Practice Test 1

Question 1

x³/25 = 36
What is a solution to the given equation? A) 6 B) 30 C) 450 D) 900

Question 2

The total revenue from sales is calculated as T = P×Q (T = revenue, P = price, Q = quantity). Which equation gives quantity sold in terms of price and revenue? A) Q = P/T B) Q = T/P C) Q = P×T D) Q = T - P

Question 3

If (x + 5)² = 4, which is a possible value of x? A) 1 B) -1 C) -2 D) -3

Question 4

Given 8j = k + 15m, which equation expresses j in terms of k and m? A) j = k/8 + 15m B) j = k + (15m)/8 C) j = 8(k + 15m) D) j = (k + 15m)/8

Question 5

|p| + 61 = 65
Which value solves this equation? A) 65/61 B) 4 C) 126 D) 130

Question 6

x² - x - 1 = 0
What values satisfy this equation? A) x = 1 and x = 2 B) x = -0.5 and x = 1.5 C) x = (1 + √5)/2 and x = (1 - √5)/2 D) x = (-1 + √5)/2 and x = (-1 - √5)/2

Question 7

(d - 30)(d + 60) - 7 = -7
What is a solution? A) 0 B) 30 C) -30 D) 60

Question 8

[2(x+1)]/(x+5) = 1 - [1/(x+5)]
What is the solution? A) 0 B) 2 C) 3 D) 5

Question 9

p = 20 + (16/n)
Which equation expresses n in terms of p? A) n = (p-20)/16 B) n = p/16 + 20 C) n = p/16 - 20 D) n = 16/(p-20)

Question 10

y = 4x
y = x² - 12
For x > 0, what is x? A) 2 B) 3 C) 4 D) 6

Question 11

2x² - 2 = 2x + 3
Which is a solution? A) 2 B) 1 - √11 C) 0.5 + √11 D) (1 + √11)/2

Question 12

|x - 9| + 45 = 63
What is the sum of all solutions? A) 9 B) 18 C) 27 D) 36

Question 13

|-5x + 13| = 73
What is the sum of all solutions? A) -146/5 B) -12 C) 0 D) 26/5

Question 14

x(x+1) - 56 = 4x(x-7)
What is the sum of all solutions? A) 5 B) 7 C) 9 D) 11

Question 15

(x - 1)² = -4
How many real solutions exist? A) Exactly one B) Exactly two C) Infinitely many D) Zero

Question 16

√(2x + 6) + 4 = x + 3
What is the solution set? A) {-1} B) {5} C) {-1, 5} D) {0, -1, 5}

Question 17

y = x² + 2x + 1
x + y + 1 = 0
For two solutions (x₁,y₁) and (x₂,y₂), what is y₁ + y₂? A) -3 B) -2 C) -1 D) 1

Question 18

If u - 3 = 6/(t - 2), what is t in terms of u? A) t = 1/u B) t = (2u + 9)/u C) t = 1/(u - 3) D) t = 2u/(u - 3)

Question 19

-16x² - 8x + c = 0 has exactly one solution. What is c? A) -1 B) 0 C) 1 D) 2

Question 20

57x² + (576 + a)x + ab = 0 has solutions with product k×a×b. What is k? A) 1/57 B) 1/19 C) 1 D) 57

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