praxis elementary math 5003 practice test

A series of tests developed by ETS to assess the skills and knowledge of prospective teachers.

Prism: 5.0cm, 7.3cm, 9.2cm. Surface area?
  • A. 149.66
  • B. 167.9
  • C. 299.32
  • D. 335.18
Correct Answer & Rationale
Correct Answer: C

To find the surface area of a rectangular prism, the formula is SA = 2(lw + lh + wh), where l, w, and h are the length, width, and height, respectively. Substituting the given dimensions (5.0 cm, 7.3 cm, and 9.2 cm) into the formula yields a surface area of 299.32 cm². Option A (149.66) likely results from miscalculating or omitting a dimension. Option B (167.9) may arise from incorrect multiplication or addition. Option D (335.18) could be a result of doubling the correct surface area without proper calculation. Thus, only option C accurately represents the surface area of the prism.

Other Related Questions

Quickly multiply 24x16?
  • A. 20x20-4x4
  • B. 20x20
  • C. 20x10+4x6
  • D. 25x10+4x15
Correct Answer & Rationale
Correct Answer: A

Option A, 20x20 - 4x4, effectively utilizes the difference of squares method. It simplifies the multiplication by recognizing that 24 can be expressed as 20 + 4 and 16 as 20 - 4, leading to a calculation of (20+4)(20-4). Option B, 20x20, underestimates the value of 24 and 16, yielding only 400 instead of the correct 384. Option C, 20x10 + 4x6, inaccurately breaks down the multiplication, leading to 200 + 24, which totals 224. Option D, 25x10 + 4x15, misrepresents the factors, resulting in 250 + 60, totaling 310. Thus, option A is the most accurate approach for this multiplication.
Liz spent 1/2, 1/3, 1/4, $15 left. Birthday money?
  • A. $360
  • B. $180
  • C. $120
  • D. $60
Correct Answer & Rationale
Correct Answer: D

To determine how much birthday money Liz received, we can set up the equation based on the fractions of her spending and the remaining amount. Let \( x \) represent the total birthday money. She spent \( \frac{1}{2}x + \frac{1}{3}x + \frac{1}{4}x + 15 = x \). Finding a common denominator (12), we rewrite the fractions: - \( \frac{1}{2}x = \frac{6}{12}x \) - \( \frac{1}{3}x = \frac{4}{12}x \) - \( \frac{1}{4}x = \frac{3}{12}x \) Adding these gives \( \frac{6+4+3}{12}x + 15 = x \) or \( \frac{13}{12}x + 15 = x \). Rearranging yields \( 15 = x - \frac{13}{12}x \), simplifying to \( 15 = \frac{1}{12}x \). Therefore, \( x = 180 \). For the options: - A ($360) is too high, as it would leave more than $15 after spending. - B ($180) results in no remaining amount after spending. - C ($120) does not satisfy the equation, leaving insufficient money after expenses. - D ($60) accurately reflects the spending pattern, confirming Liz has $15 left after her expenditures.
Shaded region shows?
Question image
  • A. 3/4 x 1/2
  • B. 3/4 x 3/4
  • C. 3/4 x 3/2
  • D. 3/4 x 3
Correct Answer & Rationale
Correct Answer: A

The shaded region represents the area of a rectangle formed by multiplying two fractions. Option A, \( \frac{3}{4} \times \frac{1}{2} \), correctly calculates the area of a rectangle with a length of \( \frac{3}{4} \) and a width of \( \frac{1}{2} \), resulting in \( \frac{3}{8} \). Option B, \( \frac{3}{4} \times \frac{3}{4} \), represents a larger area, \( \frac{9}{16} \), which does not match the shaded region. Option C, \( \frac{3}{4} \times \frac{3}{2} \), yields \( \frac{9}{8} \), exceeding the shaded area. Finally, option D, \( \frac{3}{4} \times 3 \), results in \( \frac{9}{4} \), also too large. Thus, only option A accurately reflects the area of the shaded region.
1.085/12 value?
Question image
  • A. 90
  • B. 90 * 5/1.085
  • C. 90 * 5/12
  • D. 90.5
Correct Answer & Rationale
Correct Answer: C

To find the value of 1.085/12, we need to simplify the expression. Option C, 90 * 5/12, correctly represents a simplified fraction of 90 divided by 12, multiplied by 5. This yields a value consistent with the original division. Option A (90) is incorrect as it does not involve the division by 12. Option B (90 * 5/1.085) incorrectly uses 1.085 as a divisor instead of 12, leading to an inaccurate calculation. Option D (90.5) is also incorrect as it does not relate to the division of 1.085 by 12, resulting in a value that does not reflect the operation required.