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WorksheetsMTH 101
Total questions: 63
Worksheet time: 34mins
Which of the following numbers is not rational?
0.333…
√16
√18
–7/2
If |3x – 2| = 7, what is the sum of all real solutions?
0
4/3
2
14/3
The expression √(x²) is always equal to:
x
–x
|x|
x²
Which property justifies that a(b + c) = ab + ac for all real a, b, c?
Associativity
Commutativity
Distributivity
Closure
Solve: 3/(x – 1) + 2 = 5/(x – 1)
x = 0
x = 2
x = 1
No solution
If a < b and c < 0, which must be true?
ac < bc
a + c < b + c
ac > bc
a/c < b/c
Simplify: (2x² – 3x + 1) – (x² + 4x – 5)
x² – 7x + 6
x² + x – 4
x² – 7x – 4
3x² + x + 6
The degree of the polynomial 5x³y² – 2xy⁴ + 7 is:
3
4
5
6
Factor completely: 8x³ – 27
(2x – 3)(4x² + 6x + 9)
(2x + 3)(4x² – 6x + 9)
(2x – 3)³
(2x – 3)(4x² – 9)
Rationalize: 5 / (√3 + √2)
5(√3 – √2)
√3 – √2
5(√3 + √2)
(5√5)/1
Which is not a field property of real numbers?
Every nonzero real has a multiplicative inverse
a + b = b + a
a/b ∈ ℝ for all a, b ∈ ℝ
(ab)c = a(bc)
Solve: |2 – 5x| ≤ 3
[–1/5, 1]
(–∞, –1/5] ∪ [1, ∞)
[–1, 1/5]
(–1/5, 1)
If log₂(x) = 3, then x = ?
6
8
9
5
Solve: e²ˣ⁻¹ = 1
x = 0
x = 1/2
x = 1
No real solution
Which expression is equivalent to log₅(25x²)?
2 + 2 log₅x
5 + log₅x
log₅(50x)
10 log₅x
Expand: (3x – 4)²
9x² – 16
9x² – 24x + 16
9x² + 16
9x² – 12x + 16
Solve: 4x – 7 = 3(x + 1) – x
x = 5
x = 10
No solution
All real numbers
The solution set of |x| = –4 is:
{–4, 4}
{0}
∅
{–4}
Simplify: (x⁵y⁻²)/(x³y⁻⁴)
x²y²
x⁸y⁶
x²/y⁶
x⁸/y²
If a > 0, which is always true?
√(a²) = a
√(–a) is real
(–a)² < 0
1/a < 0
Solve: 2/(x + 1) = 4/(3x – 1)
x = 1
x = 3
x = –1
x = 0
Multiply: (2x + 3)(x² – x + 1)
2x³ + x² – x + 3
2x³ – 2x² + 2x + 3x² – 3x + 3
2x³ + x² – x + 3
2x³ + 5x² – 2x + 3
Which is a perfect square trinomial?
x² + 6x + 12
x² – 10x + 25
x² + 9
4x² + 6x + 1
Evaluate: log₁₀(0.01)
–1
–2
0.01
2
Solve: ln(x – 2) = 0
x = 1
x = 2
x = 3
x = e
Which interval represents –2 ≤ 3x + 1 < 7?
[–1, 2)
(–1, 2]
[–1, 2]
(–1, 2)
Simplify: √(72x⁶y³), assuming x, y > 0
6x³y√(2y)
8x³y√(y)
6x³y²√2
36x³y√(2y)
If 5ˣ = 125, then x = ?
2
3
4
5
Write as single log: 2 ln x – ln(x + 1)
ln(x²/(x + 1))
ln(2x/(x + 1))
ln(x² – x – 1)
ln(x/(x + 1)²)
Factor: x² – 5x – 14
(x – 7)(x + 2)
(x + 7)(x – 2)
(x – 14)(x + 1)
(x – 5)(x – 2)
Which is not in ℝ?
√(–4)
√4
–√4
4/√1
Solve: 3|2
Factor: x² – 5x – 14
(x – 7)(x + 2)
(x + 7)(x – 2)
(x – 14)(x + 1)
(x – 5)(x – 2)
Which is **not** in ℝ?
√(–4)
√4
–√4
4/√1
Solve: 3|2x + 1| – 5 = 10
x = 2 or x = –3
x = 1.5 or x = –2.5
x = 7/3 or x = –10/3
No solution
The additive inverse of –(3/4) is:
3/4
–4/3
4/3
–3/4
Which is the multiplicative inverse of 0.2?
–0.2
0.5
5
1/0.2
Solve: (x – 2)² = 16
x = 6 only
x = –2 only
x = 6 or x = –2
x = 4 or x = –4
If log₆(x) = –2, then x = ?
–36
1/36
36
–1/36
Simplify: (81x⁸)^(1/4)
3x²
9x⁴
3x⁴
81x²
The solution to |x + 3| > 5 is:
(–8, 2)
(–∞, –8) ∪ (2, ∞)
[–8, 2]
(–∞, –2) ∪ (8, ∞)
Which equals log₂(6) – log₂(3)?
log₂(3)
log₂(2)
log₂(9)
log₂(18)
Solve: 5eˣ⁺¹ = 20
x = ln 4 – 1
x = ln 4 + 1
x = ln 5
x = 4 – e
Multiply: (√5 + 2)(√5 – 2)
1
9
5 – 4
0
Which polynomial has degree 4?
x³ + 2x⁴ – 1
x²(x² + x)
(x + 1)⁴ – x⁴
All of the above
Solve: 1/2 – 3/(x + 2) = 0
x = 4
x = –2
x = –8
x = 1
If a = √2 and b = √8, then a + b = ?
√10
3√2
2√2
4
The expression (a⁻²b³)/(a⁻⁵b) simplifies to:
a³b²
b⁴/a⁷
a⁻⁷b⁴
a³/b²
Solve: log(x) + log(x – 3) = 1
x = 5
x = –2
x = 5 or x = –2
No valid solution
Which is **not** a real number?
(–27)^(1/3)
(–16)^(1/4)
0^(1/5)
(64)^(1/6)
Factor by grouping: 2x² + 5x – 12
(2x – 3)(x + 4)
(x – 3)(2x + 4)
(2x + 3)(x – 4)
(x + 6)(2x – 2)
Solve: |4 – x| = x – 4
x ≥ 4
x ≤ 4
x = 4
All real x
If 2ˣ = 5, then x = ?
log₂5
log₅2
ln(3)
5/2
Simplify: (x² – 9)/(x² – 6x + 9)
(x + 3)/(x – 3)
1
(x – 3)/(x + 3)
x + 3
Which inequality is **always true** for real a?
|a| ≥ a
|a| ≤ a
a² < 0
1/a > 0
Solve: √(3x + 1) = 4
x = 15/3
x = 5
x = 17/3
x = 3
Evaluate: log₃(1/27)
–3
3
–9
1/3
Use change of base: log₇(5) = ?
ln(5)/ln(7)
ln(7)/ln(5)
log(35)
5/7
Which is equivalent to a^(3/2)?
√(a³)
(√a)³
Both A and B
Neither
Solve: (x + 1)/(x – 2) = (x – 1)/(x + 2)
x = 0
x = 1
x = –1
No solution
The number √(π²) equals:
π
–π
|π|
Both A and C
If x < 0, then |x| + x = ?
2x
0
–2x
x²
Which equation has **no real solution**?
√(x + 2) = 5
|x| = 0
log(x) = –1
√(x + 1) = –2
