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Exam Guide
Question 1. Which property of exponents justifies the simplification (5^3 \times 5^2 = 5^{5})? A) Quotient of powers B) Power of a power C) Product of powers D) Zero exponent Answer: C Explanation: The product of powers property states that when multiplying like bases, add the exponents: (a^m \times a^n = a^{m+n}). Here (3+2=5). Question 2. What is the value of (\sqrt{81})? A) 9 B) - 9 C) 27 D) (\pm 9) Answer: A Explanation: The principal (non‑negative) square root of a non‑negative number is taken, so (\sqrt{81}=9). Question 3. Express (4.2 \times 10^{6}) in scientific notation after dividing by (2.1 \times 10^{3}). A) (2 \times 10^{3}) B) (2 \times 10^{9}) C) (2 \times 10^{-3})
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D) (2 \times 10^{6}) Answer: A Explanation: (\frac{4.2}{2.1}=2) and (10^{6-3}=10^{3}); thus the result is (2 \times 10^{3}). Question 4. On a graph, the line passing through ((0,4)) and ((3,10)) has a slope equal to: A) 2 B) 3 C) 4 D) 6 Answer: A Explanation: Slope (m=\frac{10-4}{3-0}= \frac{6}{3}=2). Question 5. Which equation represents a line with y‑intercept 5 and slope (- 3 )? A) (y = - 3x + 5) B) (y = 5x - 3 ) C) (y = 3x + 5) D) (y = - 5x - 3 ) Answer: A Explanation: The slope‑intercept form is (y = mx + b); substitute (m=- 3 ) and (b=5).
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C) The lines are the same line (coincident). D) One equation is nonlinear. Answer: C Explanation: Infinitely many solutions occur when the two equations represent the same line. Question 9. Which of the following numbers is irrational? A) (0.75) B) (\frac{22}{7}) C) (\sqrt{5}) D) (3.6) Answer: C Explanation: Square roots of non‑perfect squares, like (\sqrt{5}), cannot be expressed as a ratio of integers, making them irrational. Question 10. Express the repeating decimal (0.\overline{36}) as a fraction in simplest form. A) (\frac{9}{25}) B) (\frac{4}{11}) C) (\frac{12}{33}) D) (\frac{4}{9}) Answer: B Explanation: Let (x = 0.\overline{36}). Then (100x = 36.\overline{36}). Subtract: (99x = 36) → (x = 36/99 = 4/11).
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Question 11. Which rational number is closest to (\pi)? A) (\frac{22}{7}) B) (\frac{3}{1}) C) (\frac{355}{113}) D) (\frac{16}{5}) Answer: A Explanation: (\frac{22}{7} \approx 3.1429) is a common approximation; (\frac{355}{113}) is more accurate but not listed among the simple choices—still, (\frac{22}{7}) is the closest among the options. Question 12. A function (f) is defined by (f(x)=3x- 4 ). What is (f(5))? A) 11 B) 15 C) - 11 D) 1 Answer: A Explanation: Substitute (x=5): (f(5)=3(5)-4=15-4=11). Question 13. Which of the following best describes a function? A) A set of ordered pairs where each input may have multiple outputs. B) A rule that assigns exactly one output to each input. C) Any collection of numbers. D) A graph that always passes the vertical line test.
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Explanation: As (x) increases by 1, (g(x)) decreases by 2, indicating a constant negative rate of change—characteristic of a linear function with slope (- 2 ). Question 15. Which graph represents a non‑linear function? A) A straight line passing through the origin. B) A parabola opening upward. C) A line with slope (- 4 ). D) A horizontal line. Answer: B Explanation: A parabola is curved, indicating a non‑linear relationship. Question 16. The rate of change of a linear function is also known as its: A) y‑intercept B) domain C) slope D) range Answer: C Explanation: For a linear function (y=mx+b), (m) is the rate of change (slope). Question 17. Which of the following statements about the function (h(x)=\sqrt{x}) is true? A) Its domain is all real numbers. B) Its graph passes through ((-4,2)). C) It is decreasing for (x>0).
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D) Its range is ([0,\infty)). Answer: D Explanation: Square‑root function is defined for (x\ge0) and outputs non‑negative values, so the range is ([0,\infty)). Question 18. A transformation that slides a figure without rotating or flipping it is called a: A) dilation B) translation C) reflection D) rotation Answer: B Explanation: A translation moves every point of a figure the same distance in the same direction. Question 19. Which coordinate pair is the image of point ((3,-2)) after a reflection over the x‑axis? A) ((-3,2)) B) ((3,2)) C) ((-3,-2)) D) ((3,-2)) Answer: B Explanation: Reflecting over the x‑axis changes the sign of the y‑coordinate only.
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Answer: B Explanation: Consecutive interior angles formed by a transversal intersecting parallel lines sum to (180^\circ) (supplementary). Question 23. Which of the following is a correct statement of the Pythagorean Theorem? A) In any triangle, (a^2 + b^2 = c^2). B) In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs. C) In a right triangle, (a + b = c). D) In an isosceles triangle, (a^2 + b^2 = c^2). Answer: B Explanation: The theorem applies only to right triangles and relates the squares of the side lengths as described. Question 24. Find the distance between points (A(1,2)) and (B(7,6)). A) 5 B) 6 C) 7 D) 8 Answer: C Explanation: Distance formula: (\sqrt{(7-1)^2+(6-2)^2}=\sqrt{6^2+4^2}=\sqrt{36+16}= \sqrt{52}=2\sqrt{13}\approx7.21). Nearest integer 7, but exact answer is (2\sqrt{13}). Since option C is 7 (closest), we select C.
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Question 25. A right triangle has legs of lengths 5 cm and 12 cm. What is the length of the hypotenuse? A) 13 cm B) 15 cm C) 17 cm D) 20 cm Answer: A Explanation: By Pythagoras, (c = \sqrt{5^2+12^2}= \sqrt{25+144}= \sqrt{169}=13). Question 26. The volume of a cylinder with radius 3 cm and height 10 cm is: A) (90\pi) cm³ B) (30\pi) cm³ C) (60\pi) cm³ D) (120\pi) cm³ Answer: A Explanation: Volume (V = \pi r^2 h = \pi (3)^2 (10)= 9\pi \times10 = 90\pi). Question 27. A cone has a radius of 4 cm and a height of 9 cm. Its volume is: A) (48\pi) cm³ B) (144\pi) cm³ C) (48\pi/3) cm³ D) (48\pi) cm³
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A) Strong positive linear association B) Strong negative linear association C) No association D) Curvilinear association Answer: A Explanation: Points rising together and close to a line indicate a strong positive linear relationship. Question 31. In a bivariate data set, an outlier far above the line of best fit would most likely affect the slope by: A) Increasing it B) Decreasing it C) Leaving it unchanged D) Making the line vertical Answer: A Explanation: An outlier above the trend pulls the line upward on that side, generally increasing the estimated slope. Question 32. Which of the following two‑way tables correctly represents the total number of students surveyed for favorite sport (Basketball, Soccer) broken down by gender (Male, Female) where the grand total is 120? A) [
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\begin{array}{c|cc|c} & \text{Basketball} & \text{Soccer} & \text{Total}\\hline \text{Male} & 30 & 20 & 50\ \text{Female} & 40 & 30 & 70\\hline \text{Total} & 70 & 50 & 120 \end{array} ] B) [ \begin{array}{c|cc|c} & \text{Basketball} & \text{Soccer} & \text{Total}\\hline \text{Male} & 35 & 25 & 60\ \text{Female} & 25 & 35 & 60\\hline \text{Total} & 60 & 60 & 120 \end{array} ] C) [ \begin{array}{c|cc|c} & \text{Basketball} & \text{Soccer} & \text{Total}\\hline \text{Male} & 20 & 30 & 50\
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Answer: C Explanation: ((2x)^3 = 2^3 \cdot x^3 = 8x^3). Question 34. Simplify (\frac{a^5}{a^2}). A) (a^{10}) B) (a^{3}) C) (a^{7}) D) (\frac{1}{a^{3}}) Answer: B Explanation: Subtract exponents: (5-2 = 3). Question 35. Which of the following numbers is a rational approximation of (\sqrt{2}) to three decimal places? A) 1. B) 1. C) 3. D) 2. Answer: A Explanation: (\sqrt{2}\approx1.41421356); rounded to three decimals gives 1.414. Question 36. If (y = kx) represents a proportional relationship and the point ((4,12)) lies on the graph, what is the constant of proportionality (k)? A) 2
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B) 3
C) 4
D) 5
Answer: B Explanation: (k = y/x = 12/4 = 3). Question 37. Which of the following is the correct unit rate for the proportion ( \frac{5\text{ miles}}{2\text{ hours}} )? A) ( \frac{2}{5} ) miles per hour B) ( \frac{5}{2} ) miles per hour C) 7 miles per hour D) 10 miles per hour Answer: B Explanation: Unit rate = distance ÷ time = (5/2 = 2.5) miles per hour. Question 38. The line through points ((-2,5)) and ((4, - 1)) has equation: A) (y = - x + 3) B) (y = - \frac{1}{3}x + \frac{7}{3}) C) (y = \frac{1}{3}x + \frac{7}{3}) D) (y = - \frac{1}{2}x + 4) Answer: B
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B) (2x + 7 \le 13) C) (\frac{x}{2} = 4) D) (\sqrt{x} > 3) Answer: B Explanation: Linear inequality involves a first‑degree expression with (\le,\ge,<,>). Question 42. The solution set of the inequality (4x - 9 < 7) is: A) (x < 4) B) (x > 4) C) (x < \frac{16}{4}) D) (x < 4) Answer: A Explanation: Add 9: (4x < 16) → divide by 4: (x < 4). Question 43. Which number line point best approximates (\sqrt{7})? A) 2. B) 2. C) 3. D) 3. Answer: B Explanation: (\sqrt{7}\approx2.6458), which is closest to 2.8 among given choices.
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Question 44. Convert the decimal (0.125) to a fraction in simplest form. A) (\frac{1}{8}) B) (\frac{1}{4}) C) (\frac{5}{40}) D) (\frac{2}{16}) Answer: A Explanation: (0.125 = 125/1000 = 1/8) after dividing numerator and denominator by 125. Question 45. Which of the following is NOT a property of a function? A) Each input has exactly one output. B) The graph passes the vertical line test. C) It can assign multiple outputs to a single input. D) It can be represented by an equation, table, or graph. Answer: C Explanation: By definition, a function cannot assign more than one output to a single input. Question 46. If (f(x)=2x+3) and (g(x)=x- 5 ), what is ((f \circ g)(2))? A) (- 1 ) B) 1 C) 3 D) 5 Answer: B
