684/19 = 36.
32
What is the length of the solution interval for |x + 32| < 16?
Medium
A
35
B
32
C
36
D
31
Explanation |x + 32| < 16 describes the interval (-48, -16), which has length -16 − (-48) = 32.
33
Solve for x: 15x + 10 ≥ 70
Medium
A
x ≥ 5
B
x ≥ 4
C
x ≥ 3
D
x < 4
Explanation 15x ≥ 70 − (10) = 60, so x ≥ 4.
34
If two positive integers are 13 and 5, what is the product of their LCM and GCD?
Medium
A
66
B
65
C
70
D
64
Explanation For any two positive integers, LCM × GCD = product of the numbers = 13 × 5 = 65.
35
Which is greater: 7.2 × 10^7 or 7.8 × 10^9?
Medium
A
Cannot be determined
B
They are equal
C
7.8 × 10^9
D
7.2 × 10^7
Explanation Comparing exponents first: since the exponents differ, the larger exponent wins — 7.8 × 10^9 is greater.
36
What is the compound interest on Rs. 8125 at 8% per annum, compounded annually, for 2 years?
Medium
A
1366
B
1393
C
1306
D
1352
Explanation Amount = P(1 + R/100)^2 = 8125 × (1 + 8/100)^2 = Rs. 9477, so CI = Rs. 9477 − Rs. 8125 = Rs. 1352.
37
Simplify: (7^3)^3
Medium
A
21^3
B
7^6
C
7^27
D
7^9
Explanation When raising a power to another power, multiply the exponents: (7^3)^3 = 7^(3×3) = 7^9.
38
For a = -22 and b = 29, is |a + b| equal to |a| + |b|, or strictly less than |a| + |b|?
Medium
A
Strictly less than
B
Equal
C
Cannot be determined
D
Strictly greater than
Explanation |a + b| = 7 and |a| + |b| = 51. Since a and b have opposite signs, the two are not equal, with |a+b| smaller.
39
Between which two consecutive integers does √288 lie?
Medium
A
15 and 16
B
15 and 17
C
16 and 17
D
17 and 18
Explanation 16^2 = 256 and 17^2 = 289, and since 256 < 288 < 289, √288 lies between 16 and 17.
40
A sequence is defined by a₁ = -15 and aₙ = aₙ₋₁ + 3 for n > 1. What is a12?
Medium
A
21
B
18
C
12
D
24
Explanation Each term adds 3 to the previous one, so a12 = a₁ + (12−1)(3) = 18.
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41
f(x) = -8x + 8 if x < -10, and f(x) = 7x − 9 if x ≥ -10. What is f(-6)?
Medium
A
-54
B
-52
C
-47
D
-51
Explanation Since -6 ≥ -10, use f(x) = 7x − 9: f(-6) = -51.
42
How many digits does 9^33 have?
Medium
A
29
B
30
C
34
D
32
Explanation The number of digits of 9^33 is floor(33 × log10(9)) + 1 = 32.
43
A shop offers successive discounts of 50% and 2% on an item marked at Rs. 3100. What is the final selling price?
Medium
A
1461
B
1618
C
1519
D
1521
Explanation Final price = 3100 × (1 − 50/100) × (1 − 2/100) = Rs. 1519.
44
What is the difference between the compound interest and simple interest on Rs. 4800 at 5% per annum for 2 years?
Medium
A
9
B
8
C
13
D
12
Explanation For 2 years, the difference between CI and SI is always P × (R/100)^2 = 4800 × (5/100)^2 = Rs. 12.
45
Simplify: 2^13 ÷ 2^9
Medium
A
2^-4
B
2^22
C
2^4
D
2^117
Explanation When dividing powers with the same base, subtract the exponents: 2^13 ÷ 2^9 = 2^(13-9) = 2^4.
46
2776 is NOT divisible by which of the following numbers?
Medium
A
8
B
6
C
2
D
4
Explanation 2776 ÷ 6 leaves a remainder of 4, so it does not divide evenly.
47
Solve the system for y: -6x + y = 47, 4x − y = -33
Medium
A
1
B
5
C
8
D
7
Explanation Solving the system by elimination or substitution gives y = 5 (and x = -7).
48
Solve for x: 6(x − 2) = -48
Medium
A
-7
B
-4
C
-3
D
-6
Explanation Dividing both sides by 6: x − 2 = -8, so x = -6.
49
Convert the mixed number 1 11/12 to an improper fraction.
Medium
A
24/12
B
35/12
C
12/12
D
23/12
Explanation 1 11/12 = ((1 × 12) + 11) / 12 = 23/12.
50
Solve for x: x/-10 − 23 = -20
Medium
A
-34
B
-24
C
-28
D
-30
Explanation x/-10 = -20 − (-23) = 3, so x = -10 × 3 = -30.
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51
What is the sum of 6 consecutive integers starting from 16?
Medium
A
119
B
106
C
111
D
99
Explanation The integers are 16 through 21; their sum is 111.
52
If f(x) = -5x − 1, what is f(12)?
Medium
A
-54
B
-61
C
-64
D
-60
Explanation f(12) = (-5)(12) − 1 = -61.
53
Which is greater: 6^6 or 4^6?
Medium
A
6^6
B
4^6
C
They are equal
D
Cannot be determined without a calculator
Explanation 6^6 = 46656 and 4^6 = 4096, so 6^6 is greater.
54
Factor: 6x^2 + 18x
Medium
A
x(6x + 18)
B
3x(2x − 6)
C
3x(2x + 6)
D
3(2x + 6)
Explanation The GCF of 6 and 18 (besides x) is 3, and factoring it out (along with one x) gives 3x(2x + 6).
55
What is 3/4 + 5?
Medium
A
8/5
B
6
C
-17/4
D
23/4
Explanation Using a common denominator, 3/4 + 5 = 23/4.
56
What is the difference between the compound interest and simple interest on Rs. 10625 at 4% per annum for 2 years?
Medium
A
15
B
16
C
17
D
21
Explanation For 2 years, the difference between CI and SI is always P × (R/100)^2 = 10625 × (4/100)^2 = Rs. 17.
57
What is (4.5 × 10^4) ÷ (2.3 × 10^3) in scientific notation?
Medium
A
2.46 × 10^1
B
1.96 × 10^2
C
1.96 × 10^7
D
1.96 × 10^1
Explanation Divide the mantissas (4.5 ÷ 2.3 ≈ 1.96) and subtract the exponents (4 − 3 = 1), adjusting the mantissa as needed: 1.96 × 10^1.
58
What are the solutions to 2x^2 − 22x + 48 = 0?
Medium
A
x = 4 or x = 8
B
x = 2 or x = 9
C
x = 3 or x = 8
D
x = -3 or x = -8
Explanation Using the quadratic formula with a=2, b=-22, c=48, the discriminant is a perfect square, giving x = 3 or x = 8.
59
What is the value of 3x^2 − 2x − 30 when x = -7?
Medium
A
131
B
121
C
152
D
111
Explanation 3(-7)^2 + (-2)(-7) + (-30) = (147) + (14) + (-30) = 131.
60
What is the slope of the line through (8, -16) and (5, 1)?
Medium
A
-17/3
B
-14/3
C
-3/17
D
17/3
Explanation Slope = (y2 − y1)/(x2 − x1) = (1 − -16)/(5 − 8) = 17/-3 = -17/3.
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61
What is the slope of the line through (-9, -4) and (-17, -15)?
Medium
A
-11/8
B
11/8
C
8/11
D
19/8
Explanation Slope = (y2 − y1)/(x2 − x1) = (-15 − -4)/(-17 − -9) = -11/-8 = 11/8.
62
What is 40% of 90% of 528?
Medium
A
181.08
B
190.08
C
176.08
D
158.08
Explanation 40% of 90% of 528 = (40/100) × (90/100) × 528 = 190.08.
63
What is 41.41 + 179.17?
Medium
A
221.58
B
220.58
C
-137.76
D
219.58
Explanation 41.41 + 179.17 = 220.58.
64
What is the nature of the roots of 6x^2 − 17x − 11 = 0?
Medium
A
Cannot be determined
B
Two distinct real roots
C
No real roots
D
One repeated real root
Explanation The discriminant is b^2 − 4ac = (-17)^2 − 4(6)(-11) = 553, which is positive, so the equation has two distinct real roots.
65
Does the parabola y = -6x^2 − 20x − 30 open upward or downward?
Medium
A
Cannot be determined
B
Downward
C
Upward
D
It is a straight line
Explanation Since a = -6 is negative, the parabola opens downward.
66
What is the difference between the compound interest and simple interest on Rs. 10625 at 8% per annum for 2 years?
Medium
A
59
B
71
C
68
D
79
Explanation For 2 years, the difference between CI and SI is always P × (R/100)^2 = 10625 × (8/100)^2 = Rs. 68.
67
What is the solution set of |x − 5| < 3?
Medium
A
2 < x < 8
B
x < 8
C
x < 2 or x > 8
D
0 < x < 10
Explanation |x − 5| < 3 means x is within 3 of 5, giving 2 < x < 8.
68
A trader buys an item for Rs. 1824 and wants to make a profit of 25%. At what price should the item be sold?
Medium
A
2329
B
2280
C
2307
D
2243
Explanation Selling price = CP × (1 + 25/100) = 1824 × 1.2500 = Rs. 2280.
69
What is the simple interest on Rs. 9534 at 15% per annum for 2 years?
Medium
A
2928.2
B
2817.2
C
2807.2
D
2860.2
Explanation Simple Interest = (P × R × T) / 100 = (9534 × 15 × 2) / 100 = Rs. 2860.2.
70
Convert the mixed number 7 10/11 to an improper fraction.
Medium
A
87/11
B
98/11
C
17/11
D
88/11
Explanation 7 10/11 = ((7 × 11) + 10) / 11 = 87/11.
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71
Solve the system for x: -3x + 3y = -48, 8x − 7y = 121
Medium
A
6
B
9
C
10
D
5
Explanation Solving the system by elimination or substitution gives x = 9 (and y = -7).
72
A shopkeeper marks up an item costing Rs. 426 by 28%. What is the markup amount (in Rs.)?
Medium
A
122.28
B
117.28
C
116.28
D
119.28
Explanation Markup amount = CP × 28/100 = 426 × 0.2800 = Rs. 119.28.
73
What is |20 × 15|?
Medium
A
300
B
304
C
306
D
296
Explanation |20 × 15| = |20| × |15| = 20 × 15 = 300.
74
A sequence is defined by a₁ = -10 and aₙ = aₙ₋₁ − 10 for n > 1. What is a15?
Medium
A
-150
B
-134
C
-159
D
-133
Explanation Each term adds -10 to the previous one, so a15 = a₁ + (15−1)(-10) = -150.
75
Rs. 1973 is invested at 4% simple interest per annum for 7 years. What is the total amount after 7 years?
Medium
A
2531.44
B
2554.44
C
2525.44
D
2527.44
Explanation Amount = Principal + Interest = 1973 + 552.44 = Rs. 2525.44.
76
What is 143.43 − 93.43?
Medium
A
236.86
B
49.0
C
50.0
D
51.0
Explanation 143.43 − 93.43 = 50.0.
77
Factor: 50x^2 − 35x
Medium
A
5(10x − 7)
B
x(50x − 35)
C
5x(10x + 7)
D
5x(10x − 7)
Explanation The GCF of 50 and -35 (besides x) is 5, and factoring it out (along with one x) gives 5x(10x − 7).
78
If f(x) = -11x − 3, what is f(1)?
Medium
A
-14
B
-15
C
-10
D
-9
Explanation f(1) = (-11)(1) − 3 = -14.
79
Which is greater: |43| or |-64|?
Medium
A
|-64|
B
Cannot be determined
C
They are equal
D
|43|
Explanation |43| = 43 and |-64| = 64, so |-64| is greater.
80
What is the slope of the line through (17, -1) and (16, -10)?
Medium
A
1/9
B
9
C
-9
D
10
Explanation Slope = (y2 − y1)/(x2 − x1) = (-10 − -1)/(16 − 17) = -9/-1 = 9.
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81
What is the nature of the roots of 4x^2 − 6x − 1 = 0?
Medium
A
One repeated real root
B
No real roots
C
Two distinct real roots
D
Cannot be determined
Explanation The discriminant is b^2 − 4ac = (-6)^2 − 4(4)(-1) = 52, which is positive, so the equation has two distinct real roots.
82
In an arithmetic sequence, the 10th term is -80 and the 15th term is -125. What is the 20th term?
Medium
A
-173
B
-170
C
-189
D
-191
Explanation d = (-125 − (-80))/(15−10) = -9. Then the 20th term = -80 + (20−10)(-9) = -170.
83
What is 19.1 × 10.9?
Medium
A
209.19
B
207.19
C
30.0
D
208.19
Explanation 19.1 × 10.9 = 208.19.
84
What is the y-intercept of the line 7x + 9y = 126?
Medium
A
13
B
15
C
16
D
14
Explanation Set x = 0: 9y = 126, so y = 126/9 = 14.
85
Solve for x: -2x − 22 = 24
Medium
A
-21
B
-23
C
-28
D
-19
Explanation -2x = 24 − (-22) = 46, so x = 46/-2 = -23.
86
What is the difference between the compound interest and simple interest on Rs. 5625 at 12% per annum for 2 years?
Medium
A
70
B
83
C
81
D
68
Explanation For 2 years, the difference between CI and SI is always P × (R/100)^2 = 5625 × (12/100)^2 = Rs. 81.
87
What is 19.3 × 8.9?
Medium
A
170.77
B
172.77
C
171.77
D
28.2
Explanation 19.3 × 8.9 = 171.77.
88
If f(x) = 6x + 10, for what value of x does f(x) = -32?
Medium
A
-10
B
-7
C
-11
D
-4
Explanation 6x + 10 = -32, so x = -7.
89
Three warning lights flash every 12, 9, and 20 seconds respectively. If they all flash together at the same instant, after how many seconds will they next flash together?
Medium
A
170
B
172
C
161
D
180
Explanation They will next flash together after LCM(12, 9, 20) = 180 seconds.
90
A geometric sequence has first term -3 and common ratio 4. What is the 8th term?
Medium
A
-49165
B
-49152
C
-49091
D
-49087
Explanation aₙ = a₁ × r^(n−1) = -3 × (4)^7 = -49152.
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91
What is the simple interest on Rs. 2821 at 13% per annum for 5 years?
Medium
A
1899.65
B
1833.65
C
1776.65
D
1739.65
Explanation Simple Interest = (P × R × T) / 100 = (2821 × 13 × 5) / 100 = Rs. 1833.65.
92
What is the axis of symmetry of the parabola y = -x^2 + 12x + 11?
Medium
A
x = 5
B
x = 6
C
x = -6
D
x = 7
Explanation The axis of symmetry is x = −b/(2a) = −(12)/(2×-1) = 6.
93
If 7 workers can complete a task in 5 days, how many days would 35 workers take to complete the same task (assuming the same work rate per worker)?
Medium
A
3
B
4
C
1
D
5
Explanation Total work = 7 × 5 = 35 worker-days. With 35 workers, days = 35/35 = 1.
94
Solve for x: 4(x − 7) = -88
Medium
A
-14
B
-11
C
-19
D
-15
Explanation Dividing both sides by 4: x − 7 = -22, so x = -15.
95
What is the sum of 3 consecutive even integers starting from 52?
Medium
A
165
B
170
C
162
D
160
Explanation The 3 consecutive even integers are [52, 54, 56]; their sum is 162.
96
Does the fraction 15/193 terminate as a decimal, or does it repeat?
Medium
A
Repeats (does not terminate)
B
Terminates
C
It equals exactly 0
D
Cannot be determined without long division
Explanation In lowest terms, 15/193 = 15/193. A fraction terminates only if its denominator (in lowest terms) has no prime factors other than 2 and 5. Here that is not the case, so it repeats (does not terminate).
97
An interest rate rises from 35% to 42%. What is the percent increase relative to the original rate?
Medium
A
20%
B
15%
C
7%
D
30%
Explanation Relative percent increase = (((42 − 35) / 35) × 100 = 20%. (Note this differs from the 7-percentage-point change.)
98
Express 6,000,000 in scientific notation.
Medium
A
60.0 × 10^5
B
6.0 × 10^6
C
6.0 × 10^5
D
6.0 × 10^7
Explanation Move the decimal point so only one nonzero digit remains before it: 6,000,000 = 6.0 × 10^6.
99
Which is greater: |-3| or |-46|?
Medium
A
|-3|
B
They are equal
C
Cannot be determined
D
|-46|
Explanation |-3| = 3 and |-46| = 46, so |-46| is greater.
100
What is 106.11 ÷ 13.1?
Medium
A
9.1
B
7.1
C
8.1
D
5.0
Explanation 106.11 ÷ 13.1 = 8.1.