Praxis Elementary Education Fundamentals: Mathematics (8003)
Praxis Elementary Education Fundamentals: Mathematics (8003) is a trademark of its owner, which is not affiliated with and does not endorse Test Treasure Publication or TTP Prep.
Praxis Elementary Education Fundamentals: Mathematics (8003) is a trademark of its owner, which is not affiliated with and does not endorse Test Treasure Publication or TTP Prep.
10 sample questions for the Praxis Elementary Education Fundamentals: Mathematics (8003), with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.
Sections covered on the exam: Numbers and Operations, Algebraic Thinking, Geometry, Measurement, and Data.
Question 1 · Numbers and Operations
Answer: D. 100,000
The 4 in 2,406.58 is in the hundreds place, so its value is 400; the 4 in 13.904 is in the thousandths place, so its value is 0.004. Dividing gives 400 ÷ 0.004 = 100,000. Choosing 10,000 or 1,000,000 comes from miscounting the places between hundreds and thousandths; there are five place shifts, not four or six, so the ratio = 100,000.
Question 2 · Numbers and Operations
Answer: B. a^2 + 3b
An odd number squared is odd, and 3 times an even number is even; odd plus even is odd, so a^2 + 3b is always odd. In 3a + 5, odd plus odd gives an even sum. Any product with the even factor b is even, so ab + 4 and (a + b)b are even.
Question 3 · Numbers and Operations
Answer: A. $64.26
Combining the changes as one 22% discount gives $66.30, $27.54 is the discount with tax added to it, and $59.50 leaves out the tax. Sale price: 85 × 0.70 = $59.50. With tax: 59.50 × 1.08 = $64.26.
Question 4 · Algebraic Thinking
Answer: A. 255
Each term is 1 more than twice the previous term (equivalently, the differences 4, 8, 16 double each time). Continuing: 2(31) + 1 = 63, 2(63) + 1 = 127, and 2(127) + 1 = 255. Stopping at 127 gives the 6th term, and assuming the difference stays 16 gives 47.
Question 5 · Geometry, Measurement, and Data
Answer: D. (−4, 2)
Reflecting across the y-axis changes the sign of the x-coordinate, so (4, −3) becomes (−4, −3). Translating 5 units up adds 5 to the y-coordinate: −3 + 5 gives 2, so the image is (−4, 2). Reflecting across the x-axis instead leads to (4, 8), and moving down instead of up leads to (−4, −8).
Question 6 · Numbers and Operations
Answer: C. 5,236.4
The 6 in 4,618.2 is in the hundreds place, so its value is 600, and 1/100 of 600 is 6. In 5,236.4 the 6 is in the ones place, so its value is 6. The 6 in 2,961.5 is worth 60 (1/10 of 600), and the 6 in 70.96 is worth 0.06 (1/10,000 of 600).
Question 7 · Numbers and Operations
Answer: C. 10
A perfect square has an even exponent on every prime factor. In 2^3 × 3^2 × 5, the exponents of 2 and 5 are odd, while 3^2 already has an even exponent, so including 3 (making k 30) is unnecessary. Supplying one more 2 and one more 5 makes n × k equal to 2^4 × 3^2 × 5^2, which is 60^2, so k = 2 × 5 = 10.
Question 8 · Numbers and Operations
Answer: C. 200 kg
Dividing 350 by 4 treats gravel's ratio number as the number of parts in the whole, 100 kg is the sand, and 175 kg assumes gravel is exactly half the mix. The ratio has 1 + 2 + 4 = 7 parts, so each part is 350 ÷ 7 = 50 kg. Gravel is 4 parts: 4 × 50 = 200 kg.
Question 9 · Algebraic Thinking
| Input | Output |
|---|---|
| 1 | 4 |
| 2 | 7 |
| 3 | 10 |
A student says, "The rule is add 3, so when the input is 10 the output is 10 + 3 = 13."
Answer: D. The student used the output-to-output change as an input-to-output rule; the output for 10 is 31.
"Add 3" describes how each output relates to the previous output (a recursive rule), not how an output relates to its input. The input-to-output rule is 3n + 1, so the output for 10 is 3(10) + 1 = 31. The rule "multiply by 4" fits only the first row, and 3n + 3 gives 6, not 4, for input 1.
Question 10 · Geometry, Measurement, and Data
On a town map drawn on a coordinate grid, each unit is one block. The library is at (−5, 4), the school is at (3, 4), and the park is at (3, −6). Mia walks along grid lines from the library to the school and then from the school to the park.
Answer: B. 18 blocks
The library and school share y = 4, so that distance is 3 − (−5) = 8 blocks. The school and park share x = 3, so that distance is 4 − (−6) = 10 blocks. The total is 8 + 10 = 18 blocks; subtracting absolute values (5 − 3 = 2) for the first leg leads to 12 blocks.
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